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I know that energy is equal to the work done and work is equal to the multiplication of force and displacement caused my the force in the direction of the applied force.
But when friction is involved, things seem to be unclear to me. Like if I apply a force $F$ on a object which causes displacement of $s$ and the frict... |
I know that uncertainty in measurement is different from measurement error (1).
But when it comes to classification (of uncertainty and error) and different ways of expressing uncertainty and error in measurement, it kind of feels the same.
Like,
TYPES OF ERRORS
Systematic errors
Random errors
(source).
same as in 2,... |
I was wondering whether there are instances of truly accidental degeneracy in physics i.e., degeneracies that cannot be linked with some symmetry of the system/Hamiltonian. I have the following example in mind. Consider the energy of a 2D box with sides $L$ and $2L$. Then the energy is $$E=\frac{\pi\hbar^2}{4L^2}\left(... |
At an art exhibition I saw a piece that looks like this:
There are two independent rod pendulums each with an equal mass $m$ at the end. One pendulum has a blank piece of paper attached to it. The other has a rod attached to it, drawn by the red line. At the end of this rod is pen that draws on the canvas. The pendulu... |
In the relationship r = ϵe/p−e: mixing ratio of the mass of water vapour to the mass of dry air.
Question: What is ϵe
For clarification see question Moist adiabatic lapse rate
I know that the ratio equation is a ratio of mass but how do I determine the mass of water vapour involved? Is it a function of temperature, a f... |
I would like to understand all types of forces exerted on a small particle in a Stokes flow. According to this, page 9, "stresslet" and the hydrodynamic force were defined as two different phenomena. I do understand the mathematical definition of the hydrodynamic force. Can anybody explain the terms involved in equatio... |
If we sent a short pulse of light bouncing between two mirrors far apart where one mirror was vibrating such that when the pulse was incident on it the light was doppler shifted - would the light keep blue shifting indefinitely?
Practically, the mirror would cease to be a mirror above some frequency of course
|
A sound wave is a massless packet of energy much like a photon. Would it be feasible to use these energy packets to generate electricity in the same way as solar panels. I am thinking of panels about the size of solar panels with a thousand microphones arranged in rows. These could be placed in areas that produce a lot... |
Consider a charged particle at rest in a vacuum. A traveling oscillating electric field reaches the particle, making it oscillate as well. The particle has gained kinetic energy with that interaction, so by energy conservation, the field must have lost the energy that the particle gained, right?
My question is: how doe... |
My problem involves a flywheel of moment of inertia, $I$. I would like the flywheel to start at rest and achieve a rotational velocity of $\omega$, within $t$ time. I see two approaches to the problem, but they give different answers meaning I have made a false assumption somewhere.
The first approach is an energy appr... |
Is there a misinterpretation of NIST data, in this conclusion about the order of 4s and 3d, that contradicts Hartree Fock calculations?
I understand that it is a clear conclusion based on Hartree Fock calculations, that for neutral Potassium and neutral Calcium, 4s is lower than 3d, as per afbau. And that for neutral s... |
I'm trying to understand the physics of tilt twisting in gymnastics / trampolining, and I've run into a conundrum where theory doesn't seem to agree with practice, so I'm looking for where my mistake could be.
In tilt twisting, the gymnast performs a flip, and, during the flip, also starts turning. The motion is descri... |
Both photons and gravitational disturbances travel at $c$. Given that a photon does cause a tiny stress in spacetime due to its energy, and the propagation of this stress is at the same velocity as that of the photon, is a photon then accompanied by a corresponding "pressure wave" similar to that of a plane traveling a... |
Yep, yet another question about the infamous "double-slit" experiment. I've read all the similar questions that pop up before submission of the question. I've read plenty :) over the years. I fell in love with quantum mechanics when I first read about this experiment in the 20th century and back to Young's in 1801. Cop... |
Einstein says information cannot be transmitted faster than light.
Say I set an alarm that ring at 9:00 am. I go to school, and wait until 9:00 am. Then I tell my friends that my alarm rang. If the distance of the alarm clock and school is sufficently large, I think I can say the information that alarm rang is transmit... |
Is the speed that the Earth spins on its axis constant over the course of 24 hours?
