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I am trying to understand and show that asymptotically Anti-de Sitter spacetimes are not globally hyperbolic.
Now, I have found papers that talk about global hyperbolic spacetimes with timelike boundary. This startles me. My understanding was that the existence of a timelike boundary precludes global hyperbolicity beca... |
I remember that when researching and learning about vanishing points and vantage points of art pieces, that by closing one eye and viewing a painting from an exact point in space, it would give this effect of looking through a window (correct perspective and an enhanced sense of depth).
I then noticed that whenever I ... |
Imagine a planet with the same properties as Earth, this time moving in an elliptical orbit around a heavy star of a large number of solar masses. Also imagine that the surface of this planet is as massive as that of the Earth and that you can therefore experience a normal force on it as on the Earth's surface. At a sp... |
Does there exist a book, lecture notes, or a collection of problem sets, that contains a big number of problems in path integration technique, with solutions, akin to books that contain multitudes of exercises in calculus? Exercises in the books on QFT that I've seen, like "Quantum Field Theory" by Srednicki, "Introduc... |
Background
I was instructed that a Dirac delta function (impulse from $0$ to $A$ then back to $0$ at short duration) has a white noise audio frequency type excitation distribution here
ie. It should provide equal excitation of amplitude/energy at each frequency.
This is good, as this is what I want for my application. ... |
Is the proper antichronous transformation (PT-transformation) a global or local transformation?
If global, why does General Relativity not have global Lorentz transformations?
|
A 0.60 kg ball thrown vertically upward with an initial speed of 12 m/s rises to a height of 5.1 m. (A) What is the average force exerted by the air on the ball? (B) How high would the ball have gone if no air resistance acted on it?
work done by conservative force (gravity) + Work done by non conservative force = Chan... |
For analytic functions, we know that
$$ \langle q'|F(\hat{q})|q\rangle = F[q]\,\langle q'|q\rangle\tag{1} $$
Now, suppose that $q$ depends on $\tau$, promote $F[\hat{q}]$ to a functional, and introduce a path-ordering $P_\tau$. Can we generalize this to
$$ \langle q'|P_\tau\left\{F[\hat{q}]\right\}|q\rangle = F[q]\,\la... |
I'm working on an experiment to see how the tension of a drumhead impacts the frequency of its sound, but I'm not sure as to how I could measure this.
I found this forum thread from 2012, which suggests several things. First of all, it suggests using a DrumDial, but it's very expensive and doesn't actually measure tens... |
A very good explanation for the amplitudes expected for each harmonic of an ideal string with a transverse excitation is included here.
The final equation given is:
$$b_n = \frac{2AL^2}{\pi^2\ell(L-\ell)n^2}\sin\left(\frac{n\pi\ell}{L}\right)$$
Is this also the same equation that would dictate the proportional excitati... |
When there is a vacancy in the K-shell because of electron capture or incoming energy, an electron in the higher energy level will fill the vacancy and emit a characteristic X-ray. However, I think this will create another vacancy at a higher level, let's say L-shell. Consequently, to fill the vacancy of the L-shell, a... |
I will not bother to write down the tensor product in the joint basis of A and B here in this post, where A and B are atoms/electrons and m denotes a unit cell.
The Hamiltonian for this model is given by:
$H = v \sum_{m=1}^{N} \left( |m,B\rangle \langle m,A| + \text{h.c.} \right) + w \sum_{m=1}^{N-1}\left( |m+1,B\rang... |
The system is a thin, uniform rod/pencil with perfect symmetry which is released from rest at some small angle $\theta>0$ from the vertical while being on a frictionless surface.
Then there are no horizontal forces acting on the pencil as it falls (gravity and normal force only act vertically):
\begin{equation*}
\s... |
I know that in a parallel spring system the equivalent spring constant $k$ is the sum of the spring constants $k_1$ and $k_2$ of the individual springs:
$$k=k_1+k_2$$
As discussed here, if the spring constants are different, then the extensions will be different.
To be specific, take the context where a mass is hung fr... |
Background
I am working on some personal audio processing and synthesis experiments in the sample domain. I posted here about how a resonant bandpass filter with a given $Q$ and frequency $f_0$ is essentially the same as a damped mass-spring harmonic oscillator set $k$, $m$, and $c$ to get the same $f_0$ and $Q$.
