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I recently read a paper "Meson-catalyzed fusion in ultradense plasmas" (it is behind a paywall: only subscribers to Physical Reviews E can read it) that claims that muon-catalyzed fusion in substances such as warm-dense matter lead to cycling rates many orders of magnitude greater than the rates shown for other scenari...
The Bloch-Messiah decomposition states that any Gaussian unitary can be decomposed as a sequence of passive elements and single-mode squeezers (i.e. beamsplitters, rotations, single-mode squeezing). How does one find this decomposition in practice? For example, say I have the quadratic 2-mode unitary: \begin{align} U =...
The question is: Now my question is that , why will we take the tension in the string , or in fact , the string to be making the same angle with respect to the surface as the fluid is making with the horizontal? I know the surface must make a right angle to the net acceleration experienced by it in an accelerating f...
I was reading about venturimeters , and this is what I found on net: Now my question is , where do we exactly "select" the two points required to put the bernoulli's equation? For example I select two points as follows: If I do this , then I will have a horizontal level and there will be no need to include the p...
I have derived 3 expressions for the power that a force, $\vec{F}$, transfers to a body. (A) and (B) are consistent, but (C) isn't. Where have I gone wrong with (C)? EDIT: THE MISTAKE HAS NOW BEEN SPOTTED. (Explained below.) (A.) The infinitesimal work done on a body by a variable force, $\vec{F}$, on a body as it move...
I understand that the total tension to carry and move the weight would be split between the two segments of the two-pulley system, but I don't see why it would be evenly split between the two. It makes sense to me that if, say, a block were hanging from the ceiling by two strings attached at the ceiling, the weight wo...
If a spherical body is given some velocity and it then starts pure rolling on a plane surface(not inclined), will the body come to rest if we ignore other factors like surface irregularities and air resistance? Also how and which direction does static friction act in?
The fuzzball proposal intrigues me, but I doubt its ability to match up with semi-classical low energy physics. A variation of my question was asked by the awkwardly titled post:"At the instant of fuzzball creation, do all strings instantly pop to its face?". And an answer was provided with a link to an article by Sami...
According to a paper I am reading (https://arxiv.org/abs/1904.08448. roughly page 8), an operator $K(t)$ is define as follows: $$ K(t) = i\hbar\sum_n | \dot{n}_0(t)\rangle \langle n_0(t)| \tag{1} \label{eq:1}$$ Later, it gives another form as follows: $$ K(t) = i\hbar\sum_n \frac{dP_n(t)}{dt}P_n(t)\tag{2}\label{eq:2}$$...
For example, given a spherical shell with charge $Q$ rotating on its axis, can I think of it as the composition of many concentric coils and integrate the infinitesimal magnetic moments $d\vec \mu$ to calculate the total $\vec \mu$? If so, why is that? It seems so simple but I'm having a hard time justifying it.
I was discussing this with my professor, he was saying that the Voigt model has a physical meaning in terms of actually being reproducible in physical terms when curve fitting to spectral lines. Lorentzian is the function normally associated with single atoms, not in a solid state matrix, but then he said Gaussian is j...
I'm interested in applying some simple linear response theory to a (weakly) non-equilibrium system. For example, consider a microscopic rigid body attached to a wall at a certain point, and that this body can spin freely in circles around this fixed point. The body is subject to thermal fluctuations but it also has acc...
In JJ Thompson's experiment, Why are some electrons able to pass through the slit of the anode, rather than hitting the anode plate itself? Even though electrons manage to get past the anode, will it decelerate, as the anode keeps attracting it from behind now? So electrons make a U turn.
More abstractly, the topic is: amplification of quantum uncertainty within dynamically unstable systems. I'd like to have a calculable toy model, e.g. maybe a quantum version of the famous "abelian sandpile model". We would start in a pure state in which the "grains of sand" each have an equal and uncorrelated uncertai...
How would you calculate 2 different bohm velocities in a multi species plasma, say H+ and N gas excited by a microwave reactor.
I'm trying to understand what's written in a journal paper (https://iopscience.iop.org/article/10.1088/2040-8986/ab7b01/meta) pp.19 that I'm studying. In summary, there's a bulk metal that acts as a perfect mirror at $z\leq0$. In $x$- and $y$-direction, the metal is infinite. Anywhere above $z = 0$ is air/vacuum. The p...
Ok so we have this question: Now when I take these two points: Applying bernoulli's equation to these points: taking Pressure at point 1(inside the beaker) to be $P_o$ + $\rho gd$ , and second pressure as $P_o$ , and the velocities as 0 and v , and taking any datum level (since change in P.E.going to stay constan...