As opposed to does it turn faster and slower during different hours over any given day even by a very small variation. Who has made such measurements and how were they made?
|
For SHM with a spring with mass m and uniformly stretched, its effective mass is m/3:
https://en.wikipedia.org/wiki/Effective_mass_(spring%E2%80%93mass_system)
However, all the solutions online I can find is based on Energy. Can we use Newton's law to get the same conclusion? I tried, and get effective mass of $ \frac{... |
I'm currently going through MIT OCW's Classical Mechanics Course. I'm a little confused by the section about tension in the course and would like to seek some clarification.
The course defines tension at arbitrary point p in a rope as follows. Suppose we cut a rope in two, around that point p. According to the course,... |
The elastic pendulum is a chaotic dynamical system which is equivalent to a mass attached to a string in 2 or 3 dimensions. It exhibits complex harmonic motion and chaotic behavior. Wikipedia gives a system in two variables (distance from the fixed point $x$ and angle from the fixed point $y$) that describe the motion ... |
After interesting presentation at academic days of emeritus professor of the University of Ljubljana (UL) Andrej Čadež about a notion and detecting of gravitational waves in 2016 an answer arose >what is minimal possible mass for (Schwarzchild) black hole<? Although professor didn't have time left, he just mentioned Ha... |
Suppose a wave pulse is produced in a string clamped at one end, and the other end is loose(tied with a massless ring which can move along a vertical rod, there's no friction). Now, I have searched everywhere on internet, they say the net restoring force on free end of string is zero, therefore the slope is zero, hence... |
In Rosten's review of exact RG (arXiv:1003.1366), exact RG can be recast as field redefinition, but I don't see why it should be general discussion. Could you possibly explain to me why exact RG should be expressed as field redefinition?
|
Niels Bohr in 1922:
„Thus LEWIS, who in several respects independently came to the same conclusions as Kossel, suggested that the number 8 characterizing the first groups of the periodic system might indicate a constitution of the outer atomic groups where the electrons within each group formed a configuration like th... |
Imagine my friend and I fell into the event horizon of the Gargantua, the blackhole from the movie interstellar with the mass of 100 million times of our Sun. Would I be able to tell that both of us are accelerating towards the singularity or we will be floating endlessly while maintaining eye contact? The suits should... |
I have a few questions regarding the AdS/CFT dictionary regarding the state-state map.
I have seen people identifying the empty AdS spacetime with a CFT vacuum.
What do they mean by "empty" AdS? Is it
i. AdS spacetime without considering any dynamical field or
ii. empty AdS geometry as in no black holes are to be emb... |
One can clearly see that the AdS bulk isometries form the $SO(d,2)$ symmetry of the $d$ dimensional CFT explicitly. Why does this occur: why don't the isometries of the spacetimes match up or the symmetries of the theory on both side match up in the statement of AdS/CFT? We can see it doesn't, but why would we naturall... |
In lecture 12 of his course on "Quantum field theory for cosmology", that can be found for free on the web, professor Kempf makes the following statements.
Consider a real Klein-Gordon field $\phi$ in a globally hyperbolic spacetime, with metric $g_{\mu\nu}$.
The covariant Klein-Gordon equation is
$$(g^{\mu\nu}\nabla_{... |
For a non-interacting Hamiltonian, $H = \sum_{\alpha\beta} H_{\alpha\beta} c_\alpha^\dagger c_\beta$, we can diagonalize the $H_{\alpha\beta}$ matrix to find the eigenstates, which allows us to write the Hamiltonian in diagonal form, $H = \sum_n \epsilon_n \phi_n^\dagger \phi_n$, where $\{\phi_n\}$ and $\{c_\beta\}$ ar... |
So I have seen in my uni's notes that if $\vec A = \vec r \times \vec H$ in an homogenous magnetic field then it is $\vec H = \vec \nabla \times \vec A$ , but there is no mathematical or physical explanation about it. Can someone help me?
|
I am writing this question to ascertain if it is possible to clean a Langmuir probe by biasing the probe negatively or positively with respect the plasma potential, during a glow discharge with oxygen present. The vacuum system is evacuated to moderate vacuum pressures around about a millibar. A glow discharge is then ... |
Suppose you a have a spring with a certain mass (in the sense that the spring itself has mass, not in the sense that the spring has a mass attached to the movable end) that is compressed some distance and then let go of. One end of it is fixed to a wall.
