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12383 | Why was the truncated icosahedron (i.e. soccer ball) geometry chosen for the implosive lenses in the “Fat Man” atomic bomb? | Quoting from Wolfram Mathworld: " It is the shape used in the construction of soccer balls, and it was also the configuration of the lenses used for focusing the explosive shock waves of the detonators in the Fat Man atomic bomb (Rhodes 1996, p. 195)." but further insights are not provided. (http://mathworld.wolfram.co... | Why did the scientists involved in the Manhattan Project choose the truncated icosahedron shape for the implosive lenses of the Fat Man atomic bomb, and can you explain how this geometry contributes to the optimal focusing of shock waves on a spherical plutonium core compared to other potential geometries? | 16,109 | cqadupstack-physics |
123691 | How can I calculate the relationship between power and acceleration for a beam driven photon sail? | I am writing a novel, and although I have a background in physics, I am unsure of the exact equations to use. Specifically: **For a photon-sail ship, how powerful would a driving laser need to be in order for the ship to reach an acceleration of ~0.5g?** Assuming we are only talking within the solar system here, and as... | What is the minimum power required for a laser driving a photon-sail spaceship to achieve an acceleration of 0.5g within the solar system, assuming the ship is capable of carrying passengers? | 613 | cqadupstack-physics |
90790 | Acting on a current density operator in second quantization | I have a current density operator in second quantization in the form: $\hat{J} = -i\left(\psi^\dagger \partial_x \psi - (\partial_x \psi^\dagger) \psi \right) $ operating on some state: $|\phi \rangle = \int dy (u(y) \psi(y) + v(y)\psi^\dagger (y))|BCS\rangle $ i.e its some excitation of the BCS state (not in momentum ... | How can I compute the current density operator $\hat{J} = -i\left(\psi^\dagger \partial_x \psi - (\partial_x \psi^\dagger) \psi \right)$ acting on the state $|\phi \rangle = \int dy (u(y) \psi(y) + v(y)\psi^\dagger (y))|BCS\rangle$ without encountering issues with derivatives of delta functions, and what is the resulti... | 19,365 | cqadupstack-physics |
44233 | Why is electric field zero inside a hollow metal sphere ? | The figure below shows a hollow metal sphere with a positive point charge $Q$ sitting outside it. What is the electric field at the center of sphere ? The answer is zero (look at here at the beginning of page 4), but I do not understand why?  | A hollow metal sphere is placed in the vicinity of a positive point charge $Q$. What is the magnitude of the electric field at the center of the hollow sphere, and explain why it is zero? | 34,782 | cqadupstack-physics |
123709 | Null geodesics and rotation in stationary axisymmetric space-times | It is well known that in Schwarzschild space-time, a torque-free gyroscope in circular orbit at _any_ permissible angular velocity at the photon radius will, if initially tangent to the circle, remain tangent to the circle everywhere along its world-line. This is usually explained as follows. Say I'm described by an ar... | In a stationary but non-static axisymmetric space-time, describe the conditions under which the Fermi-Walker transport of a gyroscope in a circular orbit at the photon radius would fail to keep its axis tangent to the circular path. What specific features of the space-time geometry could lead to this failure, and how d... | 1,570 | cqadupstack-physics |
28976 | Any link between decoherence and renormalization? | I have been studying decoherence in quantum mechanics (not in qft, and don't know how it is described there) and renormalization in QFT and statistical field theory, I found at first a similarity between the two procedures: on one side decoherence tells us to trace over the degrees of freedom we don't monitor, in some ... | What is the relationship between the time scales associated with decoherence in quantum mechanics and the typical energy scales involved in renormalization in quantum field theory? Can you provide a quantitative example to illustrate this relationship? | 3,260 | cqadupstack-physics |
64780 | Comparing Static Frictions | In this figure, which of the static frictional forces will be more?  _My aim isn't to solve this particular problem_ but to learn how is static friction distributed . Since each of the rough-surfaces are perfectly capable of providing the $-1N$ horizont... | When two surfaces with different coefficients of static friction are in contact and subjected to the same downward force, how do you determine the distribution of the static frictional forces between the surfaces, and which surface will exert the greater static frictional force if one surface has a coefficient of 0.4 a... | 17,782 | cqadupstack-physics |
91581 | Pauli-Fierz "massive" equation and linearized gravity | It it known that the massive spin-2 irreducible representation of the Poincare group is the traceless symmetrical transverse 4-tensor $h_{\mu \nu}$ with rank 2: $$ (\partial^{2} + m^{2})h_{\mu \nu} = 0, \quad \partial_{\mu}h^{\mu \nu} = 0, \quad h = 0. $$ These conditions may be united into one equation: $$ \partial_{\... | In the context of the Pauli-Fierz equation for a massive spin-2 field, if we set the mass \( m \) to zero, how does this affect the number of degrees of freedom of the field? Specifically, how does the reduction from a massive spin-2 field to a massless spin-2 field change the number of degrees of freedom associated wi... | 35,653 | cqadupstack-physics |
27555 | Is renormalization associated with a volume scale or with an energy-momentum and length scale? | Given that real-space renormalization blocks together small volume elements to construct larger volume elements, is it more appropriate/helpful to consider the renormalization scale to be a volume scale instead of an energy scale? | What is the relationship between renormalization scale, defined as a volume scale, and the effective energy scale in a system undergoing real-space renormalization? | 34,251 | cqadupstack-physics |
53186 | Compressible fluid flow through a branched pipe junctions | Backdrop: Designing a dust extraction system (LEV) with a branched junction. What principles allow for the calculation of volume flow rate and pressure at the inlets if the volume flow rate and pressure is known at the outlet using a _compressible fluid_? I am familiar with Continuity and Bernoulli equations using inco... | How can the volume flow rate and pressure at the inlets of a branched junction in a dust extraction system be determined from the known volume flow rate and pressure at the outlet when using a compressible fluid, and what principles or equations should be applied in this scenario? | 37,422 | cqadupstack-physics |
111746 | Why doesn't this model plane fly? | I have been designing a model plane for Design Technology for the past month or so, and today I laser cut my final design and assembled, it then tested it. Upon testing the plane does not get any lift, whereas the previous testing model which was virtually the same did. The plane is built using Balsa Wood, and Assemble... | What are the possible reasons for a model plane made of Balsa wood not achieving lift during testing, despite being similar in design to a previous successful model? Please include at least three different factors that could affect the lift of the plane, considering aspects such as weight, surface area, and wing shape. | 15,391 | cqadupstack-physics |
60346 | Nature of Perturbed state in Perturbation Theory? | I'm interested in the Nature of Perturbed state in Perturbation Theory. The first order perturbed state is given by $$\psi^{(1)}_{n}=\Sigma_{m}a_{m}\psi^{(0)}_{m}.$$ Where $$a_{m}=\int\psi_{1}^{(m)*}\psi_{n}^{(0)}d\tau.$$ Now as the Hamiltonian changes while applying perturbation. It's basis should change,My question i... | In the context of perturbation theory, if the first order perturbed state is given by $$\psi^{(1)}_{n}=\Sigma_{m}a_{m}\psi^{(0)}_{m}$$ with $$a_{m}=\int\psi_{m}^{(1)*}\psi_{n}^{(0)}d\tau,$$ explain why the unperturbed states \( \psi^{(0)}_{m} \) can be used as a basis for expanding the perturbed state \( \psi^{(1)}_{n}... | 12,490 | cqadupstack-physics |
6248 | Some Majorana fermion identities | I have been struggling with these Majorana fermion identities for quite sometime now. I would be grateful if someone can help me with them. Let $\lambda$,$\theta$ and $\psi$ be $4$-component Majorana fermions. Then apparently the following are true, * $(\bar{\theta}\gamma_5 \theta)(\bar{\psi}_L\theta)(\bar{\theta}\ga... | Given the identities involving $4$-component Majorana fermions $\lambda$, $\theta$, and $\psi$, can you verify if the following equation holds true?