It wa... |
Some time ago i saw in a QFT lecture series by the IFT UNESP that in QFT we need to discretize space by dividing it into tiny boxes of an arbitrary Volume $ \Delta V $ and then define canonical position and momentum as
$ x_i(t) = \phi(\vec{x_i}, t) \sqrt{\Delta V} $
$ p_i(t) = \pi(\vec{x_i}, t) \sqrt{\Delta V} $
Where ... |
Imagine there is an electron gun that is capable of emitting 1 electron at a time, the gun emits an electron directed at an empty space, no dust, no matter or anything that could interact with the electron. Does that electron still exist? probability wave don't count.
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If the accelerating voltage of an x-ray tube is greatly reduced, could it be made to emit photons of lower energy (UV or visible)?
|
At the "derivation" section of wikipedia page for the classical electron radius I am not able to follow the last step (citation follows):
Integrating for $r$ from zero to the final radius $r$ yields the expression for the total energy $U$ necessary to assemble the total charge $q$ into a uniform sphere of radius $r$: $... |
I am trying to understand the basic properties of BF theory, but I am unable to derive the holonomies of the fields.
In my case I want to study a more general version of $BF$ theory defined on a $4d$ manifold by the following Lagrangian
\begin{equation}
L =n B \wedge dA,
\end{equation}
with $B$ a 2 form, $dA$ the curva... |
In the Born-Oppenheimer approximation we take the full Hamiltonian of a solid, given by
$$H = T_e + T_{ion} + V_{ee} + V_{e-ion} + V_{ion-ion}$$
where the T are the kinetic energy of electrons and ions and the V are the interaction (Coulomb) potentials of electrons with other electrons, electrons with ions and ions wit... |
The scenario is that a communicating vessel or a U tube without lids is filled with water. There is a height difference between the two pipes of this tube. Then there will be hydraulic pressure and finally, the height of the liquid will flatten out. I'd like to know how long it will take to achieve equilibrium.
|
I’m trying to understand the prediction of the proton mass according to Quantum Chromodynamics (QCD). I know that the proton is composed of quarks and gluons, and that the mass of the proton is not simply the sum of the masses of these constituent particles.
I’ve read that only about 1% of the proton’s mass comes from ... |
I think the question is self-explanatory: Quantum mechanics insists that electrons have no dimensions as point-like entities, while there is a minimum (non-zero) boundary for length called the Planck length.
|
I have come across the following operation in two electrodynamics textbooks, which I find problematic: When evaluating an integral over a Laplacian in a spherically symmetric function, the radial term $\frac{1}{r^2}\frac{\partial}{\partial r} \left(r^2 \frac{\partial \Phi}{\partial r} \right)$ is evaluated simply as $\... |
I am new to research in fluid mechanics and for one of my experiments, I'd like your help.
I need to write a force balance on a polymer film in a cylindrical tank at a fixed position.
The film moves back and forth in the z-direction, depending on the turbulent flow around. It is fixed by a clamp that is mounted on the ... |
my questions stemmed from reading the article in Physica E. Vol. 86, 10-16.
(https://www.sciencedirect.com/science/article/pii/S1386947716311365)
Why does the graphene Fermi velocity $v_F$ appear in Eq.(11) in this article,?
Eq.(11) is as follows:
$$
\frac{\partial \Omega_p(z,t)}{\partial z}+\frac{1}{v_F}\frac{\partial... |
Looking for a definition of preselection I find either statistical or electoral definitions. I was trying to find something similar to What is postselection? or What is postselection in quantum computers? but for preselection in physics. Does it just mean to prepare a state?
Here is an example: https://arxiv.org/abs/14... |
I'm dealing with a patent appeal and one of the main disputes is over something I would declare common knowledge. However, our patent attorney would like to have a publicly accessible reference to one of the equations that is used in the affected patent.
The equation describes the transfer of light from a light source ... |
For example, a book rests upon a table, on earth the weight of the object is balanced by the normal reaction force exerted by the table on the book but in reality, the normal contact isn't the reaction of the weight but is present due to Pauli's exclusion principle. let's say this scenario is in deep space, with no wei... |
This might a dumb question, but why macroscopic object stops their motion when a resistive force is applied to them? By stoping, I do not mean why the force reduces the speed of the object by stealing its energy. Let me explain.