Suppose for this question that the spring is horizontal, so gravi... |
I'm really confused on the discretization stuff on this chapter of P&S. My question is related to the computation of the Action in scalar field theory done in page 285. When they compute the action of the real scalar field, they get
$$
\int d^4x\left(\frac{1}{2}(\partial_\mu \phi)^2-\frac{1}{2}m^2\phi^2\right)=-\frac{1... |
In the Kronig–Penney model, we assume that the periodic potential of the crystal is modeled as a square well.
The period of the potential is $d$, where $d=a+b$.
$a$: the width of the zero potential region, and
$b$: is the width of the barrier.
And with the standard assumptions of the Kronig–Penney model, and Bloch's th... |
One day I study the simple gravity pendulum, which an angle is less than $\frac {π}{2}$.
It doesn't consider friction and air drag.
In the simple gravity pendulum, My textbook says ”assume the rope isn't slack“.
And also wikipedia says “The rod or cord on which the bob swings is massless, inextensible and always remain... |
What is the physical reason why there is no mixing between left-handed and right-handed Weyl spinors in the massless case of the Dirac theory?
Why does the chirality of a massive particle change depending on the reference frame you are in and thus it’s always a mixing of the left-handed and right handed component?
|
The Hamiltonian formulation of general relativity - either in the ADM formalism or in Ashtekar variables - is straightforwardly a gauge theory. While the BRST formalism has primarily been developed to quantize such theories, it can be applied to such theories without the quantization step, in the sense that we identify... |
I am aiming to measure the strength of an electric field at different positions in space. The electric field is generated by a coil, which is driven by an AC current. This work is based on this paper: https://pubmed.ncbi.nlm.nih.gov/25680320/
the following is a sketch of the probe I am using:
It is basically a wire wr... |
In chapter 3 of "Quantum fields in curved space" of Birrell and Davies, the authors make the following statements.
Consider a real Klein-Gordon field $\phi$ in a globally hyperbolic spacetime, with metric $g_{\mu\nu}$.
The covariant Klein-Gordon equation is
$$(g^{\mu\nu}\nabla_{\mu}\nabla_{\nu}+m^{2})\phi=0$$
Let $\ove... |
I've been learning about magnetic mirrors and how the pitch angle determines whether a particle will be trapped in it or not. I've also learnt about how, when a plasma is trapped, collisions between the electrons and ions in the plasma change their pitch angles, meaning that some are able to scatter out of the mirror.
... |
Bohr's model of electron orbitals is outdated. To what extent has Bohr's rule of atomic structure with $2n^2$ electrons per shell been redescribed? Is the Schroedinger equation based on Bohr's rule of atomic orbital structure with $2n^2$ electrons per shell? If not, do we still adhere to the $2n^2$ rule?
|
In the literature the swallow tail like behaviour is prominently seen for small-large AdS black hole phase transition for the Free Energy vs Temperature Plot. Recently I was trying to reproduce the results of this paper and when I tried to produce the above mentioned plot I got something strange which I don't understan... |
suppose there is a hollow conducting sphere with a charge inside it, but not in the center of the sphere. then there is a point charge like $q'$ outside this sphere. here is my question: does the $q'$ outside of the sphere change the electric potential and the electric field of the center of the sphere?
<br. My idea is... |
Consider an ideal pulley with two blocks of same mass, say $m$, in equilbrium. ($T$ represents tension force).
One of the blocks is lifted up to a certain height, say $h$, while the other block remains at rest. During this time, the string would get untaut, so the tension in string would be zero. An external force is ... |
In section 13.3 of his book [1], Nakahara computes the non-Abelian anomaly for a chiral Weyl fermion coupled to a gauge field by making use of an operator
$$
\mathrm{i}\hat{D} = \mathrm{i}\gamma^\mu (\partial_\mu+\mathrm{i}\mathcal{A}_\mu \mathcal{P}_+) = \left(\begin{matrix}0 & \mathrm{i}\gamma^\mu\partial_\mu P_- \\ ... |
If I were to drop most objects to a level floor, they would land with a thud or bounce a few times without gaining any lateral velocity.