The expression of Josephson current including the second harmonic between two s-wave superconductors is $$ I_{J}=I_{1}sin(\phi)+I_{2}sin(2\phi) $$ I try to calculate $I_{2}$ by following derivation in Section 18.7 Bruus & Flensberg. The Hamilitonian is $H=H_{0}+H_{t}$. $H_{0}$ is unperturbed Hamilitonian and is made ou...
Q. Photoelectric effect supports quantum nature of light because There is minimum frequency of light below which no photoelectrons are emitted. Electric charge of photoelectrons is quantized. Maximum kinetic energy of photoelectrons depends only on the frequency of light and not on its intensity. Even when metal su...
Studying MRI, I found that excitation is done by applying B1 (RF) and Gz simultaneously. But, I think that if those are applied at same time, slice selection cannot be done correctly because Gz will continuously changing the resonance frequency of the area. If Gz is applied first, and thus resonance frequency of the sp...
In finite elements method, when point load is applied to a particular node of elastic solid continuum medium (e.g. soil), does it affect nodal forces in the rest of the mesh (i.e. does each node experience a fraction of the applied load as a result of force distribution) or is it assumed that it only affects that one n...
Suppose we work in 1+1 spacetime and consider only a scalar field. In canonical quantization of QFT, a state is a density on "configuration on a time slice" (Let's forget the fact that there is no measure theory on such space). And path integration tells us how propagate from one slice to another. So my question is, in...
The setup is : To measure the position of a moving particle, we send a light beam and we calculate the time required ($t_0$) for the light to travel to the particle, reflect and come back. we can use the equation $x_0 = \frac{ct_0}{2}$. By measuring the delay in the arrival time of the reflected wave, there seems to be...
We have a crystall with $N$ atoms. A Schottky defect is one of the atoms leaving their points in the lattice and going to the surface with $N' = cN^{2/3}$ possible atom places. I want to compute the (Boltzmann) entropy of a crystal with $N_S$ Schottky defects, where $1 \ll N_S \ll N'$. My first attempt: We pick $N_S$ a...
Let $\rho_1$ be the pure one-photon state described by the ket $$|\psi_1\rangle = \int dk\ A(k)a^\dagger(k)|0\rangle$$ for a complex amplitude function $A(x)$ and an empty ket $|0\rangle$. This state is obviously coherent, since non-diagonal terms with amplitudes $A(k)A^*(k')$ contribute to the density matrix. The main...
I was learing about group theory in QM and stable about symmetry breaking. I find it very interesting and search some stuff and even looked on wikipedia and found this: https://en.wikipedia.org/wiki/Explicit_symmetry_breaking. At the bottom I saw that the perturbation term "is the term which explicitly breaks the symme...
Let's suppose that there are two streams of sea water, flowing on a flat inclined surface. Both of the streams are distant, independent of each other and parallel to each other. Now lets image I put a magnet in between the streams, such that it isn't in contact with either of them and is equidistant. Since seawater is ...
Imagine there is a Neutron star Displaced a small distance from our accessible 3d slice in the direction transverse to that 3d slice. It will bend the space around it. It will also bend the space of 3rd dimension but beings in 3rd dimension will not be able to observe that mass. This would mean we will observe gravity ...
It is often said that matter curves space (or rather spacetime) in general relativity. But why should matter curve space one way and not the other way? So it seems like a metaphor, I guess. I read somewhere that space (spacetime) in general relativity works like an indexing. The relation between two nearby measured poi...
Given the following $d$ dimensional dilaton-gravity-Maxwell low-energy effective action in the target space of a bosonic string: $$S=\frac{1}{2\kappa^2}\int d^dx\sqrt{-G}e^{-2\Phi}\left[R-\frac{1}{12}g^{\alpha\beta}g^{\mu\gamma}g^{\nu \delta}H_{\alpha\mu\nu}H_{\beta \gamma \delta}+4g^{\mu\nu} \partial_{\mu} \Phi \parti...
I've been struggling with this exercise (7.19 in Classical Mechanics by John Taylor) for a long time. What do they mean by "You need to find the components of this acceleration relative to the table"? Could someone help me?
I was doing a question which was to find the number of generalized coordinates needed to describe a particle with the motion: $x(t)=2a\sin(\omega t) $ $y(t)=a\cos(2\omega t)$ So I solved it and found the equation of motion to be: $(y-a)=\frac{-x^2}{2a}$ So what I am confused about is what can be called a constraint equ...
