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Questions tagged [time-reversal-symmetry]

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Time reversal in electromagnetism

In classical electrodynamics, we know that under time reversal the electric and magnetic potentials should transform as $$\phi'(x,t)=\phi(x,-t) \qquad A'(x,t)=-A(x,-t) $$ Now, using $(+,-,-,-)$ ...
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Berry connection and time reversal symmetry

I am seeing how the Berry connection $\mathcal{A}(k)$ transforms under time reversal symmetry. I seem to have a hiccup over something simple. I may have overcomplicated things but I think it points to ...
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C and T Symmetry of Free Dirac Lagrangian

I want to show the $C$ and $T$ symmetry of the free Dirac Lagrangian $$\mathcal{L}=\overline{\psi}\left(i\gamma^\mu\partial_\mu-m\right)\psi.$$ Following the notation of Peskin, Schroeder, we have ...
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Time reversal transformation of the complex scalar field

consider a complex scalar field $\phi$ $$\phi(t,x)=\int\frac{d^3k}{\sqrt{2\omega_k(2\pi)^{3}}} \big(a_ke^{i\vec{k}\cdot\vec{x}-i\omega_kt} +b^\dagger_ke^{-i\vec{k}\cdot\vec{x}+i\omega_kt}\big)$$ By ...
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Is time reversal symmetry true on the microscopic level?

I often hear that on the microscopic level, time-reversal symmetry is true for all physical processes. However, I can easily come up with counterexamples that seem to disprove this: Two particles of ...
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Interpretation of time reversal

It is known that for time reversal operation $T$, $T|\vec r\rangle=|\vec r\rangle$ and $T|\vec p\rangle=|\vec -p\rangle$. Considering $\langle T \vec r|T\vec p \rangle$. $\langle T \vec r|T\vec p \...
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Time-reversal invariance and resonances

I'm having problems understanding the relevance of time-reversal symmetry for scattering amplitudes when we have resonant states. Although my question is essentially conceptual, it was raised by an ...
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Are the thermoelectric effects reversible?

On the one hand, it is commonly said that thermoelectric effects are reversible. For Wikipedia they are thermodynamically reversible because as the factor of merit ZT approaches infinity, the ...
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Is there such a thing as an anti-boson?

Can there be an anti-boson that when interacting with normal bosons, creates matter, like when anti-matter creates energy when interacting with matter? I know that anti-particles can be considered ...
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Recipe to determine symmetries of quadratic fermionic Hamiltonian in second quantisation

Consider an arbitrary 1D chain (of length $N$) of fermions with an arbitrary quadratic Hamiltonian of the form $$\mathcal{H}=\hat{\Psi}^\dagger H \hat{\Psi}$$ with $$\hat{\Psi}=\left(a_1, a_2, ...,...
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Is the violation of time-reversal always associated with the violation of time-translation and vice-versa?

Is the violation of time-reversal symmetry always associated with the violation of time-translation symmetry? What about the converse? Is it possible for one to be violated while the other remaining ...
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Why is time-reversal represented by an antilinear and antiunitary operator? [duplicate]

Operators related to physical transformations in quantum mechanics are usually unitary and linear except time-reversal which is both antiunitary and antilinear. What is the explanation for this ...
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Reversibility in newtonian mechanics

It will be slightly different from related questions. When we write newton's differential equation $$\ddot{x}=\frac{d^2x}{dt^2}=m\,a$$ we see that reversing time doesn't change the force, but it ...
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How to prove time reversal symmetry in a system (given a hamiltonian)

The generic hamiltonian for a particle that interacts with an electromagnetic field can be written as: $$H=\frac{1}{2M}\sum_{i}\left(P_i-\frac{q}{c}A_{i}(X_j)\right)^2+V(X_j)+q\phi (X_j)$$ Where $(\...
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What is the physical significance/importance of anti-unitary operators?

Time-reversal symmetry is an anti-unitary operator. I understand the mathematical definition of this, but what are the implications? What should/would one expect from anti-unitary operators? Are ...
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Van Vleck cancellation and Kramer's degeneracy

In the second page of the paper here, under equation 3, it claims that $(\hat{H_1})^{\uparrow \downarrow}_{nk} = -(\hat{H_1})^{\downarrow \uparrow}_{kn}$, which they call 'Van Vleck cancellation (...
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Are broken time reversal symmetry and inversion symmetry forbidden in a Weyl semimetal?