But a fragile object will not only break into two or more pieces, but the pieces will usually move laterally across the floor.
I suppose the center of mass of the system probably rema... |
This is somewhat philosophical than physics.
In gauge theories, it is true (more like the first principle) that
\begin{equation}
\text{ physical observable } \Rightarrow \text{gauge invariant}
\end{equation}
However, I wonder if the reverse direction also holds. That is:
\begin{equation}
\text{ Any gauge-invariant quan... |
Are there any amount of protons, electrons and other subatomic particles inside neutron stars?
I wonder if there are protons or electrons inside neutron stars trapped by their gravity and degeneracy pressure...How many electrons/protons are there if so?
|
I have canonical electromagnetic stress-energy-momentum tensor defined as:
$T_{\mu\nu}=\frac{1}{4}\eta^{\mu\nu}F_{\alpha\beta}F^{\alpha\beta}-F^{\mu\lambda}F^{\nu}_{\,\,\lambda}-F^{\mu\lambda}\partial_{\lambda}A^{\nu}\qquad (*)$
and I need to show that it is not symmetric.
I tried to calculate:
$T_{\nu\mu}=\frac{1}{4}\... |
I have Gaia photometry g, bp, and rp. My final goal is to find the photometric temperature but first I need to account for reddening by finding the extinction coefficient. I’m really stumped on how to do this when all I have is the photometry.
|
I am currently checking my work against an answer and I understand most of it except I am having difficulty understanding the signs in a particular part. The question is as follows:
(a) Derive the gluon propagator for $\mathcal{L}_{\text {fix }}=-\frac{1}{2 \xi}\left(n^\mu A_\mu^a\right)^2$ :
$$
G^{A_\mu^a A_\nu^b}(p)... |
I understand that an measurement operator always returns its eigenvalues, with a probability. I also understand that it is a postulate of QM, so why can't prove it Why is the measured value of some observable $A$, always an eigenvalue of the corresponding operator?
However, I would like to see that an operator in a ran... |
In the GRB system, we combine the three primary colors, red, green, and blue, to make some new colors.
It's easy to understand the production of yellow because the wavelength of yellow is between red and green. So as cyan and purple.
However, violet, which is notated as grb(127, 0, 255), how do you understand it?
Vio... |
This question is inspired from The Sun is giving us a low entropy, not energy.
I accept the claim that sunlight must be a low entropy source of energy, given that it maintains the entropy gradient necessary for life (along with other sustained departures from thermodynamic equilibrium, like weather). We can also show t... |
What happens to the strength of the Casimir effect when the Casimir plates are curved instead of being completely flat. Does this have an effect on the negative vacuum pressure at different points other than what would be expected given the distance between the exact points on the curved plates?
|
Suppose I have two rigid bodies, B1 and B2, I have the position of B2 relative to B1 as a standard homogenous transformation T_12 Similarly I the transformation of B1 relative to the origin as T_01.
When I want to compute the location of B2 relative to the origin, which order do I multiply the matriies?
|
If a white light is incident on a face of a thin prism, then all colors have the same incident angle. A dispersion occurs in the prism, but only the ray of one color will be parallel to the base of the prism assuming the state of minimum deviation. However, a thin prism is always in the state of minimum derivation, so ... |
I read that eventually matters that fall into the event horizon will be shredded into fundamental particles and soon ended up in the singularity but if I were to shatter a piece of glass panel into smithereens while inside the event horizon then wouldn't the entropy increase? Or it increases ever so briefly then start ... |
I was reading the book optics by zajac and hecht. It was a nice one until physics optics, i got that interference becomes when the light is coherent and monochromatic, and it is the superposition of electromagnetic wave, but how i can solve the problems with that? i no understand how to procedure to solve it, is anythi... |
A system is approach to equilibrium, if its state is independent of initial conditions and the ensemble (probability distribution over the states of the system) is time invariant.
A system is ergodic, if every microstate of the system is equally probable.