I am looking for Lecture Notes or videos closely following Peskin & Schroeder QFT chapter 6 and chapter 7 (Radiative Correction). I will be glad if someone suggest that.
If I think heat as transfer of energy from hot body to cold body, how I calculate difference $\Delta Q$. Shouldn’t $Q$ be used instead?
In the images below I have drawn a double pendulum system with the pivot hub and a stopper A which is imagined to be fixed to some large wall. In both scenarios 1 and 2 the system is initially at rest and there is a wedge and square stopper fixed at the end of the proximal arm to prevent clockwise rotation. Both frict...
The orbital period of Mars, is, as anyone can find at Wikipedia, $T=686.98$ d, and the semi-major axis of its orbit is $a=2.2794\cdot10^{11}$ m. This gives $T=2\pi\sqrt{\dfrac{a^3}{GM}}=686.84\text{d}$. Of course, $M$ is the mass of the Sun. I'm no physicist, but a mathematician. But I think that this discrepance (abou...
Can anyone summarize or point me toward references for why someone would choose one diffusion model over another, particularly in relation to radiation transport during a nuclear blast? The diffusion models I am looking for information on are: Implicit Monte-Carlo Gray Multi-group Discrete Ordinate I am working on fa...
What is "point of interest" and why isn't there a Zref for determining electron beam quality with TRS 398? ((To what depth do you put the ion chamber when you do high energetic electron beam quality with TRS 398?))
Suggestions to better formulate my question are also highly appreciated. To better explain my question let me start with a very familiar case: Suppose we have a two-band insulator described by $$H = \sum_{\boldsymbol k, n} \varepsilon^n(\boldsymbol k)\ d^\dagger_n(\boldsymbol k)d_n (\boldsymbol k), \qquad n \in\{0,1\}...
I have a conceptual misunderstanding/confusion, for which I will give two examples to illustrate my problem. Example 1: In Bohr's atom, de Broglie describes the atomic electrons as waves, where the length of the orbit is given by an integer number of wavelengths $$2\pi r = n\lambda$$ Here, the electron is described as ...
I'm studying the Foldy-Wouthuysen Transformation on Bjorken-Drell's book and I got stuck strying to replicate some calculations. First of all, introducing the transformation $\psi'=e^{iS}\psi$ we get to the equation $i\frac{\partial \psi'}{\partial t}=H'\psi'$, where $$H'=e^{iS}\left(H-i\frac{\partial}{\partial t}\righ...
I would really appreciate some help with a question I have about the TISE (Sch. tipe independent equation). This is a linear equation and linear combination of the solution should be solution too. The problem is that for the free particle, which solution can be written like exp[-ikx], a linear combination using gaussia...
It is known that a spacetime variation of the dimensionless gauge coupling constants of the standard models would lead to a violation of the Einstein equivalence principle (EEP). This point is discussed for example in Uzan 2011 or Will 2018. Hence an measurement of the variation of the couplings would be in direct cont...
I am trying to generate an equation that describes the mass balance of a gas in a fixed volume. The application is simulating the sweep out time of the cell in a laser-based instrument which measures the concentration of the gas. I think this should be something like: $$dC/dt = F*Cin - F*C + C$$ where $C$ is the mole f...
Assume that I have some function $g(r,\theta,\phi)$ which I have expanded in a multipole series: $$ g(r,\theta,\phi) = \sum_{\ell=0}^\infty \sum_{m=-\ell}^{+\ell} g_{\ell m}(r)\, Y_{\ell m}(\theta,\phi). $$ If I have scalar function $f(x)$, is there a concise way of calculating the multipole expansion of their composit...
In a schematic notation, the scattering matrix element $$\langle p_{out}|S|p_{in}\rangle := 1 + i (2 \pi)^4 \delta^4(p_{in} -p_{out}) M$$ between an incoming state with momentum $|p_{in}\rangle$ and an outgoing one with momentum $\langle p_{out}|$ is by construction a dimensionless quantity, which implies that $M$ has ...
what is the EMF generated by a conducting rotating rod of mass $m$ and length $l$ in free space without magnetic field. the rod is roating with angular speed $w$? also find the current if the rod has a varying resistivity ρ= ρx
I am currently learning about dielectrics and capacitors in my physics class and part of what I have learned is conflicting. For starters the book says that capacitors do not interrupt current flow, but then in the textbook it goes onto to say that it does interrupt current flow across the capacitor gap as charge begin...