$$
(\bar{\theta}\gamma_5 \theta)(\bar{\psi}_L\theta)(\bar{\theta}\gamma^\mu \partial_\mu \psi_L) - \frac{1}{4}(\bar{\theta}\gamma_5 \theta)^2 (\bar{\psi}_L\gamma^\mu \p... | 23,757 | cqadupstack-physics |
134366 | Is real voltage always the real part of complex voltage? | If I have a complex voltage $V_z$ is real voltage $V$ (i.e. the voltage used in the normal ohms law and the voltage we normally talk about) always given by $V=Re(V_z)$. Does the same apply to current? and if it is not the case how do we find $V$ from $V_z$? | If a complex current \( I_z \) is expressed as \( I_z = I + jI' \), where \( I \) is the real part representing the actual current, what is the relationship between the real current \( I \) and the complex current \( I_z \)? How can you express the real current in terms of the complex current? | 8,773 | cqadupstack-physics |
47723 | Lennard Jones liquid vapour phase transition | I am trying to generate a phase diagram of pressure versus temperature in a NPT ensemble using molecular dynamics method. I am using the Lennard Jones potential with 108 particles and Berendsen thermostat and barostat to fix the parameter. In order to observe phase transition I plot the radial distribution function (RD... | What could be the reasons behind the absence of a significant discontinuity in density during the liquid-vapor phase transition in my molecular dynamics simulation using the Lennard-Jones potential, despite observing a clear transition in the solid-liquid phase? | 13,622 | cqadupstack-physics |
37801 | Misaligned Mirror on Michelson Inferometer | If one of the outer mirrors on a Michelson interferometer was to be misaligned by a small angle of theta, what would be the shape of the interference pattern in the detector plane? What would happen to this pattern as the other mirror moves? | If one of the outer mirrors on a Michelson interferometer is misaligned by a small angle \( \theta \), how will the interference pattern change as the mirror is gradually tilted? Quantitatively, how does the spacing of the fringes in the interference pattern depend on the angle \( \theta \)? | 11,022 | cqadupstack-physics |
76852 | Nonlinear waves and shock formation | In the cases of nonlinear acoustics, why is shock formation unlikely when the dispersion is strong when compared to the nonlinearity of the wave? | In nonlinear acoustics, how does the ratio of dispersion to nonlinearity quantitatively affect the likelihood of shock formation in a wave? Provide a specific example or mathematical expression to illustrate your answer. | 32,911 | cqadupstack-physics |
79860 | Why is a laserpointer able to "erase" a glow-in-the-dark sticker? | a while ago I tried to charge a glow-in-the-dark sticker using a simple red laser pointer. It was a large sticker, of the type used to mark emergency exits and fire extinguishers here in Germany. I thought I could draw a picture this way, with glowing strokes. To my surprise, the exact opposite happened - the sticker w... | What physical phenomenon explains why the glow-in-the-dark sticker darkens when illuminated with a red laser pointer, instead of becoming more luminescent? | 7,098 | cqadupstack-physics |
27118 | Asymptotic Completeness, generalized free fields, and the relationship of thermodynamics with infinity | Asymptotic completeness is a strong constraint on quantum field theories that rules out generalized free fields, which otherwise satisfy the Wightman axioms. If we were to take a limit of a list of continuous mass distributions $\rho_n(k^2)$ that approaches a distribution in some topological sense, however, is there an... | Given the asymptotic behavior of the imaginary component of the mass \(1\) propagator at time-like separation \(I(t) = -\frac{\cos(t+\pi/4)}{4\sqrt{2\pi^3 t^3}}\) and the expression for \(I_\beta(t)\) as
\[
I_\beta(t) = \frac{J_1\left(\sqrt{2\beta(\sqrt{\beta^2+t^2}-\beta)}\right) K_1\left(\sqrt{2\beta(\sqrt{\beta^2+... | 8,058 | cqadupstack-physics |
25219 | How does atmospheric seeing evolve over time? | I am writing an automated target selection application in which the seeing at the time of observation is an important factor: some fields are important to observe under good seeing, others, less so. Of course, it can only choose based on current conditions, not the conditions a few minutes in the future under which the... | How can I model the temporal variations in seeing at an astronomical observation site based on the global statistics I have, and what statistical methods can I use to generate simulated seeing values for my automated target selection application? | 22,542 | cqadupstack-physics |
78040 | Experimental relationship between linear dependence and superposition | From Griffith's _Introduction to Electrodynamics_ > The principle of superposition may seem obvious to you, but it did not have > to be so simple: if the electromagnetic force were proportional to the > _square_ of the total source charge, for instance, the principle of > superposition would not hold, since $\left(q_1+... | If the electromagnetic force were proportional to the square of the total source charge, derive and explain why the principle of superposition would not hold. Specifically, calculate the combined force acting on two point charges \( q_1 \) and \( q_2 \) placed a distance \( r \) apart if the force \( F \) is defined by... | 14,542 | cqadupstack-physics |
76354 | Geometric interpretation of Electromagnetism | For gravity, we have General Relativity, which is a geometric theory for gravitation. Is there a similar analog for Electromagnetism? | Is there a geometric framework similar to General Relativity that describes the fundamental interactions of electromagnetism, and if so, what are the key mathematical principles involved in this theory? | 17,132 | cqadupstack-physics |
7280 | Is contextuality required in quantum mechanics? | I still don't really understand what contextuality means in reference to quantum mechanics. If someone could give a clear definition that would be great. It sounds like it means you can't always relate the state of a system to its wavefunction or something? That confuses me since it seems to violate quantum mechanics. ... | What is the significance of contextuality in quantum mechanics, and does it necessitate acceptance in all interpretations of the theory? | 20,946 | cqadupstack-physics |
72311 | How the dielectric rigidity depends on the shape of material? |  A research article says that, "The conical shape improves the dielectric rigidity", but how I am not able to understand. | How does the conical shape of a dielectric material influence its dielectric breakdown voltage compared to other shapes, and what quantitative measurements can be used to evaluate this effect? | 33,757 | cqadupstack-physics |
13369 | Trace of energy momentum tensor in $CFT_1$ | There is a standard procedure to show that for CFT's in dimension $d\geq 2$, the trace of stress tensor vanishes. I think I can't apply those steps when I only have one dimension, say time, because if we could then we can show that stress tensor trace $T_{tt}$ (which is basically it) also vanishes which may not be true... | In a one-dimensional conformal field theory (CFT), does the trace of the stress tensor \( T_{tt} \) always vanish? What conditions must be met for it to vanish, or can you provide a specific example where it does not vanish? | 13,616 | cqadupstack-physics |
126981 | Mapping a continuum XY model to a discrete one | A low energy expansion of a system I am currently investigating is described by this XY-like model: $$ H_1 = \int_0^\beta \mathrm{d} \tau \int_{\left[ 0, L \right]^2} \mathrm{d}^2 x \left( J \left( \nabla \theta \right)^2 + K \left( \partial_\tau \theta \right)^2 \right) $$ It is essentially an anisotropic XY model. It... | What are the critical values of coupling constants \( J \) and \( K \) for the isotropic XY-like model described by the Hamiltonian \( H_1 \) when the critical temperature is \( T = 2.20 \), and how can these values be related to the critical values of \( J_{xy} \) and \( J_z \) in the lattice model \( H_2 \) to ensure... | 21,714 | cqadupstack-physics |