The assumption behind Boltzmann entropy is that every microstate... |
In section 4.2 of An Introduction to Quantum Field Theory by M.E.Peskin and others, it derives interaction ground state by observing the time evolution of ground state in free field theory (pg.86), and then expands the expression in eigenstate of Hamiltonian of interacting field theory,
$$e^{-iHT}|0\rangle = e^{-iE_{0}... |
Can one define what is the double differential capture cross section for a neutron, and how one would construct an experiment to calculate the double differential cross section as a function of energy and angle on a target material? Which quantities would you need to measure to calculate this quantity as a function of ... |
Number of modes inside a cavity for laser action is proportional to the volume now if I open the sides of the cavity then volume of the cavity becomes infinite so number of mode actually increase....so how. Open cavity helps to get small number of oscillating modes???
|
Consider the NN Ising model as
\begin{equation}
H = -J \sum_{<ij>} \sigma_{i} \sigma_{j} - h \sum_{i} \sigma_{i}
\end{equation}
This model has a global $\mathbb{Z_{2}}$ symmetry in the absence of $h$. We know that phase transition occurs when $d>1$.
We can write the continuum field theory for that model as -
\begin{equ... |
I understand that the equation of state of the vacuum is assumed to be $P = -\rho$ due to the Lorentz invariance of its stress-energy tensor. But this argument assumes flat spacetime. We know at cosmological scales that spacetime is not flat.
I was wondering whether the true cosmological vacuum equation of state is $P_... |
In the paper General Laws of Black hole Dynamics, Hayward has proposed a formula for trapping gravity of an outer trapping horizon given by
$\kappa$ = $\frac{1}{2}$ $\sqrt{-e^f \mathcal{L}_- \Theta_+}$ $\bigg|_H$
In the above mentioned paper, Hayward has defined surface gravity to be this, but I couldnt find any reason... |
Why can't we consider that a particle in a box is an example of a standing wave?
The ends are fixed by the fact that the potential outside is infinite. The only difference being that it is a de Broglie wave, and the amplitude is the probability density. So a quantum particle, because it has wave-like properties, behave... |
So, I am reading a paper on Quantum Brachistochrome and on the second page they say that they are doing a variation w.r.p. $<\phi|$, (which is a lagrange mulriplier) of the following action:
$$ S(\psi, H, \phi, \lambda) = \int dt [\frac{\sqrt{< \dot{\psi}|(1-P)| \dot{\psi}>}}{\Delta E} + (i<\dot{\phi}|\psi> + <\phi|H|... |
Clausius' theorem states that
$$\oint\dfrac{\delta Q}{T}\leq 0,$$
$=$ for reversible cycles and $<$ for irreversible ones.
For a cycle with two reversible paths connecting points $a$ and $b$,
$$\oint\dfrac{\delta Q}{T}= 0\implies \int_{a,\text{ path 1}}^b\dfrac{\delta Q_{\text{rev}}}{T}+\int_{b,\text{ path 2}}^a\dfrac{... |
A white is time reversal of a blackhole at least mathematically, I know it can't exist but may I know if it can form accretion disc similar to those stellar mass black holes. Does it spins on it's axis and emit relativistic jets?
|
I've been wondering what happens to the chemical potential $\mu$ of a particle (more specific, a fermion) with a mass m that freezes out around a temperature of $T\sim m$. I understand that the chemical potential is red-shifted if the particle decouples while being highly relativistic or highly non-relativistic and mai... |
I would like to request recommendations for good textbooks, theses, or papers that discuss the topic of quantum statistics of light, covering aspects such as stochastic properties and squeezed states. Additionally, I would appreciate suggestions for source material focusing on experimental methods in this field. Thank ... |
Usually, the Dirac equation is introduced as the equation $D \psi = 0$, which is form invariant under Lorentz transformations ($\Lambda$), when $\psi$ transforms as a spinor $\psi' \to S(\Lambda) \psi$. It is then shown from the properties of the $\gamma$ matrices that when $S(\Lambda) = \Lambda_{1/2}$, then $D' \to S(... |
The general one particle state in a simple infinite well of size $L$ is a superposition of all the Hamiltonian eigen-states:
$$\tag{1}
\psi(x, t) = \sqrt{\frac{2}{L}} \sum_{n = 1}^{\infty} c_n \, e^{-\, i E_n t/\hbar} \, \sin (n \pi x / L),
$$
where the energy levels are
$$\tag{2}
E_n = \frac{n^2 \pi^2 \hbar^2}{2 m L^2... |
In Jerusalem lectures by Harlow Pg. 53 it is said that
At the beginning of the
evaporation process the radiation that comes out is entangled with the remaining black
hole. But eventually it must start coming out entangled with the earlier radiation,
since eventually the final state of the radiation must be pure.
