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T-Symmetry and spatial symmetry of a multivariate conserved quantity

Definition: A reversible system is defined to be any second-order system that is invariant under the map. $t \mapsto -t$ $y \mapsto -y$ Suppose there exists a multivariate function ...
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0answers
32 views

Are $\psi ^{*}(x,t)$ and $\psi(x,-t)$ solutions of the same Schroedinger equation?

I have this question: Let $\psi(x,t)$ solution of the Schroedinger equation for a particle under a potential V(x) independent of time. Are $\psi ^{*}(x,t)$ and $\psi(x,-t)$ solutions of the same ...
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0answers
42 views

Questions regarding reversible processes, entanglement, and time reversal symmetry [closed]

Can we, a priori, state that a physical state is entangled with its environment? Its hard for me to come up with a reason for why we can't. For my next question, consider a physical state: ...
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0answers
51 views

Clarification regarding Eq. (2.6.21) Weinberg Vol. 1

While reading the action of time reversal operator for massless particles, I was going through the derivation for Eq. (2.6.21) from Weinberg Vol. 1 which proceeds as follows $$ \begin{aligned} ...
3
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0answers
26 views

Parity and Time reversal when the number of space or time dimensions is even

There's a side remark in the middle of section 2.6 of Weinberg I that I find a bit unclear. Suppose that $L(p)$ is a boost that carries the four momentum $k^\mu=(0,0,0,M)$ to $p^\mu$, and that ${\bf ...
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1answer
72 views

Re: The $T$-matrix, Feynman amplitudes, and getting the scattering corrections from the interaction Hamiltonian

I'm running in circles about something in Scattering Theory at the moment. Let me summarize. In quantum theories we are interested in finding experimentally measurable quantities such as scattering ...
3
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2answers
89 views

Is QFT time symmetric, and how is it implemented?

In electromagnetism, while the Maxwell equations are time symmetric, there is a choice to restrict solutions specifically to retarded potentials, imposing a time direction on the equations. And in ...
2
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1answer
95 views

Why does time always flow forward?

According to the BBC Earth " Physics says that any event in our day-to-day lives could happen in reverse, at any time".Then why can't we just turn time backwards?
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1answer
80 views

Does time symmetry still holds when a particle drops into a black hole?

When a particle drops into Earth, it hits the ground and rebounds, if time reverse, it is equivalent to another particle moves with same speed but opposite direction. But at the case that a particle ...
2
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2answers
170 views

Why does time-reversal mean negation of time i.e. $t\mapsto -t\;?$

Disclaimer : This is a follow-up to this question. For long time, I've been pondering of this but couldn't come to a stern conclusion to the question: Why is time-reversal the negation of time ...
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1answer
98 views

Time reversal $t\rightarrow -t$: $0,10,20,30,40,50$ to $-50,-40,-30,-20,-10,0$ or $0,-10,-20,-30,-40,-50\;?$

Time reversal symmetry is defined as $$T:t\mapsto-t\;.$$ Suppose, a stroboscopic film of a ll falling from a certain height to the ground is run forward with time-instances given as: ...
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86 views

Superconducting Order Parameter and Time Reversal Symmetry

How to understand the following definition of a time reversal operation $K$ given in the review by Sigrist and Ueda: $$K a_{\mathbf{k},s}^{\dagger} = \sum_{s'} (-i\sigma_y)_{s,s'} a_{-\mathbf{k},s'}$$ ...
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2answers
147 views

Is there really a direction of time?

Laws of physics are (almost) time symmetric, so a time-reversed description of a physical process is as qualified as the original one. What's the reason then, that in reality one version seems to ...
5
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2answers
121 views

Time reversal symmetry of transverse field Ising model

Is the transverse field Ising model time-reversal invariant? Specifically consider a non-integrable variant: \begin{equation} H = -J \sum_i^{L-1} \sigma_i^z \sigma_{i+1}^z + g \sum_i^L \sigma_i^x + h ...
3
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0answers
71 views

Is $PT$ always a symmetry in (2+1)D?

Is the combination of parity $P: (x,y,t)\to (-x,y,t)$ (sometimes also called reflection $R$) and time reversal $T: (x,y,t)\to (x,y,-t)$ always a symmetry in (2+1)D theories with Lorentz or Galilean ...
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0answers
51 views

trying to grasp time reversal invariance

I've recently come across the idea of time reversal invariance, and I think I almost have a handle on it, but it's not quite there. My issue isn't with the apparent paradox of emergent phenomena that ...
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1answer
30 views

How would certain situations hold up in time-reversal symmetry

According to time-reversal symmetry, if I reversed time, the laws of physics would still hold up, so if I dropped a ball to the ground, then in reverse order all of the light and sound and frictional ...
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3answers
78 views

In most physical cases, the elements of a group can be represented by unitary matrices. Why no time-reversal?