82610 | Adjoint of a Wave Function | Why is the adjoint of a function simply it's complex conjugate? Normally with a vector we consider the adjoint to be the transpose (And the conjugate? I don't know why), so does this concept carry through to these functions? Should I imagine the conjugate of a wave function to actually be a column vector? Further what ... | What is the mathematical relationship between the adjoint of a wave function, its complex conjugate, and how does this relate to the representation of wave functions as vectors in Hilbert space? | 15,593 | cqadupstack-physics |
14761 | Where does the smell of electrostatic charge come from? | Everybody knows you can produce electrostatic charge rubbing two different materials together. But have you ever smelt e.g. at the plastic after charging it? There actually is a distinct electrostatic charge smell :-) While normally smelling involves the transport of molecules, what you are smelling here, is the electr... | What is the mechanism behind the distinct smell often associated with charged materials, and how can it be quantitatively measured in terms of the electric field strength or the concentration of charged particles released during the process? | 31,582 | cqadupstack-physics |
91627 | Can we explain Huygen's principle taking into account Maxwell's predictions? | Descartes gave the corpuscular model (1637) of light. Corpuscular model was further developed by Issac Newton. Model predicted that if the ray light (on refraction) bends towards the normal then the speed of light would be greater in the second medium. Focault proved it to be false in 1850. Before this, Huygens had put... | How can Huygens' principle be reconciled with Maxwell's theory of electromagnetism, particularly in the context of light waves produced by oscillating charges? | 11,893 | cqadupstack-physics |
86391 | How many bits are encoded on the surface of the smallest black hole? | Here's my guess ($157\, \textrm{bits}$) and how I got there. Please feel free to disregard completely and give your own answer. My understanding (please correct any wrong assumptions as there may be many): The smallest black hole is a "Planck particle", which is a Planck mass in size, and has a theoretical radius of $5... | What is the information content, in bits, of the smallest hypothetical black hole, assumed to have a radius of \(5.72947 \times 10^{-35}\, \mathrm{m}\), based on the Holographic principle and the concept of Planck areas? | 8,145 | cqadupstack-physics |
62638 | How does this paper relate to standard QED? | This paper proposes a microscopic mechanism for generating the values of $c, \epsilon_0, \mu_0$. They state that their vacuum is assumed to contain ephemeral (meaning existing within the limits of the HUP) fermion/antifermion pairs. This affects the mechanism of photon propagation as follows: > When a real photon propa... | How does the proposed microscopic mechanism for photon propagation involving ephemeral fermion/antifermion pairs relate to the renormalization of photon velocity in standard quantum electrodynamics (QED)? Specifically, how does this mechanism account for the finite speed of light compared to the "infinite bare velocity... | 18,521 | cqadupstack-physics |
77813 | How far can the human eye see? Any ending point or infinite? | How far can the naked human eye see if unobstructed? (straight ahead on perfectly flat land). Is there a stopping point or is it infinite when you look in the sky? Is there any situation that the human eye can see infinite? What are the factors that determines how far we can see? The photon flux density and...? Physics... | What is the maximum distance that a naked human eye can see in a straight line on perfectly flat land, and what factors limit this distance? | 15,007 | cqadupstack-physics |
57055 | Summing up magnetic fields | In the case of a complex shape filiform distribution of current, are we allowed to determine the magnetic field created by sections of the distribution and then summing them up, like we do with a discrete distribution of charge when calculating the electric field? Thank you | Given a complex shape filiform distribution of current, can you calculate the total magnetic field at a point in space by integrating the contribution from infinitesimally small segments of the distribution, similar to how one would calculate the electric field from a continuous charge distribution? Provide the mathema... | 33,710 | cqadupstack-physics |
83232 | Can you help me with physics lab calculations? | My question is, how do you find the torque of a rotating spool with a connected string being pulled down by its hanging mass? So in this experiment we had a machine with two rotating discs, one on top of the other, and as we spin a disc, the machine counts how many of 200 lines on the edge of the disc pass through a se... | If a spool with a radius of 0.05 m is attached to a disc and a mass of 2 kg is hanging from a string wrapped around the spool, what is the torque produced by the hanging mass on the spool? Also, if the measured angular acceleration of the disc is 4 radians per second squared, what is the moment of inertia of the disc-s... | 14,979 | cqadupstack-physics |
39055 | How can the Air friction force be applied to an object? | Suppose we have an object and we throw it straight upward in the air. How do we apply the Air friction force to this object while moving upwards and after that downwards? Sorry if it's easy because I'm still a novice! | If an object is thrown straight upward with an initial velocity of 20 m/s, and the air friction force acting on it is 0.5 times its weight, how high will the object rise before it starts to descend? Assume the acceleration due to gravity is 9.81 m/s². | 9,455 | cqadupstack-physics |
119531 | Why does water freeze from top to bottom | I was wondering why water freezes from up to bottom and not the other way around. The reason I question this is because in a Video I came across, I discovered water freezes from top but surely with the current knowledge I would say it should be opposite because we know cool air drifts down while hot air drifts up so si... | Why does water freeze from the top down instead of from the bottom up, and what are the thermodynamic principles that explain this phenomenon? | 10,693 | cqadupstack-physics |
54200 | Superconducting gap, temperature dependence: how to calculate this integral? | Tinkham (page 63) states that the temperature dependence of the gap energy of a superconductor $\Delta(T)$ can be calculated using the following integral:  How can this actually be carried out? I am not sure how to approach this problem or re-arrange th... | How can the integral expression for the temperature dependence of the gap energy of a superconductor, given by the equation from Tinkham (page 63), be evaluated numerically to determine the value of \(\Delta(T)\) at a specific temperature, say 10 K? | 22,931 | cqadupstack-physics |
122088 | What is the cut-off for quantum superposition? | Is there an explanation as to how macro objects aren't in superposition? At what size do objects stop being in a state of superposition? | At what size or mass do classical objects transition from being in a quantum superposition to exhibiting definite states, and what physical principles govern this transition? | 12,037 | cqadupstack-physics |
77053 | How much faster is the fusion we make on earth compared to the fusion that happens in the sun? | I have come across many websites that states that the proton-proton fusion which is the dominant type of fusion that powers the suns, is extremely slow and that is why the sun is still burning to that day. But also I have read that the sun fuses 620 million tons of Hydrogen every second, so that is considered fast for ... | How much faster is deuterium-tritium (D-T) fusion compared to proton-proton fusion in terms of the time it takes to release the same amount of energy? Provide the quantitative comparison based on the energy output and the rates of fusion for both processes. | 7,994 | cqadupstack-physics |