Why... |
I apologize for any difficulty in expressing my review. Allow me to briefly summarize the material and then pose my question.
Review
In David Tong's string lecture note, he derives the OPE between stress tensor and the primary field $\mathcal{O}$ in the following way (in 2 dimension):
Consider the conformal transforma... |
The classical Heisenberg model is described in terms of the three-component unit vector $S_a(x)$, which is a function of position,
$$H=\int d^dx\frac{1}{2}\sum_{a,i}\left(\partial_i S_a(x)\right)^2.$$
$S_a$ obeys Poisson bracket relations like angular momentum
$$ \{ S_a(x), S_b(y) \} =\epsilon_{abc}S_c(x)\delta^{(d)}(x... |
Jerusalem lectures by Harlow does a good job in giving a heuristic derivation of firewalls. But the details are not done and no reference is given except for a "related" calculation by Giddings. Harlow says
"I will not describe this in detail here, but one can see without too much difficulty that even fairly mild deco... |
While cleaning my fountain pen, I spilled some water on the table. The water drops had some ink dissolved in them. When these drops dried up, the deposited pigment density was visibly much higher near the edge of the drop, than at the bulk. Why does this happen?
|
Why is it that the standard model gives very even charge and spin for elementary particles that can easily be compared to each other as integers and simple 1/2, 1/3, fractions whereas some particles like the Higgs Boson and Top quark are billions of times as big as the neutrino?
|
I try to drive The Klein-Gordon equation for a massless scalar field in case of FRW metric:
$$
ds^2= a^2(t) [-dt^2 + dx^2]
$$
So I start by:
$$\left(\frac{1}{g^{1/2}}\partial_{\mu}(g^{1/2}g^{\mu\nu}\partial_{\nu}) \right)\phi = 0$$
The determinant of the metric is $(\sqrt{-g}=a^4)$. So that the equation leads to:
\begi... |
I tried writing equivalent resistance as a functional equation of x with x as the lower limit, but couldn't proceed further.
Is there a better way to approach the question?
$$\frac{(x+1)f(x+2)}{(x+1)+f(x+2)} + x = f(x)$$
|
In the book "Mathematical Introduction to Conformal Field Theory" by Schottenloher, the author introduces in Chapter 9 one axiomatic definition of what a CFT in two dimensions is. The first three axioms are the Osterwalder-Schrader axioms for a QFT in Euclidean signature. The theory is defined to be a collection of $n$... |
The Maxwell's Lagrangian density is given by the equation, $$\mathcal L = -\frac{1}{4} \space F_{\mu\nu} \space F^{\mu\nu},$$ where $F^{\mu\nu} = \partial^\mu A^\nu - \partial^\nu A^\mu$.
Hence, one can rewrite the Lagrangian density into the following, $$\mathcal L= \frac{1}{4} (\partial_\mu A_\nu - \partial_\nu A_\mu... |
The Schwinger model or $(\text{QED})_2$ essentially is quantum electrodynamics defined in $1 + 1$ spacetime dimensions. In https://arxiv.org/abs/2305.02361 they use the Hamiltonian formulation to represent the Schwinger model on the lattice and use a $\mathbb{Z}_2$ approximation of the $U(1)$ symmetry.
After doing some... |
I have a problem from statistical mechanics which puzzles me as I never had a course in statistical mechanics.