In Dresselhaus's group theory page 19, a theorem writes: Every representation (of a Hamitonian's group) with matrices having non-vanishing determinants can be brought into unitary form by an ...
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1answer
51 views

Reversal of time, an absurd concept? [closed]

Consider a specific case of a hourglass. Here, because of gravity sand flows down and reaches the equilibrium state when all the sand is in the lower half. This way we can keep a measure of time. From ...
4
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2answers
121 views

Is black hole formation reversible if physics law holds even in time reverse?

As we know many situations still fulfill physics law if time is reversed, such as particle collision. But how about black hole formation? Suppose a star is turning to a black hole and starts to have ...
5
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1answer
114 views

Superconductivity and time-reversal symmetry

Let us consider a system of a 1D edge of a 2D topological insulator in proximity to an s-wave superconductor. The system is described by the Hamiltonian: $$ H =\frac{1}{2} \int \mathrm{d}x \ ...
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0answers
48 views

time reversal symmetry is broken by magnetic field

In literature, the saying "the time reversal symmetry is broken by the external magnetic field" appears very often. How to understand this statement?
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1answer
139 views

Behavior of the Electric- and Magnetic-field under time reversal and parity

The behavior of the electric- $\mathbf{E}$ and the magnetic-field $\mathbf{B}$ und time reversal and parity can be calculated in different ways. My first solution is to study the transformation ...
3
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1answer
112 views

Is there a bulk signature of topological nontriviality for a 3D free fermion band insulator?

Is there such thing as a 3D Chern invariant (or some other quantity) that I can use to test an insulating quasiparticle spectrum is a topologically trivial or non-trivial insulator? Does one exist ...
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2answers
219 views

Why exactly does the time-reversal operator need to be antilinear?

I checked many books and they all state that time-reversal operator is anti-linear. But why do we need it to be anti-linear? Please explain where this need actually arises.
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0answers
45 views

Does Time-Reversal Violation imply a microscopic Arrow of Time?

I have a questions regarding the relation of time reversal violation and existence of a microscopic direction of time. It seems to me that the following definition for T-symmetry and arrow of time ...
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0answers
41 views

Time-reversal transformation for two-component bosonic models

Consider a two-component bosonic model $\mathcal{H}=-t\sum_{i\sigma}{b_{i\sigma}b_{i+1\sigma}^\dagger}+h.c. +\sum_{i\sigma\sigma^\prime}U_{\sigma\sigma^\prime}n_{i\sigma}n_{i\sigma^\prime}$. Here ...
2
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1answer
189 views

Why does circularly polarized light break time-reversal symmetry?

I've encountered some interesting paper on 2D materials where authors use circularly polarized light to break time-reversal symmetry to split energy levels. Here you can find the paper: ...
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1answer
83 views

Time-reversal procedure for spin

What's the physical reason/explanation for the fact when time is reversed then, in addition to momentum of fermion, spin is also reversed?
1
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1answer
98 views

$Z_2$ invariant and Wannier states switching partner

I have been reading about $Z_2$ topological invariant recently. However, after some literature survey, I still cannot understand $Z_2$ invariant in language of time reversal polarization. Basically, ...
2
votes
1answer
131 views

Why is the position vector invariant under time reversal?

I'm pretty sure I'm misinterpreting something, but my reasoning for why it is not is that when you reverse time, the trajectory in which $x$ follows, namely $x(t)$, changes direction, so that at any ...
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0answers
25 views

Can a macroscopic passive system break the time-reversal symmetry spontaneously?