109478 | Any recommendations for self-studying physics? | I'm new to this forum so I hope this post falls under the guidelines of what's acceptable. I'm currently finishing my grade 11 year of high school and I have hopes of attending one of the prestigious schools in the US such as MIT, Harvard, Stanford, Princeton, etc. I would love to be able to study physics in university... | What are the key mathematical concepts and topics in physics that I should focus on studying in order to prepare for university-level physics, particularly if I want to gain a solid understanding of the subject? | 5,840 | cqadupstack-physics |
62506 | Purpose of Grover's algorithm? | How is the output of Grover's algorithm useful if the result is required to use the oracle? If we already know the desired state, what's the point of using the algorithm? So can you give me a concrete example of an oracle function. For example if the indexed items in a Grover search were, for example arbitrary patterns... | In a quantum search algorithm similar to Grover's, how would you design an oracle function to determine if an unknown face image matches any faces within a given set of patterns? Additionally, can you explain the differences in efficiency between this quantum approach and a classical correlation-based algorithm? | 2,245 | cqadupstack-physics |
95719 | What is the mass required for a star to have the gravity equivalent to a black hole? | At what mass does the light from stars ( I am talking about stars and not black holes) fail to escape the star's gravity? Is it the same (minimum) mass required for an object to be called a black hole? | What is the minimum mass a star must have for its gravity to prevent light from escaping, and is this mass equivalent to the threshold required for an object to be classified as a black hole? | 29,068 | cqadupstack-physics |
119830 | Why is work in a constant electric field equal to the force times distance? | Let's say, for example, that an infinite plate generates a constant electric field that exerts a force of 6N on a 1C charge. To move the charge from a distance of 5m to 1m from the plate, the work done is given by 6N * 4m = 24Nm. The way this has always been explained is that we apply a 6N force over the 4m distance. H... | If a uniform electric field exerts a force of 6N on a 1C charge, how much work is done when moving the charge from a distance of 5m to 1m away from the plate, considering that an opposing force of 6N is also applied in the opposite direction of the electric field during the entire move? What is the total work done on t... | 35,124 | cqadupstack-physics |
14138 | Why exactly does current carrying two current wires attract/repel? | When to parallel wires carrying currents in same direction I1 & I2. http://www.youtube.com/watch?v=43AeuDvWc0k this video demonstrates that effect. My question is, why **exactly** does this happen? I know the reason, but I'm not convinced with it. One wire generates the magnetic field which is into the plane at another... | When two parallel wires carrying currents I1 and I2 in the same direction are placed close to each other, what is the net force experienced by the wires, and how is this force quantitatively expressed in terms of the currents and the distance between the wires? | 20,872 | cqadupstack-physics |
68822 | Proof for the completeness of eigenfunctions of a self-adjoint operator | I always heard the eigenfunctions of a self-adjoint operator form a complete basis. Where can I find a proof in infinite dimension space? Presumably readable for physicists. | What is the significance of the completeness of eigenfunctions for self-adjoint operators in infinite-dimensional Hilbert spaces, and can you provide a concise proof or reference that is accessible for physicists? | 8,879 | cqadupstack-physics |
83934 | Change in weight by the change in mass of Earth and its radius | If the mass of Earth is four-times bigger, and the radius of Earth is two- times smaller, what would be my new weight compared to my current weight? | If the mass of Earth were quadrupled and its radius halved, how would my weight change compared to my current weight? | 8,939 | cqadupstack-physics |
66733 | Does a point exist in the real world | In mathematics we can have an infinite number of points between two integers. This is really circular logic since a point is defined as infinitely small. Does a point exist anywhere in the physical world or is it simply a convenient mathematical abstraction with no place in reality. **Is space actually divided into inf... | If space and time are considered to be continuous, what implications does this have for our understanding of physical phenomena, particularly in the context of the concept of quantization in quantum mechanics? | 23,586 | cqadupstack-physics |
99113 | Why is there water coming out of a car’s tail pipe? | I notice yesterday that my neighbor’s car had water coming out of the exhaust pipe in the morning. My first response was since the hot exhaust is hotter than the cold tail pipe, heat is transferred from the hot exhaust through the pipe, and with enough moisture in the exhaust, enough heat leaves such that the humid air... | When water condenses from the exhaust of a car during cold mornings, is the primary source of this water more accurately attributed to (i) the combustion of gasoline, which produces water as a byproduct, or (ii) the moisture in the air, especially considering that this phenomenon is more noticeable in winter than in su... | 4,819 | cqadupstack-physics |
119369 | Have I calculated Angular Acceleration correctly? | I am teaching myself basic mechanics from a standing start. I am trying to understand Angular Acceleration and have set myself a problem to solve. My answer 'feels' wrong, so I'd like some help to understand if I've misunderstood, or miscalculated anything. I've taken many liberties with rounding, please ignore, this i... | An object is traveling around a circular path with a radius of 40 m. It has a speed of 50 mph at point A and slows down to 40 mph at point B after 5 seconds. Calculate the angular acceleration of the object in radians per second squared. | 15,429 | cqadupstack-physics |
18567 | Can the field generated by a magnet domain extend to infinity? | As a thought experiment let us assume that we have isolated a magnetic domain. This domain is of finite size and we know its dimensions. Assuming that we can measure an infinitesimal field, will there be a certain region beyond which the field won't be applicable? The instinctive answer to this question is no, but if y... | Given a magnetic domain of finite size, if we assume it produces an infinitesimal magnetic field, at what distance from the domain can we measure a significant decline in the field strength, and what factors would influence this decay? | 17,973 | cqadupstack-physics |
130362 | Spectral series' formula of a given atom (other than hydrogen-like)? | The hydrogen spectral series is given by the Rydberg formula: > The energy differences between levels in the Bohr model, and hence the > wavelengths of emitted/absorbed photons, is given by the Rydberg formula: > > $${1 \over \lambda} = R \left( {1 \over (n^\prime)^2} - {1 \over n^2} > \right) \qquad \left( R = 1.09737... | Using the Rydberg formula, calculate the wavelength of the photon emitted when an electron transitions from the n=3 energy level to the n=2 energy level in a hydrogen atom. Provide your answer in nanometers. | 25,603 | cqadupstack-physics |