I know two particles in a Bell state cannot be written as a product state as they are entangled. But what if I had a classically correlated state$$\rho = \frac{1}{2}(|11\rangle\langle 11| + |00\rangle\langle00|)$$How do I write this as a product state?
I know that there is a particle model that describes the absorption of electromagnetic radiation in matter - A photon with energy E can excite ("absorbed") an atom if it has energy gap of the same size E. What about a wave model for absorption, or is it only a particle phenomena ?
What is the entropy generated by opening up a vacuum chamber of volume $V$ to the atmosphere? (let's say with some constant ambient pressure $P_{atm}$) I was reading about Joule expansion, but it doesn't seem to apply as easily in this case since the environment always stays at a constant $P_{atm}$ and more so seems to...
$\newcommand{\ket}[1]{|#1\rangle}$ I'm hoping to find an algorithm to do three point function calculation for generic excited states in the Ramond sector of 2d free fermion. In the NS sector, it's straightforward to use the Wick contraction to extract the result. For the R sector, modes are integer modes. In some sense...
Recently I was asked in a test what would happen if the refractive index of a medium was negative. Is it possible really? The refractive index is the ratio of the speed of light in a vacuum and another medium. It can't be less than $1$ also the speed of light is the fastest in a vacuum. So how come it'll be negative? D...
I was reading but it is unclear to me what Newton is trying to say in his second corollary, it is in the page 91 of the pdf and 84 of the book here is a photo of the proposition
Don't worry this time isn't about doubleslit but I'll still use it for my question. Imagine an electron is emitted from the source and I shall allow a certain amount of time to lapsed so as to provide sufficient time for that electron to cross the slit, now is the probability of finding the electron in-between the sour...
I am currently delving into the intricacies of Einstein's theory of relativity and striving to grasp its fundamental essence and implications. Your assistance would be greatly appreciated. Here's my thought experiment concerning special relativity: Suppose my friend and I are moving toward each other at a relatively hi...
I am self-studying group theory from Lie Algebras in Particle Physics by H. Georgi and I am having trouble following some of his arguments. In section 7.2 titled Weights and roots of $SU(3)$ he starts out by finding the weights of the generators \begin{equation} T_3 = \begin{pmatrix} \frac{1}{2} & 0 & 0\\ 0 & -\frac{1}...
I have heard that Fredric Paul schuller gave a lecture on Quantum field theory once. Can someone provide me with the lecture notes of that course?
The generalized optical theorem is given by: \begin{equation}\label{eq:optical_theorem} M(i\to f) - M^*(f\to i) = i \sum_X \int d\Pi_X (2\pi)^4 \delta^4(p_i-p_X)M(i\to X)M^*(f\to X).\tag{Box 24.1} \end{equation} In https://arxiv.org/abs/2306.05976 eq. (3.21): $$\begin{equation} -2i\left(M(i\to f) - M^*(f\to i)\...
After going through the questions and answers, I still have a question lingering in my mind. So, an observable is defined as a Hermitian operator whose eigenvectors make up a basis for the state space. But why is it so important that this basis covers the entire state space? Could it be because if it doesn't, we can't ...
Is there a relativistic effect at play that explains the following thought experiment, that I am unaware of? The apparatus depicted in the image has two straight bars in the middle emitting light from both ends. In the reference frame that is moving with the apparatus the following measurements are made: A = B, and α =...
I have the resulting interference field (the intensity at each point in the field is known) from several radiation sources. How can I find the wavelengths of the sources? The coordinates of the sources are also known. The wavelength can be from 1 to 256. The field size is 256 by 256. The full code can be found here. ...
Let's say we have a 2d sea of electrons. The energy states of these electrons will be quantised because of some sort of boundary condition on the system, and therefore there are only an integer number of available energy eigenstates. Therefore, assuming that all electrons occupy an energy eigenstate (Which is an assump...
Say it's a normal double slit experiment, and the particle is detected on some position on a wall after the slits. How much info could be deduced from the position? I know it's not exactly a path per se in a classical sense, but, based on the position of detection on the wall, how much info could be known about how the...
Only some fraction of the total mass of a main sequence star produces energy in the star's centre through the pp-chains, or in heavy stars, the CNO-cycle. My question is about the mass fraction where the greatest part of the total energy production takes place, say 90% of the total energy production. Presumably, this m...