I know there are many systems can break T-symmetry if the internal source ALREADY chooses a direction of T. Without any driving source inside the system, can T-symmetry be broken spontaneously?
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0answers
43 views

Break time-reversal symmetry in photonic system without using bias magnetic field

In photonic system, e.g, photonic crystals, people usually use ferromagnetic material or so called Tellegen medium which acts as effective field bias to break the time-reversal symmetry. I just want ...
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1answer
50 views

Reversing time for a closed system of particles

For a closed system of particles, the lagrangian in classical mechanics is $$L=\sum \frac{1}{2}mv_a^2 - U(\mathbf{r_1},\mathbf{r_2}, \cdots)$$ For an arbitrary position function $x(t)$, to see the ...
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1answer
144 views

Time reversal symmetry and real symmetric Hamiltonian matrix

In the literature (like those in quantum chaos), it seems that time-reversal symmetry implies that the Hamiltonian of the system is a real symmetric one, instead of just being complex Hermitian. Is ...
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1answer
78 views

Time reversal in quantum mechanics

If the time reverse operator is defined as \begin{equation} \mbox{T}|\psi(t)\rangle=|\psi(-t)\rangle \end{equation} I am now considering time reversed $\hat x$ and $\hat p$ (of course in Heisenberg ...
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4answers
4k views

How would the laws of nature behave if we reversed time?

Suppose a ball falls from a certain height and reaches the ground. Later on, somehow we managed to reverse time. Now on reversing time, will the ball move upward to reach the same point from where it ...
5
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1answer
260 views

What is a d + id superconductor and why does it break time reversal symmetry?

There are a lot of publications dealing with d-wave and d + id superconductivity, but I found no satisfying answer what exactly makes a superconductor d + id and why they break time reversal symmetry. ...
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0answers
56 views

Conservation Laws and time-reversal symmetry [duplicate]

In most dynamics books I've read they refer to conservation laws and their associated symmetries, cf. Noether's theorem. I know that the conservation of momentum is a result of the homogenity of ...
2
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1answer
206 views

How does time reversal symmetry work in topological insulator?

I am doing microelectronic devices with topological insulators. Can some one explain time reversal symmetry in a topological insulator to electrical engineering student like me?
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1answer
385 views

How to show time reversal symmetry does not break in the tight binding Hamiltonian for the honeycomb lattice?

The Hamiltonian of the honeycomb lattice is $$ H=\sum_{k\sigma}t(k) a_{k\sigma}^\dagger b_{k\sigma}+h.c $$ Where $t(-k)=t^*(k)$. If we do a time reversal transformation(according the answer to this ...
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0answers
64 views

Time Reversal Bulk Hamiltonian

This questions is from pages 68 and 69 of: http://fizipedia.bme.hu/images/1/14/Topological_insulators.pdf For a lattice, time reversal invariance of the bulk corresponds to the equation (Eqn 6.11): ...
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1answer
163 views

Is time reversal symmetry broken in (conventional) superconductors?

How can one see it from BCS wavefunction and BCS Hamiltonian? i.e. $$H_{BCS}=\sum_{k\sigma}\epsilon_k c_{k\sigma}^\dagger c_{k\sigma}-\Delta^*\sum_k c_{k\uparrow}^\dagger ...
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1answer
676 views

Meaning of Time Reversal Symmetry

I was wondering if someone could give a simple explanation of what is meant by time reversal invariance. Is it analogous to spatial translational symmetry? If so, how? By spatial translational ...
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1answer
58 views

Parity transformation is proper orthochronous?

In 3+1 dimensional spacetime the parity transformation is $$P^\mu_{\;\,\nu}=\begin{pmatrix}+1&&&\\&-1&&\\&&-1&\\&&&-1\end{pmatrix}.$$ This is ...
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1answer
56 views

Time reversal on superposition: I think [duplicate]

Imagine I have a box, and in it, I have a photon in a superposition of state |1> and |0>. I look into the box and register that the photon is in state |1>. Now, if I have ALL information in the ...
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90 views

$\mathbb{Z}_2$ topological insulators which obey inversion symmetry as well

According to Fu & Kane (2006), systems with simultaneous time-reversal invariance and inversion symmetry have their $\mathbb{Z}_2$ topological invariant given by the product of the parity ...
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0answers
130 views

Compute $Z_2$ Invariant of 2D Topological Insulators without Computing the Eigenstates

For 2D Time-Reversal Invariant systems ($T H(\vec{k}) T^{-1} = H(-\vec{k}) $), there is a formula by Fu-Kane-Mele in order to determine whether the system belongs to either one of distinct topological ...
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2answers
161 views

Simplest example of spontaneous breaking of time reversal symmetry

Consider a two-dimensional fluid flow, confined to a square, where the bottom is held at a higher temperature than the top. With appropriate choices of the parameters, this will form a single ...
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3answers
204 views

Collisions and time-reversal

Shorter version: I am wondering if non-elastic collisions preserve time-symmetery; i.e., given a set of objects with positions and velocities known at a given time, we can calculate forward in time ...