63872 | What happens to the energy not absorbed by a radio? | If a radio tunes to a specific frequency, where does the excess energy go? If one continues to hit the resonant frequency, shouldn't the wire begin to melt at some point from too much energy? | If a wire is exposed to a resonant frequency that matches its natural frequency, and continuous energy is supplied to it, what is the maximum power it can withstand before reaching its melting point, assuming the wire has a specific heat capacity and thermal conductivity? | 4,209 | cqadupstack-physics |
55006 | Could there be a small-scale observation of dark energy? | The amount of dark energy in the universe is pinned down fairly precisely by fluctuations in the cosmic microwave background, if I understand correctly. So in that sense there's very good evidence of its existence. What I'm wondering is, could there ever be a laboratory-sized experiment that demonstrates its effects? F... | If two super-light ping pong balls are placed in a vacuum in space, such as on the ISS or Voyager 1, what would be the estimated distance between them after a certain period due to the effects of dark energy? Please calculate this distance over the span of one year, assuming the influence of dark energy is constant. | 21,460 | cqadupstack-physics |
135043 | Mathematical physics text with plenty of applications | I'm looking for texts on mathematical physics. I've seen various other threads, but the texts recommended in those threads were mathematical methods of theoretical physics texts, that is to say those texts focused on the math methods useful for physicists and assumed the applications of those methods would be covered i... | What are some recommended textbooks that effectively integrate mathematical concepts with their applications in physics, particularly for topics in multi-variable calculus, linear algebra, real analysis, and abstract algebra? | 35,064 | cqadupstack-physics |
93268 | Nothing can travel faster than the speed of light. In what frame of reference? | Since frames of reference are arbitrary, I can define a frame of reference that moves backwards with a speed greater than $c$, then any static object in that frame of reference is already traveling forwards faster than $c$! So what does "nothing can travel faster than light" exactly mean, and where does it apply? | If we assume a hypothetical frame of reference is moving backward at a speed greater than the speed of light (c), what implications does this have on the observed speeds of static objects within that frame, and how does this relate to the principle of causality in physics? | 32,707 | cqadupstack-physics |
80739 | Amplitude and phase in vector wave field | Is it possible to make some separation of amplitudes and phase for a general vector-wave field? For example, like a paraxial approximation of a complex scalar field of the form $$\Phi(x,y,z) = A(x,y,z)e^{i\theta(x,y,z)}.$$ If this is possible, what are some common methods? | What are some common methods for separating amplitudes and phase in a general vector-wave field, and can you demonstrate this with the paraxial approximation of a complex scalar field given by $$\Phi(x,y,z) = A(x,y,z)e^{i\theta(x,y,z)}$$? | 30,864 | cqadupstack-physics |
62277 | Smallest force to move a brick | Having a brick lying on a table, I can exert horizontal force equal to $\mu m g$ to a middle of it's side, and it will start moving (assume $\mu$ is the friction coefficient). However, can I make the brick moving with less horizontal force? May be, applying it not to a middle of a side can help? I have no idea of how t... | What is the minimum horizontal force required to move a brick resting on a table, if I apply the force at the edge of the brick rather than the middle, considering the coefficient of friction $\mu$ and the mass of the brick $m$? | 2,567 | cqadupstack-physics |
106017 | Restrained expansion of a piston/cylinder | Suppose an ideal gas in a piston cylinder has some initial pressure $p_1$, volume $V_1$, and temperature $T_1$. A pin, which holds the piston in place, is suddenly removed, and the gas quickly expands. Once equilibrium is reached, the final pressure of the gas is $p_2$. I am looking at a textbook solution which claims ... | Is it valid to assume that the pressure of an ideal gas remains constant at $p_2$ throughout the entire expansion process, immediately after the piston is released? How would you describe the work done during the expansion if the process were not ideal and included irreversibilities? | 25,259 | cqadupstack-physics |
118938 | Three equal mass points on the string | Help me please to solve my problem. I have three equal point masses on the line string. $L$ is a distance between masses. $P$ is a pulling of the string. I know that the potential energy of that system is equal to $$E=\dfrac{P}{L}(x_1^2+x_2^2+x_3^2-x_1x_2-x_2x_3),$$ where $x_1(t), x_2(t)$ and $x_3(t)$ are mass deviatio... | Given three equal point masses \( m \) placed on a linear string, with a distance \( L \) between each mass, derive the expression for the potential energy \( E \) of the system as a function of the deviations \( x_1(t), x_2(t), \) and \( x_3(t) \) from their equilibrium positions, knowing that the potential energy can... | 26,836 | cqadupstack-physics |
46571 | How do Zener diodes maintain the potential across their terminals? | My physics book has a topic about Zener diodes being used as voltage regulators in the reverse bias. Well, I'm curious to know how does a Zener diode maintain the potential across its terminals after it has undergone avalanche breakdown? Does it start conducting in full offering almost zero resistance? If so, how can t... | How does a Zener diode maintain a constant voltage across its terminals while in avalanche breakdown, and what is the relationship between current and voltage in this state? | 20,808 | cqadupstack-physics |
94653 | Work of an adiabatic/ compresion: sign? | As far as I am concerned the adiabatic work it is given by: $$ W_{adi}=\frac{P_{f}V_{f}-P_{i}V_{i}}{\gamma -1}$$ While I have seen in other examples that it is used with $1-\gamma$ in the denominator changing the sign of the result. Is there something that I should have in mind when using it or am I missing something? ... | In a certain adiabatic process involving an ideal gas, the initial pressure \( P_i \) is 2 atm, the initial volume \( V_i \) is 3 L, the final pressure \( P_f \) is 4 atm, and the final volume \( V_f \) is 1.5 L. Given that the specific heat ratio \( \gamma \) for the gas is 1.4, calculate the adiabatic work done \( W_... | 21,967 | cqadupstack-physics |
15653 | Infinite-range 1D Ising model + Hubbard-Stratonovich-Transformation | I have a probably quite simple question RE the HST. After some work, I obtain as the partition function for the infinite range 1D Ising model $$Z = \int_{-\infty}^\infty \frac{dy}{\sqrt{2\pi / N\beta J}} e^{-N\beta f(y)}$$ where $$f(y)= \frac{J}{2} y^2 - \frac{1}{\beta} \ln[2\cosh(\beta(h + Jy))]$$ Now I want to evalua... | In the context of the infinite range 1D Ising model, the partition function is given by
$$Z = \int_{-\infty}^\infty \frac{dy}{\sqrt{2\pi / N\beta J}} e^{-N\beta f(y)}$$
where
$$f(y) = \frac{J}{2} y^2 - \frac{1}{\beta} \ln[2\cosh(\beta(h + Jy))].$$
Using the method of steepest descent, can you derive the conditi... | 21,660 | cqadupstack-physics |
108630 | If the axis of rotation is fixed, is it ok to say clockwise torque? | I know that the direction of torque is along the axis of rotation, but would it be acceptable to say, for example considering a vertical thin rod in the x-y plane with a force acting on the bottom end towards the left, 'it is a clockwise torque about the centre of mass' (even though strictly speaking the torque's direc... | Given a vertical thin rod situated in the x-y plane, with a force applied at the bottom end towards the left, calculate the magnitude of the torque about the center of mass of the rod if the force has a magnitude of 10 N and the distance from the center of mass to the point of force application is 0.5 m. Consider that ... | 25,657 | cqadupstack-physics |