Imagine you have a damped pendulum (using the small angle aproximation):
$$
\frac{d^2 \thet... |
I want to know the actual definition of 'momentum' and why the formula of 'momentum' is $p=m×v$ ; where $m$ and $v$ are respectively the 'mass' and 'velocity' of the body ?
We generally say the definition of 'momentum' as the product of 'mass' and 'velocity' of the body. That is $p=m×v$.
For example- We know that $F=m×... |
Evere molecule consists of atoms that vibrate around their equilibrium positions. This can be viewed from a classical or a quantum perspective. However, I found a seeming inconsistency between these two approaches: in the first approach the particle is moving, but in the second approach (the expected value of) its posi... |
I'm studying the quintessence model from a dynamical system point of view. I denoted the scalar field for the dark energy as $\phi$, so I have the following Klein-Gordon equation for the field $$\nabla_\mu\nabla^\mu \phi-\frac{\partial V}{\partial \phi}=0.$$ Considering a homogeneous, isotropic, spatially flat FLRW met... |
I came across the following statement, while studying a Newtonian model for cosmic expansion:
"If $R(t)$ is the scaling factor, we can define the Hubble parameter as $H(t)=\frac{\dot{R(t)}}{R(t)}$, being $t$ the cosmic time."
What is the definition of cosmic time? Is it the same for all observers?
|
I am looking for an experimental technique to measure/create a temperature map of a small object (few mm diameter), like in terms of IR camera.
However, all IR-cameras I encountered measured temperatures higher than -20 C, and I would need something around 10K. (With 10K I mean the temperature of the object, not of the... |
Given that during pair production a very small amount of energy from the photon becomes gravitational potential energy in the particles, I was curious how this would be affected by general relativity? I was also curious as to whether this would mean that pair production requires higher and higher frequencies of light i... |
I am confused about the derivation of the boundary condition relating the perpendicular components of magnetic field across the boundary.
In my optics course, the instructor used the fact that $\epsilon$ might vary spatially. And so he used this equation
$$ \vec{\nabla} \cdot(\vec D)=\rho$$
And then took a closed surfa... |
I made a simple LC Tank circuit which oscillates at 166 kHz. Looking at it using my oscilloscope I can see one cycle of the sine wave takes about 6 microseconds.
Now if I stick and antenna to this I should be ale to emit electromagnetic waves at 166 kHz frequency which has a wavelength of about 1.8 kilometres!
How can ... |
While solving a particular classical mechanics problem , I was told that for a system of particles to be bound under their mutual forces, their initial energy (With Respect To the COM) must be less than 0. An example of this is maybe when we derive the expression for the escape velocity of a body from a given planet. H... |
The standard Damped one-dimensional Harmonic Oscillator with sinusoidal driving force has equation
$$\frac{d^2}{dt^2}x(t)+2\zeta\omega_0\frac{d}{dt}x(t)+\omega_0^2x(t)=\frac{1}{m}F_0\sin(\omega t).$$
Here is $\zeta>0$ for damping.
The solutions of this system are linear combinations of a transient function (that goes t... |
I'm reading that many articles are using the "axial anomaly equation" (e.g. Fermion number fractionization in quantum field theory pag.142 or eq (2.27) of Spectral asymmetry on an open space), and I know what axial anomaly in QFT is, but I'm not sure to what equation they are referring to. Can someone help me?
The arti... |
Imagine swinging wood stick using hand (say it's a 1-meter long cylinder with 2 centimeter diameter, just for the sake of argument). When doing it fast (angular velocity = $\omega_1$), it will create a whooping sound. This sound has a frequency band ($f_{1,min}$ to $f_{1,max}$). To simplify, we assume the the band is r... |
I'm currently trying to prove Planck's constant, with the use of a NaCl-kristal and X-ray.
But when I use the formula $n\lambda=2dsin\theta$, with $n=1,\ \lambda = hc/E,\ E=qU,\ U=35kV,\ \theta = 7.3$ it gives a $d$ half the literary value of around $141\ pm$ instead of $282\ pm$. Why do I get half, and what did I do w... |
I'm trying to compute the double Higgs scatter in QFT framework. Is it correct if I use the scalar propagator for this process?