So we have a series of a resistor and conductance and we assume that $Q/C=IR$ giving rise to the ODE
$$\frac{Q(t)}{C}=-\dot{Q(t)}R + \delta U(t)$$
where $\delta U(t)$ is the voltage fluctuation due to thermal ... |
I've been studying the double slit experiment, particularly focusing on the approach that involves solving the Schrödinger equation for a free particle in two spatial dimensions. Specifically, I'm using the time-dependent Schrödinger equation:
$$
i\hbar \frac{\partial \Psi(x,y,t)}{\partial t} = -\frac{\hbar^2}{2m} \le... |
Good afternoon,
the standard description of spontaneous emission in quantum optics is - to my knowledge - via coupling of an excited atom to vacuum modes of the em-field, which are still occupied at $T \to 0$ due to zero-point fluctuation. These vacuum modes then cause "stimulated emission" at the corresponding wavelen... |
When looking at data for Na-22 decay (e.g. here: https://www.nndc.bnl.gov/nudat3/DecayRadiationServlet?nuc=22Na&unc=NDS ) it shows that for every 100 decays, there should be:
99.94 gammas with 1274keV,
179.91 gammas with 511 keV,
however when looking at spectra, it seems that the 511 keV peak is around 5-10 times highe... |
I want to study a system coupled to a bath, however I do not fully understand how to implement/think of the Hamiltonian. For simplicity say the bath is given by a spin chain (PBC), e.g. Ising-like
$$H_B=\sum \sigma^j_z \sigma_z^{j+1}$$
and I want to couple it to a single spin $H_S=\sigma^S_z$ at, say site 1 via couplin... |
The following question from Griffiths Electromagnetism states :
Suppose that f is a function of two variables (y and z) only.
Show that the gradient ∇ f = (∂f/∂y)y + (∂f/∂z)z transforms as a vector under rotation.
Now I was able to solve this question using the Chain rule for partial derivatives and basic 2D vector tra... |
I am working on calculating the Green's function for a Hamiltonian $H = H_0 + V$ numerically, where I'm specifically interested in $G(\omega) = \frac{1}{\omega - H + i\epsilon}$ at $\omega = 0$.
A challenge arises due to the eigenvalues of $H_0$ containing several zeros. This causes $G_0(\omega) = \frac{1}{\omega - H_0... |
Suppose we have a Hamiltonian given by
\begin{align}
H &= \omega a^{\dagger}a + \omega b^{\dagger}b + g a^{\dagger}b^{\dagger} + g^{*} ab
\end{align}
where the operators obey the usual commutation relations $[a,a^{\dagger}]=1$ and $[b,b^{\dagger}]=1$
then the standard way to diagonalize such Hamiltonian is to define op... |
It appears to be a well-known fact that a probability distribution on phase space will tend towards the distribution that maximizes entropy. The Wikipedia article on maximum entropy states:
"The motivation is twofold: first, maximizing entropy minimizes the amount of prior information built into the distribution; secon... |
How to derive Ix in this case?
|
How to use the non-equilibrium Keldysh Green's function to solve a driven harmonic oscillator?
A quantum harmonic oscillator $H_0 = \omega_0 a^\dagger a $ is coupled to a pump field E(t) (refer to the figure below),
The driven Hamiltonian reads, $H(t) = H_0 + E(t)(a+a^ \dagger)/\sqrt{2}$
After a delay $\Delta t$, we... |
I saw that there are radars which can detect people behind walls so I wonder what are the limitations of radars when it comes to detecting people behind solid objects and if radars can have thick radome made out of ceramic material.
|
Do neutrons in the nucleus (isotopes) affect the frequency of electron transitions through valence shells?
|
A few weeks ago the inside of my car windshield was fogged up and my older kid used her finger to draw a face in the condensation.
Weeks later, the windshield fogged up again, and the face became visible again. My younger kid asked why.
“The older kid's fingers left an oily residue on the windshield,” I said, which se... |
I want to understand the relation between several different definitions of canonical transformation. I am studying the answer by Qmechanic in this post
Let us define a canonical transformation as a transformation that satisfies $(\sum_ip_idq^i-Hdt)-(\sum_iP_i dQ^i-Kdt)=dF$ for some generating function $F$. Any possible... |
I watched a YouTube video by Scienclic showing a spaceship experiencing a peculiar optical illusion when going faster and faster in space, I wonder is there a version for the sound? Like I'm driving faster and faster on a busy traffic then I think most of the sound are coming from ahead despite the sources are actually... |
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