24469 | Why are do neutral atoms shrink as their valence shells approach 8 electrons? | Why do neutral, unbonded atoms shrink in size as they approach having 8 electrons in their valence shells? A good example is elements 3 through 10 in this table, that is, lithium (1 valence electron) through neon (8 valence electrons). * * * For posterity, below is my earlier _incorrect_ version of my question. It's in... | What is the trend in atomic radius for elements with increasing valence electrons, specifically from lithium (1 valence electron) to neon (8 valence electrons), and what underlying quantum mechanical principles explain this trend? | 34,942 | cqadupstack-physics |
128965 | XCrysDen Structure file | Does anyone know how to directly convert a .cif file to a Xcryden structure file(.xsf) ? I know how to extract the lattice vectors and the atom positions from a .cif file, but don't whether the .cif file contain the conventional lattice vectors that need to generate a .xsf file. Thanks. | What are the steps to convert the lattice vectors and atomic positions from a .cif file into a valid .xsf file, and do .cif files typically contain conventional lattice vectors? Additionally, how can one verify if a .cif file contains these vectors? | 31,859 | cqadupstack-physics |
16271 | Why does a ping pong ball change direction when I spin it on a table? | When I spin a ping pong ball on the table, it rolls forward in the opposite direction of the spin, and then eventually changes direction and rolls backward. Here's a video demonstrating the effect. Why does that happen? | When a ping pong ball is spun on a table in one direction, it initially rolls forward and then reverses direction to roll backward after a short time. Calculate the coefficient of friction between the ball and the table if the ball experiences this change in motion due to friction. Provide your reasoning and any necess... | 27,466 | cqadupstack-physics |
31731 | Effect of boundary conditions on partition functions | While computing partition functions in statistical mechanics models (say) on a 2d lattice one usually makes use of "circular boundary conditions" which thus gives the lattice topology of a torus. It makes the expressions, and calculations simpler; and one usually assumes that in the infinite volume limit boundary effec... | If a 2D lattice with periodic boundary conditions is modified to have the topology of a surface of genus \( g \), how does the partition function \( Z \) change in relation to \( g \) compared to the standard toroidal case? Provide a formula for \( Z \) in terms of \( g \) if possible. | 10,547 | cqadupstack-physics |
31927 | critical density to create macroscopic nuggets of nuclear matter | Is there a critical size that an hydrogen bomb detonation needs to have in order to produce neutron-degenerated matter? Does anyone knows if matter in this state would be stable at ambient temperature or pressures? is there any way we can obtain stable "nuggets" of nuclear matter? | What is the minimum yield in megatons of a hydrogen bomb necessary to create neutron-degenerate matter, and would such matter remain stable at standard temperature and pressure? | 22,966 | cqadupstack-physics |
80251 | Where can get channel waveguide dimension data ny nx na ns | I need channel waveguide dimension to test my waveguide mode solver. Can someone help me? | What are the optimal dimensions for a channel waveguide to support a single transverse electromagnetic mode at a wavelength of 1550 nm? | 25,887 | cqadupstack-physics |
25683 | Impact location that created the moon | I was reading an article today about the 1000th orbit of the Lunar Reconnaissance Orbiter, and as many of you know NASA created an animation that simulates the history of the moon. It is speculated that the moon was formed after a planet the size of mars slammed into the earth and some of that debris and debris from th... | What is the estimated location on Earth where the collision with the Mars-sized body, believed to have contributed to the formation of the Moon, is thought to have occurred, and are there any geological remnants or evidence from that event? | 797 | cqadupstack-physics |
85 | What's with the very slightly larger mass of the neutron compared to the proton? | Neutron mass: 1.008664 u Proton mass: 1.007276 u Why the discrepancy? On a related note, how does one go about measuring the mass of a neutron or proton, anyway? | Calculate the mass difference in atomic mass units (u) between a neutron and a proton using the provided values: neutron mass = 1.008664 u and proton mass = 1.007276 u. What is the significance of this discrepancy in terms of nuclear stability? | 13,439 | cqadupstack-physics |
64296 | Some Dirac notation explanations | Equation for an expectation value $\langle x \rangle$ is known to me: \begin{align} \langle x \rangle = \int\limits_{-\infty}^{\infty} \overline{\psi}x\psi\, d x \end{align} By the definition we say that expectation value is a sandwich: $\langle \psi|\hat{x}|\psi\rangle$. So: \begin{align} \langle \psi|\hat{x}|\psi \ra... | Given the expectation value of an observable \( \hat{x} \) in quantum mechanics defined as \( \langle \psi | \hat{x} | \psi \rangle = \int_{-\infty}^{\infty} \overline{\psi(x)} x \psi(x) \, dx \), where \( \psi(x) \) is a normalized wave function, calculate the expectation value \( \langle x \rangle \) for a particle i... | 5,039 | cqadupstack-physics |
122741 | Capillary action meniscus height in a tube fitted inside another tube? | I was thinking about how would capillary action change in a tube (classic example) and in a tube fitted inside another tube (considering water as the liquid involved). Height of liquid column:  where: $\gamma$ = liquid-air surface tension $\theta$ = con... | Considering a liquid with a surface tension of $\gamma = 0.0728 \, \text{N/m}$, a contact angle of $\theta = 0^\circ$, and a density of $\rho = 1000 \, \text{kg/m}^3$, calculate the height of the liquid column $h$ in Example #2 (a tube of radius $c = 1 \, \text{mm}$) using the capillary rise formula given by:
\[
h = \... | 37,414 | cqadupstack-physics |
91345 | 3-point correlation function for a massive scalar field | I am a little bit perplexed as to how to compute the three-point correlation function for a massive scalar field, I know that it should be equal to zero. I need to show that: $\lim_{T\rightarrow \infty (1-i\epsilon)} \int D\phi \phi(x_1) \phi(x_2) \phi(x_3) = 0$ How to show this? Edit: I forgot to mention without using... | How can I demonstrate that the three-point correlation function for a massive scalar field approaches zero in the limit \( T \rightarrow \infty (1 - i\epsilon) \) without using the generating function \( Z[J] \)? Specifically, I need to evaluate the expression \( \lim_{T\rightarrow \infty (1-i\epsilon)} \int D\phi \, \... | 27,780 | cqadupstack-physics |
41803 | Bandgap Spacing in Photonic Crystals | I am doing some self-study on photonics and have encountered the following question: > _We know that amorphous electronic crystals such asamorphous silicon have a > bandgap. Can amorphous photonic crystals also have a bandgap? Roughly how > large would the spacing, d, have to be for a bandgap centered around ~ 600 > nm... | Can you determine the required spacing \(d\) for a photonic crystal to exhibit a bandgap centered around ~600 nm, using the equation \(n\lambda = 2d \sin(\theta)\) with \(n = 1\) and \(\theta = \frac{\pi}{4}\)? What is the value of \(d\)? | 35,394 | cqadupstack-physics |
94778 | Derivation of the Thermal Noise Spectrum | The thermal noise spectrum is given by: $$\mathcal{S}(f) = \frac{\hbar f}{2(e^{\frac{\hbar f}{kT}} - 1)}$$ This equation seems really similar to the Dirac-Fermi distribution but where does it come from? | What is the value of the thermal noise spectrum \(\mathcal{S}(f)\) at a frequency \(f = 1 \text{ THz}\) for a system at a temperature of \(300 \text{ K}\), given that \(\hbar \approx 1.055 \times 10^{-34} \text{ Js}\) and \(k \approx 1.381 \times 10^{-23} \text{ J/K}\)? | 34,470 | cqadupstack-physics |