In much of the literature floating around, it is commonly implied that an important part of obtaining a Weyl semimetal phase is to break either time reversal symmetry or inversion symmetry. However, ...
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Relation between topological insulators and breaking of time reversal symmetry

Whenever one talks about topological insulators, the breaking of time reversal symmetry is always mentioned. Is there an intuitive reason as to why one need time reversal symmetry to be broken in ...
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What does the time reversal of stimulated emission look like?

The lay-person level explanation that we give for stimulated emission goes something like this: because photons are Bosons, they "like" to be in the same state, therefore when a photon is passing by ...
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Time reversal symmetry breaking in tight binding models

What are the ways to break time-inversion symmetry of the model (in particular I am interested in how to do that in some tight binding model for fermions with spin). For sure one can break it with ...
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Time reversal of Bloch Hamiltonian (at TRIM points)

I know that time-reversal symmetry requires the Bloch Hamiltonian $H(\textbf{k})$ to transform as: $$ \Theta H(\textbf{k}) \Theta^{-1}=H(-\textbf{k}) $$ where $\Theta$ is the time-reversal operator. ...
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Photon time dilation paradox

When traveling at the speed of light (v=c), left under the radical you would have 0. This answer would be undefined or infinity if you will (let's go with infinity). The reference time (T0) divided by ...
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Causal explanation of Vaidman's group “Asking photons where they have been” experiment?

There is this surprising "Asking photons where they have been" PRL 2013 article about experiment where they are able to "ask photons" which mirrors they have visited: by vibrating each mirror with ...
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Time-reversal of a black hole merger

General relativity is time reversal invariant. There are solutions though which are physically not reasonable. An example are white holes which are a valid solution of Einstein‘s field equations, but ...
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Is the QFT vacuum T-invariant?

A quantum vacuum corresponds to closed loops of particle-antiparticle pairs, in the language of Feynman diagrams. There is no relation between $E$ and $p$ for these particles, i.e., they are not on ...
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Time reversal symmetry for Zeeman fields

For a magnetic field along $\hat{x}$ the hamiltonian is given by: $H_{z}=V_x(c^{\dagger}_{\uparrow}c_{\downarrow}+c^{\dagger}_{\downarrow}c_{\uparrow})$. If we follow the usual prescription of ...
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Is the Schrödinger-Newton equation time-reversal symmetric? What about PT-symmetry or similar symmetries?

I tried to figure it out myself. If you take the integro-differential form of the equation, a complex square of the time-dependent wavefunction appears.. It seems to me that this means the equation ...
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In a spinless system with time reversal symmetry, is $E_n(k)=E_n(-k)$ always true?

I am studying TR-symmetry from: "Group Theory" by Dresselhaus, Dresselhaus and Jorio and there's a point that I cannot quite understand. The point is under eq. (16.17). In general, we know that the ...
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Berry curvature and time reversal symmetry

When the time reversal operator, $\hat{\Theta}$ acts on a phase, $e^{i\phi}$ it gives $e^{-i\phi}$. Since the Berry phase factor is $e^{i\gamma}$, where $\gamma$ is the Berry phase, if the Berry ...
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Time-reversal operator in Phase Space Representation

Consider the simplest possible case in which the time reversal operator $\hat{\mathrm{T}}$ is given by the operation of complex conjugation $\hat{\mathrm{K}}$. We can view $\mathrm{T}$ is an anti-...
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If $x(t)$ be a known trajectory does the $x(-t)$ represent the retracing trajectory?

Assertion If there is time-reversal invariance, Newton's law (for a system described by one generalized coordinate $q$) $$m\frac{d^2}{dt^2}q(t)=F\Big(q(t)\Big)\tag{a}$$ implies that if $q(t)$ is a ...
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Optical physics and principle of reversibility [duplicate]

I know that if a ray is incident at the medium boundary at critical angle, the ray after refraction moves towards the medium boundary. So, is it possible that if a ray is passed through the medium ...
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Experimentally, how much field do you need to break topological surface state

For topological insulator, one has topological surface conduction channel which is protected by time reversal symmetry right? Imagine we have Bi2Se3 or SmB6 that has topological surface state(TSS). ...
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Does this experimental confirmation of thermodynamic irreversibility at the quantum level mean that information can be created/destroyed over time?

