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Questions tagged [time-reversal-symmetry]

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Time reversal invariance of physical laws stated mathematically

There is a logical argument stated in many physics books that laws of physics obey time reversal invariance. A common example that is given is two colliding balls in a snooker game. If we observed ...
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Have researchers managed to “reverse time”? If so, what does that mean for physics?

According to press releases, researchers have reversed time in a quantum computer and violated the second law of thermodynamics. What does that mean for physics? Will it allow time travel? Further ...
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Time Reversal of electric field in Euclidean signature (Wick Rotation)

This is a follow up to this question: How to Perform Wick Rotation in the Lagrangian of a Gauge Theory (like QCD)? I am wondering if their (6), using that $E^i_M = F^{0i}_M = i F^{0i}_E = i E^i_E$, ...
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Real symmetric matrix in Wigner's theorem

A consequence of Wigner's theorem is that if a Hamiltonian matrix obeys time reversal symmetry then it is real-symmetric. It seems to me that for this to make sense then "real symmetric" should be a ...
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Integer quantum Hall conductance and time-reversal symmetry

If we have a (2+1)-dimensional electronic gapped system with a unique ground state and it has a nonzero integer quantum Hall conductance, then the system (or its ground state) must break the time-...
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Action Of Time-Reversal Operator On Spherical Harmonics

Given some spherical harmonic of the form $ \textbf{Y}_l^m = (i)^lY_l^m$ Where $Y_l^m$ is a standard spherical harmonic, I would like to find the action of the time-reversal operator $T$. My attempt ...
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spinless and time reversal symmetry breaking of p-wave pairing in topological superconductors

In the context of Majorana zero modes, I often hear that the p-wave pairing is effectively 'spinless' and time reversal symmetry broken. I understand that s-wave and p-wave refer to the spin portion ...
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General formulation of time reversal symmetry action on fermions

I'm wondering about a general way to define the action of time reversal on a fermion field $\psi$. From a few sources I've read (e.g. appendix A of Witten's paper on fermion path integrals), it seems ...
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Are there any time-periodic solutions to Einstein's equations apart from black holes?

Are there any solutions to Einstein's equations which are periodic in time? A black hole only has mass, charge and angular momentum according to the no-hair theorem. (Although this might just mean in ...
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Time reversal of a QM Hamiltonian

I'm interested in the time reversal properties of a term in the non-relativistic QM Hamiltonian proportional (up to a true scalar) to $$ H \propto (\vec S_1 \times \vec S_2) \cdot \vec L $$ The ...
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Time reversal for fermionic fields

I have some doubts about the way we apply time reversal to Dirac's Lagrangian in QFT. Looking for the transformed field, $\psi^t(x)$, I've found sources (see below) that claims: $$\psi^t(x) = \gamma^...
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What goes wrong, theoretically, when we reverse time?

(Please bear with me if this is a stupid question; I'm not a physicist, just a curious student.) I know that Noether's Theorem links symmetries to conserved quantities: the fact that the laws of ...
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Action of complex conjugation on Hamiltonian

Consider a finite-dimensional non-relativistic QM system with hamiltonian $H$. Let $K$ denote the complex conjugation operator. What does $K H K$ simplify to, if the system is: (a) spin-zero; (b) spin-...
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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 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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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 $[\hat{x},\hat{p}]=i\hbar$ "...