99276 | Definition of quantum anharmonicity | I have been reading research papers in mathematical physics for some months now, and I've seen the the term "anharmonic oscillator" quite frequently. At first I assumed that given a Schrodinger equation $$\frac{d^2u}{dx^2}+(E-V(x))u=0$$ where $E$ is the energy, and $V(x)$ is the potential function. If $V(x) = x^2 +$ hi... | What are the key characteristics that define an anharmonic oscillator, and how does the potential energy function impact its behavior compared to a harmonic oscillator? | 1,684 | cqadupstack-physics |
87298 | Transparency of gypsum and concrete for RF waves | Is there a database (or any other source) of graphs of average transparency of various materials (cardboard, concrete, gypsum etc.) as a function of wavelength? | What are the average transparency values of cardboard, concrete, and gypsum at different wavelengths, and how do they compare to each other graphically? | 16,886 | cqadupstack-physics |
96057 | How two photons interfere in a double slit experiment | I have a very basic question about photons in double-slit experiment. I am not good at math, and have some Quantum mechanics knowledge. Math free explanation would be very good to me. When we do double slit experiment with single photon at a time, it will be detected at some location of screen. Over the time period the... | In the double-slit experiment, when two photons are sent through the slits one after the other, do their associated probability waves interact with each other to create an interference pattern, and if so, how do these interactions compare to the interference pattern observed with single photons? | 26,338 | cqadupstack-physics |
51879 | How to guarantee that a kilogram of antimatter will quickly annihilate another kilogram of matter? | What I mean is, suppose we could somehow get a kilogram of matter and contain it safely. Now lets say we want to make a bomb using this kilogram, now, we have two ways, either store another kilogram of matter inside the bomb itself and let the matter and the antimatter touch each others when we want to bomb to detonate... | What factors would influence the annihilation rate of one kilogram of antimatter when it comes into contact with one kilogram of matter, and how could these factors be manipulated to achieve a faster reaction rate in an explosive scenario? | 34,849 | cqadupstack-physics |
18694 | Why is static friction omitted here? And comparison with this problem on Newton's second Law. Solutions are all provided | The problem itself is short, but my concept question is...long. So be prepared. Note that problem 1 and problem 2 are related to my concept questions, so I am not taking advantage of asking two in one. **Problem #1** ! Note it should read "to the right with an ac... | Consider a system consisting of two masses, \( m_1 = 2 \, \text{kg} \) and \( m_2 = 5 \, \text{kg} \), where \( m_1 \) is placed on top of \( m_2 \) and there is a horizontal force \( F \) acting on \( m_2 \). If the acceleration of the system is \( a = 3 \, \text{m/s}^2 \), what is the minimum coefficient of static fr... | 16,352 | cqadupstack-physics |
87224 | Where does energy in electricity come from? | In a simple battery-wire-lightbulb circuit the moving electrons in a wire generate electromagnetic field, and that field transports energy. And the bulb goes light. But where does the energy come from in the first place? It obviously cannot be 'generated' because of the conservation law, so it has to previously be some... | In a circuit with a battery, wire, and lightbulb, how is the electrical energy transformed into light and heat energy in the bulb, and what role does the potential difference play in this energy transformation? Additionally, when moving a magnet inside a coil, how does this induce current without a direct potential dif... | 29,421 | cqadupstack-physics |
36075 | Is it really to solve problem below by using, in the main, Gauss law? | There is an infinite cylinder surface which uniformly charged along and has a surface charge density, which can be represented as $$ \sigma = \sigma_{0}cos(\varphi ), $$ where $\varphi$ - polar angle in a cylindrical coordinate system (it means that z-axis is matches with cylinder axis). There need to find z-component ... | What is the expression for the z-component of the electric field \( |\mathbf{E}_z| \) at a point along the axis of an infinitely long cylinder with a surface charge density given by \( \sigma = \sigma_{0} \cos(\varphi) \), where \( \varphi \) is the polar angle in cylindrical coordinates? Use Gauss's law to derive your... | 4,406 | cqadupstack-physics |
107687 | Physical meaning of taking twice the real part of a Fourier transform | In my previous question, Calculating the coherence length from a spectrum, it turned out that I can calculate the coherence length of my light source from the autocorrelation function, which can be obtained by taking the fourier transform of the spectrum, according to the Wiener-Khinchin theorem. In one of the answers,... | What is the physical significance of taking two times the real part of the Fourier transform of the spectrum when calculating the autocorrelation function, as described by the Wiener-Khinchin theorem? Also, can you explain why the expression for the Fourier transform without taking the real part is claimed to be equiva... | 30,974 | cqadupstack-physics |
63236 | What's the physical difference between the quantities $\langle v_{i}v_{j}\rangle$ and $\langle v_{i}\rangle\langle v_{j}\rangle$? | What's the physical difference between the quantities $\left\langle v_{i}v_{j}\right\rangle $ and $\left\langle v_{i}\right\rangle \left\langle v_{j}\right\rangle $? Where $\left\langle v_{i}\right\rangle$ is the mean value of the $v_{i}$ velocity component with $i=1,2,3$. (Same story with $v_{j}$.) This is in the cont... | What is the physical significance of the difference between the correlation $\left\langle v_{i}v_{j}\right\rangle$ and the product of the means $\left\langle v_{i}\right\rangle \left\langle v_{j}\right\rangle$ in the context of analyzing the velocity components of stars within galaxies? How can this difference inform u... | 35,613 | cqadupstack-physics |
45099 | Simple model of edge states for a two-dimensional topological insulator | Quantum spin Hall states or, topological insulators are novel states of matter that have insulating bulk and gapless edge states. Are there any simple models that show these features? See e.g. the article > Xiao-Liang Qi and Shou-Cheng Zhang, _The quantum spin Hall effect and > topological insulators._ The pdf file is ... | What are the conditions under which gapless edge states emerge in the effective Hamiltonian for mercury telluride topological insulators, and how would you mathematically derive these edge states from the Hamiltonian provided in the referenced article? | 1,364 | cqadupstack-physics |
46247 | Spin-orbit coupling constant for rubidium | I have come across the following question in my course notes: The $5s\to 5p$ transition in rubidium is split into two components with wavelengths of 780nm and 795nm respectively. For the $5p$ state, calculate the spin-orbit coupling constant $a$. I have calculated the spin orbit splitting energy to be $E=\frac{3}{2} a$... | What is the correct method to calculate the spin-orbit coupling constant \( a \) for the \( 5p \) state in rubidium, given the wavelengths of \( 780 \, \text{nm} \) and \( 795 \, \text{nm} \) for the \( 5s \to 5p \) transition, and how can I verify if my previous calculation of \( a = 1.67 \times 10^{-19} \, \text{J} \... | 21,973 | cqadupstack-physics |