Also I've found that I've four possible diagrams: the three $s,t,u$ channels and the point, $x$ like diagram.
So when I try to do the $M$ amplitude I get a something that goes like the inverse... |
I know that in the case of a Yang-Mills $\rm SU(2)$ gauge symmetry, the covariant derivative is written as:
$$D^{\mu} = \partial^{\mu} + i\frac{g}{2}W^{\mu}_{a}\tau^{a}$$
With $g$ is the coupling constant, $W^{\mu}_{a}$ the gauge fields and $\tau^a$ are the Pauli matrices.
My question is whether there is any reason why... |
I was studying the conservation of momentum and energy and a question came to my mind. Both energy and linear and angular momentum are "numbers" that represent the symmetries in the interactions that our universe has (rotational, translational and temporal), so both momentum and energy are related to force. My question... |
Spurred by reading a recent obituary of Penzias, who with Wilson discovered the cosmic microwave background, I was led to read their letter in a 1965 issue Astrophysical Journal Letters, which was published side-by-side with a companion letter in that same issue by Dick, Peebles, Roll and Wilkinson.
The DPRW letter lay... |
Just as the title proclaims, I have a Fourier transformation I am trying to determine. Here is the Fourier transformation in its full form:
\begin{equation}
\int\frac{d^3q}{(2\pi)^3}e^{i\mathbf{q}\cdot\mathbf{r}}\left(\frac{\sqrt{4m^2+\mathbf{q}^2}\log(4m^2/(4m^2+\mathbf{q}^2))}{\mathbf{q}} - 2\right)\frac{a}{\mathbf{q... |
Can Leggett-Garg inequality be used to falsify superdeterminism, Bohmian mechanics and other realist interpretations of quantum mechanics?
https://en.wikipedia.org/wiki/Leggett_inequality
https://en.wikipedia.org/wiki/Leggett%E2%80%93Garg_inequality
Since many people are still working on those interpretations, i am dou... |
in our university project, we are developing a tsunami simulation using the Shallow Water Equations. For our project, we have decided to allow users to enter an epicentre and the magnitude of an earthquake, then put in the coordinates of a coastal city, and calculate a rough estimate saying when the tsunami resulting f... |
Is it possible to prove that
$$\displaystyle c = \frac 1 {\sqrt{\epsilon_0 \mu_0}}$$
using Maxwell's equation in integral form?
Recently, I saw this kind of proof by Professor Walter Lewin in one of his 8.02x lectures. But I could not understand the derivation in the video lecture.
Here is the link to the lecture (Deri... |
I am currently writing an investigation for my high school diploma, and I am a little rusty on uncertainties and error propagation. So I was wondering whether I could get some help on a doubt I had.
In my experiment, I investigate the relationship that exists between the parachute vent hole radius and the drop time. I ... |
if we listen to some audio signal on a wired earphone, then does the wire of the earphone act as a transmitter antenna to emit the audio signal as radio waves even though its strength might be negligible?
|
Consider the following Lagrangian:
$$
\mathcal{L} = \frac{Ma^2\dot\theta^2}{6} +\frac{1}{2}ma^2\left(4\dot\theta^2 + \dot\phi^2 + 4\dot\theta\dot\phi\cos(\theta - \phi) \right) - \frac{a^2k}{2}\left( 21 - 16\sin\theta - 8\sin\phi + 4\cos(\theta - \phi) \right) - Mga\sin\theta - mga\left(2\sin\theta + \sin\phi \right)
$... |
Does exist, if it make sense, a formula to describe the energy of a gluon, since its creation to its absorption, like the formula of Planck for the photon $\hbar\nu$?
|
I would like to understand how to calculate the 1-loop self-energy for spinons coupled to a $\rm U(1)$ gauge field. For context, I am going through Nagaosa & Lee's "Gauge theory of the normal state of high-Tc superconductors" and Nave & Lee's "Transport Properties of a spinon Fermi surface coupled to a $\rm U(1)$ gauge... |
A thought crossed my mind that I realized was hard to conceptualize so I decided to simplify the question by putting it in terms of event horizons.