I've got a second degree in engineering and a solid grip on the basics of physics. Now, I'm itching to take a deep dive into the worlds of general and special relativity. I've explored some introductory stuff and feel ready to level up my understanding. Any recommendations for books, online courses, or other resources?...
I recently came across this post by Valter Moretti concerning the utility of von Neumann algebras in mathematical physics. In it, he mentions The closure of von Neumann algebras with respect to the strong operator topology is the feature that makes them more interesting than simple $C^*$-algebra of operators. Simultan...
Is a locally volume-preserving deformation (in which the determinant of the deformation gradient (a.k.a Jacobian) is unity) is also globally volume preserving?
my professor told me that in Kerr metric, there is a zone of causality violation around the ring singularity, but he was saying this in the context of $M^2>a^2$, does this also apply to the cases when $M^2< a^2$ and $M^2=a^2$?
What would be the pressure, temperature and density gradients with altitude of atmosphere with ideal gas considerations? That is no convection or radiation. Most of the answers I have seen are assuming the pressure gradient is equal to the weight of the gas between the point. But why? If we assume ideal gas, it should ...
Norton's dome is a thought expriment that shows Newtonian mechanics is non-deterministic. It has the shape of a dome (see exact details of its construction on the linked page) with a rather peculiar property, if you place a ball at the very top of the dome there is a whole class of solutions to its spatial evolution, o...
I have always been confused with the differences and relation between many-body theory with and without temperature. Suppose I have a theory described by some Hamiltonian $H = H_{0} + V$, where $H_{0}$ is the free part (typically, the kinetic energy) and $V$ some interaction (say, polynomial in the creation and annihil...
I understand that a wave function cannot penetrate through a barrier that has infinite potential. However when the wave function reflects off from the barrier what does this look like? If we're in a well, does this create a standing wave? or If its just a barrier, does the wave function just move of and move in the opp...
Suppose some (coherent) light propagates onto a one-dimensional barrier with two open slits, each of length $\delta$ and separated by a distance $s$ (we can assume the centroid is known and placed at $x=0$). Diffraction through the barrier can be modeled by a beam splitter unitary $U$ coupling system spatial modes $a(x...
I integrated a jerk-function three times (acceleration, velocity, position) to get the resulting function $s(t)$ for the position. I am not sure how to use the SI units or dimension in the function. This is my function. Putting in the time $t$ as a simple number the result will be the meters the object has passed. $$\ ...
I'm trying to understand the magnetic anisotropy of single-molecule magnets. I know that spin states $\alpha$ and $\beta$ are degenerated and an unpaired electron could be in one of them. When a molecular system shows zero-field splitting $(H_{ZFS} = DS_z^2 + E(S_x^2 - S_y^2))$, the spin states split in doublets (for a...
Lets say two bodies experience head on collision with each other. It is said in my textbooks that it is found that the ratio of relative velocities of the two bodies before and after collision is fixed for a certain combination objects. But no reasoning or proof is provided for this quantitative relation in the textboo...
It is well known that the Hamiltonian of General Relativity is a linear combination of constraints. This poses a challenge in quantum gravity. If a state $\psi$ solves the constraints ($\hat C_\alpha \psi = 0$), then there is no time evolution ($e^{i t \hat H[N,N^a]}\psi = \psi$). This "problem of time" is usually disc...
Please consider this scenario: Laser light is split into two beams, one of which is sent on a path that takes it through a slab of glass, where light's speed is about two-thirds of what it is in air. The other beam travels an identical-length path, entirely in air. When the beams recombine, will the interference be con...
What is the meaning of the change $dt^2\to-dt^2$ and $dr^2\to-dr^2$ in the Schwarzschild metric, leading to: $$g=-c^{2}d\tau^{2}=(1-\frac{2GM}{c^{2}r})c^{2}dt^{2}-(1-\frac{2GM}{c^{2}r})^{-1}dr^{2}+r^{2}d\omega^{2}$$ Is gravity attractive or repulsive? Is there an event horizon?
I was going through this question :- In the answer it says : If there would be no friction between monkey and the rope, the monkey will slide down the ground. It is the frictional force which take him in upward direction. But my question is that , the monkey is accelerating upwards with an acceleration a, so the ...
I might be asking a very elementary question here. How do we identify where static friction is acting or kinetic friction is acting? For example, Consider this case: Now, here we are talking about "sliding" a body along the ground with the least possible force.. If we are talking about sliding , then that would mean...