18236 | "Completeness" of eigenvectors in a complete, commuting set | This question was originally the one below dashed line. Now after further discussions, it has boiled down to this question: Is the following construction possible? Suppose we have a 3 dimensional ket space in which the basic vectors are simultaneous eigenvectors of two observables $\xi_{1}$ and $\xi_{2}$ such that they... | In a 3-dimensional ket space with observables \(\xi_1\) and \(\xi_2\) that have eigenstates represented by the vectors \(|a,b\rangle\), \(|a,d\rangle\), and \(|c,b\rangle\), can \(|c,d\rangle\) be absent without violating the condition for a complete commuting set? If this is true, what implications does this have on t... | 32,110 | cqadupstack-physics |
61196 | Does Earth produce metallic elements in its core? | Does Earth produce metallic elements in its core? | What are the predominant metallic elements found in Earth's core, and what is their estimated concentration by weight? | 1,779 | cqadupstack-physics |
74656 | Simulating the effects of external forces on a small population | I am looking to simulate the effects of external forces on a small population but I am having difficulty figuring out how I should go about doing such a simulation. My simulation consists of having small "atom" like objects that jostle about randomly and depending on the type of external force, the "atoms" will react d... | How can I create a simulation that models the movement and interaction of individuals in a population in response to the introduction of money, taking into account their personal characteristics and the properties of the money, such as its perceived value and scarcity? | 30,909 | cqadupstack-physics |
57178 | Determining the probability of a particular site having a particular spin in an Ising model | Given an Ising model, we have the energy formula: $E= - \sum_i h_i S_i - \sum_{i \neq j} J_{ij} S_i S_j$ and we have the probability of a given state, given the energy of that state and the temperature: $P(\\{S\\}) \sim e^{-E(\\{S\\})/kT}$ (where the normalization constant is the partition function). The question I am ... | Given the energy formula of the Ising model \( E = - \sum_i h_i S_i - \sum_{i \neq j} J_{ij} S_i S_j \) and the probability of a state \( P(\{S\}) \sim e^{-E(\{S\})/kT} \), how would you compute the probability that a specific site \( i \) has a spin of \( +1 \) at a temperature \( T \)? Are there efficient computation... | 10,543 | cqadupstack-physics |
78605 | Single-site superfluid wave function and coherent state | The Superfluid wavefunction in Bose Hubbard model can be written as $|\Psi_{SF}\rangle=\frac{1}{\sqrt{N!}}(b_{k=0}^{\dagger})^N|0\rangle$ in the U=0 limit, whereU is the onsite interaction, N is the total particle number, k=0 denotes the lowest energy state and $|0\rangle$is the vacuum state. By Fourier transform, $b_{... | In the U=0 limit of the Bose-Hubbard model, the superfluid wavefunction is expressed as a product of local coherent states. If there are N particles distributed equally across M lattice sites, what is the probability amplitude for finding a specific site occupied by a particle, and how does this probability vary with r... | 38,076 | cqadupstack-physics |
80701 | Sandstone getting soaked with water | I have seen someone putting a sandstone in water. With only about 10% of the stone sitting in the water. One could see the stone getting soaked with water. So there must be a force, which lets the water climb up through the stone against gravity. What is that force? Or is there some other effect present? | What is the primary force or phenomenon that enables water to rise through a sandstone despite only a small portion being submerged, and how does this relate to the concepts of capillarity and porosity? | 15,944 | cqadupstack-physics |
103177 | What is Photoproduction | I wonder what photoproduction means in the context of pion decay and vector meson dominance? What is the reaction formula, Feynman diagram for such a photoproduction thing? Is it simply a reaction where the final state is a bunch of photons? | What is the reaction formula for the photoproduction of pions through vector meson dominance, and can you provide a Feynman diagram representation of the process? | 5,228 | cqadupstack-physics |
67776 | Properties of gravity | If all objects in the solar system suddenly went cold to the core, including the Sun, would it gravity play any different role? I guess what i am trying to ask, is there any relation between energy and gravity? | If all objects in the solar system, including the Sun, suddenly became cold to the core, how would this affect gravitational forces between these objects, and is there a quantitative relationship between the thermal energy of a body and its gravitational influence? | 28,644 | cqadupstack-physics |
123019 | Diamagnetism of a degenerate electron gas for weak fields | In the book "Statistical Physics, Part I ($3^{{\rm rd}}$ edition)" by Landau and Lifshitz, at $\S59$ when he treats the diamagnetic part of the magnetisation of a degenerate electron gas for weak fields ($\mu_BH\ll\varepsilon_F$, where $\varepsilon_F$ is the Fermi energy), he says that the energy levels of the orbital ... | Can you derive the expression for the number of states of a particle in a degenerate electron gas, specifically explaining how the magnetic field \( H \) influences this count? What is the factor of \( 2 \) in the expression \( 2\frac{VeH}{(2\pi\hbar)^2c}{\rm d}p_z \) accounting for, and how do we arrive at this result... | 29,925 | cqadupstack-physics |
86915 | Does the Higgs boson contribute to the Casimir effect? | I read that all bosons contribute to the casimir effect with an attractive force. http://math.ucr.edu/home/baez/physics/Quantum/casimir.html Does the Higgs boson contribute to the Casimir effect? Could it be the missing 5%? | Does the Higgs boson contribute to the Casimir effect, and if so, what quantitative relationship can be established between its contribution and the total force observed in the Casimir effect? | 15,328 | cqadupstack-physics |
98525 | Is the second derivative of the effective potential always the mass square of the particle? | In quantum field theory, we can calculate the effective potential of a scalar field. My question is whether the second derivative of the effective potential always represents the mass square of the particle? Why or why not? $$ m_{eff}^{2}=\frac{\partial^{2}V_{eff}(\phi)}{\partial\phi^{2}} $$ For example, consider a sca... | In the context of quantum field theory, consider a scalar field with a one-loop effective potential defined as \( V_{eff}(\phi) = \frac{1}{4!} \lambda_{eff}(\phi) \phi^{4} \). If the field is at a non-zero value \( \phi \neq 0 \), can you determine whether the second derivative of the effective potential, \( \frac{\par... | 25,039 | cqadupstack-physics |
121475 | How to cancel infinite mass corrections for quantities without counterterms? | I'm trying to understand how infinite mass corrections are cancelled for a particle that is massless at tree level. In short the problem is that we have infinite diagrams, but we don't have a counterterm for them since they don't exist at tree level. As a simple example consider a theory with three charged Weyl fermion... | In a theory involving three charged Weyl fermions and a complex scalar field, where a small Majorana mass is generated for one of the fermions due to symmetry breaking, how can one show that the infinite mass corrections are cancelled in the context of loop corrections, especially considering the absence of a tree-leve... | 12,704 | cqadupstack-physics |
13991 | two distant galaxies seen from earth | From the Earth If we observe two galaxies that are diametrically opposed and each 1000ly far from the earth. the separation distance between the galaxies will be 20000ly? really question is: if the galaxies were separated from Earth 10Gly. then the separation distance between galaxies would 20Gyr? | If two galaxies are located 10 billion light-years (10 Gly) away from Earth and are diametrically opposed to each other, what is the separation distance between the galaxies in light-years? | 19,818 | cqadupstack-physics |
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