If I am an observer approaching black hole "A", and I track another blackhole "B" in the distance, as I fall toward A's event horizon would blackhole B's event horizon appe... |
A positively charged particle travels horizontally northward and enters a region where a field may exist. This region may contain only a magnetic field, only an electric field, or both a magnetic field and an electric field. When the particle enters the region, the particle does not speed up or slow down, but it does d... |
When you want to describe a Classical gauge theory, you need the following objects :
A (pseudo)-Riemannian manifold $M$ (your spacetime)
A Lie group $G$ describing the local internal symmetry of your theory.
A principal $G$-bundle $P$ over $M$. The gauge field $A_\mu$ will be describe by a connection and the field-str... |
My teacher told me bouncing ball (100% elastic) is oscillatory motion that does not have a stable equilibrium position and restoring force. It is just to and fro motion and thus called oscillatory motion but unlike most other oscillatory motions it does not have mean/stable equilibrium position and restoring force whic... |
I am taking an introductory physics course, and the chapter we are on is about electrostatics.
One section of our textbook has talked about the electric field generated by a charged object that is infinite in one or more dimensions (such as a point in 0 dimensions, a line in 1 dimension, or a plane in 2 dimensions.)
We... |
I've seen mainly two definitions of generalized momenta, $p_k$, and I wasn't sure which one is always true/ the correct one:
$$p_k\equiv\dfrac{\partial\mathcal T}{\partial \dot q_k}\text{ and }p_k\equiv\dfrac{\partial\mathcal L}{\partial \dot q_k}.$$
I've seen mostly written the $2$nd one. Notice that if the potentia... |
Some people requested what was the context of the question and this is where it comes from:
"Given the dispersion relation: $w^2=w_0^2+A^2k^2$ ( $w_0$ and $A$ are constants)
Which frequencies can propagate in the medium provided by the relation (each frequency needs to have a linear λ)
Calculate C and Cg (group velo... |
my questions stemmed from reading the article in Physica E. Vol. 86, 10-16. (https://doi.org/10.1016/j.physe.2016.10.014) Why does the graphene Fermi velocity $v_F$ appear in Eq.(11) in this article,? Eq.(11) is as follows: $$\frac{\partial \Omega_p(z,t)}{\partial z}+\frac{1}{v_F}\frac{\partial \Omega_p(z,t)}{\partial ... |
Hello I am to solve whether it is possible for body of mass $m$ to move around stable circular orbit in potentials: ${V_{1} = \large\frac{-|\kappa|}{r^5}}$ and ${V_{2} = \large\frac{-|\kappa|}{r^{\frac{1}{2}}}}$. I have read about Bertrand's Problem and is it sufficient to check if the parametr $\beta^{2} = 3 + \large\... |
Or is it entirely based on the existence of an event horizon?
Does the fact that black holes radiate depend on any properties of its interior?
|
This simulation has me confused about the conservation of energy. If both blocks have equivalent mass, and the velocity of the COM is equal, then they have translational kinetic energy equal to $K_{translational} =\frac 12(mv^2)$. However, the block on the right also has rotational kinetic energy equal to $K_{rotationa... |
I have read this question (in the comments):
Late response, but the energy really comes from the gravitational field, which exists outside the event horiz0n and in space. This field is what lets us measure the "mass" of the black hole. Loosely speaking, the field, not the mass, "is" the gravity of the black hole. Sinc... |
I'm trying to understand how momentum is conserved when gymnasts twist mid-air while they are doing a flip. In this post, I will refer to the movement of his feet over his head as "rotation", and the movement of his body on its own axis as "twisting". Take this video: when he does his layout (the flip at the end of th... |
Can Raman spectrometets detect Rayleigh scattering?
The sample I have got turned blue after annealing.
And I am wondering if this happened because of Rayleigh scattering. I saw some articles about Rayleigh scattering and it seems like Raman can detect it at 0 cm$^{-1}$ area.
If detecting is possible, how should I chang... |
This is a simple thought experiment that hopefully demonstrates that gas pressure is an invariant in relativity.
Consider two very long sealed rectangular boxes that contain equal gas pressure when at rest in the same reference frame. A flexible hose connects the two boxes. One of the boxes (A) remains at rest and the ... |
What is the simplest experiment that I can perform to see interference of $|HH \rangle + |VV \rangle $, assuming this is an entangled state of two photons in two different polarizations?