Trying to Understand the lower bound on the Schrodinger Operator of the Hydrogen atom. Using the kato-rellich theorem. My education has been in physics and i am slowly adding to my mathematics toolset.I am yet to study fuctional analysis exrensively the following problem is in my way to understanding the following theo...
In the Michelson-Morley experiment, why didn't they assume or conclude that ether is homogeneous and permeate all of space instead of coming from an unspecified source or direction dubbed the ether wind? I mean the signals detected in the interferometer are always cancelled out regardless the relative positions of Eart...
Let's suppose that there's a container that is filled with gas and liquid as seen in the picture, and that the surface areas $S$ and $2S$. My book says that when the container gets rotated so that surface areas get reversed, the pressure force on the bottom decreases. Can you explain how this is true? First, since the...
Can a moving object deacceleration caused by interaction with enviroment be measured while the object passes through a region populated by dark matter?
During Sunset we see the lower part of the sky changing into red colour wich is of course due atmospheric thickness increased... The higher parts of the sky are still blue suggesting that as blue light is rather scattered this colour should be formed due blue light coming from a thinner part of the atmosphere which cou...
For $x^\mu$ with $\mu_0=t, \mu_i = x^i$ and $\eta_{\mu v}$ the metric tensor with diagonal (-1,1,1,1) and zeros elsewhere, the condition for equivalence of inertial frames is stated as for some "coordinate transformation" $x \to x'$, (1) $\eta_{\mu v} dx'^\mu dx'^v = \eta_{\mu v}dx^\mu dx^v$ or equivalently (2) $\eta_{...
In the superfluid state of $\rm{}^4He$, it is known from neutron scattering measurements and Monte Carlo simulations that about 10% of the $\rm{}^4He$ atoms condense into the lowest energy state. Said another way, the largest eigenvalue of the diagonalized one-particle density matrix is about 10%. However, at low tempe...
I'm new here! I am trying to demonstrate what is the influence of spin-down (Helicity -1) of photons in radiotherapy using LINACs. The question is, when an electron interacts with a photon in a process such as the Compton effect, the spin of the electron can influence the polarisation of the resulting photon, but it do...
I encountered the following problem: A parallel plate capacitor has plate area $A$ and plate separation $d$.The space between the plates is filled up to a thickness $x<d$ with a dielectric of dielectric constant $K$. Calculate the capacitance of the system. Here's how the solution was given in the textbook: The given ...
I'm doing an experiment involving inductance between two coaxial solenoids of the same length where I measure the rms value of the alternating current through the outer solenoid and rms value of the induced voltage of the inner solenoid (as far as I know this is basically a transformer). I'm trying to figure out if an ...
Assume that an LED is placed in a closed-loop of wire (ring) being located on the table. A bar magnet located a specific distance away from the table/ring is released to fall under the influence of gravity toward the center of the ring. We know that the LED would glow due to the induction of an electric field in the ri...
Please provide very simple and specific examples/explanations when answering. Some have described Electric Potential as “work done per unit of charge”, but what exactly does “per unit of charge” mean? Isn’t that the same as Eletric Potential energy?
Here is my question: Accelerated particles emit radiation. What about a particle that is in free fall, does it also emit radiation?
We have this pulley system where $m_1 = m_2$ = 1 kg. Considering the rope AB is cut, what would be the work done by the resultant force acting on $m_1$ during 1 second after cutting? The naive approach would be to just consider $m_1$ to be in free falling, so only weight will act on it, and you will get $mgh$, where $h...
When moving through a dielectric medium (like water) at constant, superluminal velocity, a charged particle produces electromagnetic radiation. This is called the Cerenkov effect, and the energy emitted by the particle per unit length per unit frequency is given by the Frank-Tamm formula. On the other hand, a charged p...
The answer given says that 2 & 3 are primitive unit cells.How can a hexagon be a primitive unit cell.Can someone explain?
Suppose I have a quantum statistical mechanics system in the grand-canonical ensemble. It is given by some Hamiltonian $H = H_{0} + V$, where $H_{0}$ is the free part and $V$ an interaction. The state of the system is described by a mixed state (i.e. density matrix) $\rho_{\beta,\mu} := e^{-\beta H - \mu N}$, with $N$ ...
Im working on a numerical method for the Ising model. I'm asked to calculate both the absolute magnetizetion and the specific heat capacity: $$c = \frac{\beta^2}{N} \left( \langle H^2 \rangle - \langle H \rangle^2 \right)$$ $$m_{\text{abs}} = \frac{1}{N} \langle \lvert \sum_{x} s_x \rvert \rangle$$ When plotting the r...