According to this article, https://phys.org/news/2015-12-physicists-thermodynamic-irreversibility-quantum.html, physicists recently confirmed thermodynamic irreversibility at the quantum level. Does ...
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Is the speed of a pendulum symmetric? [closed]

Suppose a pendulum moves with simple harmonic motion and there is some point P which it passes: will the time to go from O to P be equal to the time taken to go from P to O when it is coming back from ...
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PT-symmetry in Energy Band of Crystals

According to this source, it is proved that, in absence of spin-orbit coupling, spatial inversion symmetry (as a part of point-group symmetry which operates as $\hat{S}\psi(\vec{r})=\psi(-\vec{r})$) ...
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Difference in symmetries of Second quantized and First quantized Hamiltonian [duplicate]

The following is stated in (among others) the articles Topological insulators and superconductors: ten-fold way and dimensional hierarchy - Shinsei Ryu, Andreas Schnyder, Akira Furusaki, Andreas ...
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Clarifying PT symmetry

I understand that if a Hamiltonian remains invariant under the following transformations then it is PT invariant, \begin{eqnarray} \mathrm{Parity \; reversal:} \; \; \hat{p} \to -\hat{p} \; \; \...
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Why goes $i\rightarrow-i$ under $\mathcal{PT}$-transformation?

Question in the title. What I understand is that under $\mathcal{PT}$ reversal $\hat{p}\rightarrow\hat{p}$ and $\hat{x}\rightarrow-\hat{x}$ and then since the commutation $[\hat{x},\hat{p}]=i\hbar$ "...
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If the equation of motion is not invariant under time reversal, is the Lagrangian not either?

Suppose the Euler-Lagrange equation of a system $$\frac{\partial L}{\partial q}=\frac{d}{dt}\Bigg(\frac{\partial L}{\partial \dot{q}}\Bigg)$$ is known to be not invariant under the discrete ...
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Time Reversal Operator in Sakurai's Book

In Sakurai's Modern Quantum Mechanics, Eq(4.16) says that $$\begin{align} |\alpha\rangle &= \sum_{a^\prime}|a^{\prime}\rangle\langle a^{\prime}|\alpha\rangle \overset{K}{\rightarrow} |\tilde{\...
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Does reversing time give parity reversed antimatter or just antimatter?

Feynman's idea states that matter going backwards in time seems like antimatter. But, since nature is $CPT$ symmetric, reversing time ($T$) is equivalent to $CP$ operation. So, reversing time gives ...
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Propagator for scattering running backward in time

I came across this difficulty while working through Sakurai's Modern Quantum Mechanics on my own. (For those familiar with Sakurai's approach, skip to the blockquote and surrounding paragraphs.) The ...
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What is invariance of an equation?

I'm confused. Suppose we have a Schrodinger equation with a time-independent Hamiltonian: \begin{align} i\frac{\partial}{\partial t}\psi(x, t) = H\psi(x, t). \tag{1} \end{align} Under time reversal ...
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Experimental proof of time-reversibility in microscopic classical physical laws [duplicate]

All the laws of classical mechanics are time-reversible. But the experiments that we carry out on systems, mostly measure macroscopic parameters which are time-irreversible. We know for a reason that ...
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Why is the proton anti-proton annihilation and pair production asymmetric?

This is a follow up question to this question. The process of annihilation is very well explained. However while the annihilation is a step-by-step process the pair production does not seem to follow ...
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Topological insulators with time-reversal symmetry: How to derive Z2 invariant from the zeros of $<u_i(k)|T|u_j(k)>$?

Following the book ''Topological Insulators and Topological Superconductors'' by B. Bernevig (esp. chapter 10.1), I want to understand how to derive a Z2 invariant starting from the zeros of the off-...
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Schrödinger's equation - Time reversal

While reading a book about interactions I've come to this paragraph: https://gyazo.com/8c45d9f005558394d42d317fe88a8b5d How exactly did we get the minus on the right hand side? The way I think it ...
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What are the implications that the Hamiltonian of a material lacks time reversal symmetry?

When reading about topological insulators and the quantum Hall effect, I've read that some Hamiltonians of the crystal structure representing the "materials" lack time reversal symmetry. My question ...
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Is there a precise definition for a “parity”, “time-reversal” or “chiral” symmetry in general quantum spin systems?

By "quantum spin system" I mean a physical system with qu-$d$-its (called "spins", for possibly different $d$) distributed somehow over space and a Hamiltonian that is a sum of arbitrary local ...