Ideally I want an operation that causes the probabilities of measuring HH or VV to oscillate.
|
Let’s say I have two metal sheets in a 2D plane. The first one has area A, the second one is infinitely long, and they are separated from each other by a distance d. How can I find the capacitance between them?
|
As I understand it, a perpetual motion machine does continuous work without additional energy input. If a perpetual motion machine of the second kind exists, it violates the second law of thermodynamics and decreases the entropy of the universe. But how does this violation make it a “perpetual” motion machine?
I’ve see... |
Are they not supposed to be the same operator according to Schrödinger equation?
$$
i\hbar\dfrac{\partial}{\partial t}\psi = H\left(\vec{r},-i\hbar\nabla,t\right)\psi
$$
Apparently $[t,i\hbar\dfrac{\partial}{\partial t}] = i\hbar$, while $[t,H] = 0$
|
I was always told that spacetime in general relativity was a Lorentzian manifold, that is, a Pseudo-Riemannian manifold $ (M, g) $ with metric signature $(+, -, -, -)$ or $(-, +, +, +)$ and that that is all the mathematical detail needed to understand the theory.
But in the theory we use covariant derivatives and Chris... |
As is well-known, number operator $N=a^{\dagger}a$ with the commutation relation $[a,a^{\dagger}]=1$ has non-negative integer eigenvalues. I am looking for a similar expression for an operator ($A(a^{\dagger},a)$) which includes all integers, is there such an operator ? I don't like to impose a naive guess such as $A|... |
This question concerns the first 2 paragraphs of this text.
I am struggling to visualize why molecules on the flat surface experience more net inward force than those on a curved surface. If we have 2 surfaces of water which both have the same number of molecules and one is curved, why does the curved one experience le... |
We know that an accelerated electric charge produces electromagnetic radiation.
We also know that acceleration is relative to an observer.
Take electrically neutral observers A and B, who are accelerating relative to each other. B is at rest with C, a piece of electrically charged matter. This means C is accelerating w... |
Standard motion equations for movement of singular point within absolute space-time, looks like this:
$$
\vec{a} = const.
$$
$$
\vec{v_{T+Δt}} = \vec{v_{T}} + \vec{a} Δt
$$
$$
\vec{p_{T+Δt}} = \vec{p_{T}} + \vec{v_{T}}Δt + \frac{1}{2} \vec{a} Δt^2
$$
It is a system with constant acceleration $\vec{a}$ ($m s^{-2}$).
Sys... |
I am trying to understand momentum is conserved after collision between a point mass and a rotating object. I understand that during a collision between two point mass, momentum is conserved. Also that when a collision occurs with rotating objects (for example when a still cylindre is dropped on a rotating cylindre) an... |
Suppose I have a 2-qubit mixed state given by $\rho$ whose concurrence is $C$. I am interested in finding the optimal pure state decomposition of $\rho=\sum_{i=1}^4 p_i|\psi_i\rangle\langle\psi_i|$ such that $C(\psi_i)=C$. Is there any way to get this decomposition or at least any relationship between $|\psi_1\rangle, ... |
Are there real-world physical systems to which higher dimensional ($d>3$) Ising models correspond?
|
The problem
A ball with radius $R$ slips on a surface with speed $v_{cm}=v_0$, so that the velocity of the center of mass, decreases and the angular velocity $\omega$ increases. The ball starts a pure rolling motion when $v_{cm}=\omega R$.
The question
My question regards the conservation of angular momentum, and the c... |
If we assume the universe is a closed 3-sphere, how big was the universe after inflation, compared to nowadays? Was, relatively, most space already there? If we envision the universe as a 2-sphere, a balloon, how big was the balloon back then compared to its present size, assuming the universe continues at least 500 ti... |
Given a very non-homogenous large object (mainly water) that's vitrified (cooled down without ice formation) and stored in liquid nitrogen, how do you heat it up to room temperature without ice formation?
I have the following physics-related subquestions:
what exactly happens to a vitrified object while warming up? Ho... |
I wonder about Kirchhoff's first law in charged conductors. Consider:
$$j = \sigma E \implies \nabla \cdot j = \sigma (\nabla \cdot E) = \frac{\sigma \rho}{\epsilon_0}$$
This means that Kirchhoff's first law does not hold true if the conductor is charged ($\rho \neq 0)$
But is not that exactly the case with any conduct... |
I am trying to simulate a coupled qubit-resonator system, and want to extract the Purcell decay rate of the qubit. For that, I initialise the qubit in state $\left|1\right>$ and fit the probability of being in state $\left|1\right>$ as function of time.
I am doing the simulation with and without the Rotating Wave Appro... |
Is the direction of kinetic friction always opposite to the direction of velocity of the object? I have found various contradicting statements about this. Which side has it right? The interesting case is when the velocity is in x-direction but the acceleration is (partly) in y-direction.
To clarify what I mean, let's i... |
in the Boyd's book about non-linear optics he defines the non-linear polarization for sum frequency generation, under particular symmetries, as
$$
\left[\begin{array}{c}
P_{x}(2 \omega) \\
P_{y}(2 \omega) \\
P_{z}(2 \omega)
\end{array}\right]=2 \epsilon_{0}\left[\begin{array}{llllll}
d_{11} & d_{12} & d_{13} & d_{14} &... |
I am working on a project for my degree to model a CNOT gate and I'm trying to do this with the Lindblad equation.
$$
\dot{\rho} = -\dfrac{i}{\hbar} [H, \rho] + \sum\limits_i \gamma _i (L_i \rho L _i ^{\dagger} - \dfrac{1}{2} \{ L _i ^{\dagger} L_i , \rho \})
$$
In the case of modelling a single qubit that might underg... |
I've been stuck on this problem for days, but I just don't get it.
I have, as per title, the Continuity and Euler's equation for a fluid in this form:
$$\frac{\partial \rho}{\partial t} + \nabla(\rho v) = 0$$
$$\frac{\partial(\rho v)}{\partial t} + v \cdot \nabla(\rho v) = -\nabla P$$
Where, $\rho$, is the density of t... |
I'm looking for a (fairly) mathematically-rigorous resolution to the following). Suppose an electron is moving through an electric field in some region: $$\Omega \subset \mathbb{R}^d \ ,$$ where $d = 2,3$. We know that the electron - as a charged particle - will experience a force from this field. We also know that the... |
I understand how to work with and describe squeezed single modes going through a beamsplitter, and can conceptually talk about what's happening. If I now take a source of squeezed light that has multiple modes, which are entangled with each other (bipartite/tripartite/etc states), how does this interfere when:
I send ... |
Is it that oscillatory motion must be to-and-fro motion about a mean/stable equilibrium position, or it does not qualify as true oscillatory motion? Or, is it that most of the oscillatory motion has a mean/stable equilibrium position, about which is it does to-and-fro motion, but it is not a must condition/not necessar... |
In the dual slit experiment, we can view the diffraction pattern as the constructive and destructive interference of two waves from the superposition of a single photon. If we analyse the paths through the two slits, we see that two waves emitted at the same time time from the source, only arrive at the screen simultan... |
Let us assume that the quantum system consists of Hilbert space $H$ with basis vectors $|i\rangle$. The initial state $|\Psi(0)\rangle$ evolves in discrete time steps such that $|\Psi(t+\delta t) \rangle = U|\Psi(t)\rangle$.
Furthermore, I assume that each unitary operator is followed by a projective measurement with t... |
From page 21 of "Conformal Field Theory" by Di Francesco, Mathieu, and Sénéchal, the free Fermion Lagrangian is given by:
$$L=\frac{i}{2}\psi_i T_{ij}\dot{\psi}_j-V(\psi)$$
Where the $\psi$ and $\dot{\psi}$ are Grassmann numbers. The antisymmetric part of $T_{ij}$ couples to:
$$\psi_i\dot{\psi}_j-\psi_j\dot{\psi}_i=\ps... |
Working in the mostly + convention, for a timelike geodesic in Minkowski spacetime we have the requirement that (c=1):
$$u^\alpha u_\alpha=-1$$
and that it of course obeys the geodesic equation.
If we consider a stationary observer located at the origin there are two vectors which satisfy such condition, namely
$$u^\al... |
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