# On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order

@article{Volovik2013OnTB, title={On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order}, author={Grigory E. Volovik}, journal={JETP Letters}, year={2013}, volume={98}, pages={491-495} }

The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the breaking of the time translation symmetry is observable only if the charge Q is not strictly conserved and may decay. This dichotomy is resolved in systems with quasi-ODLRO. These systems have two well separated relaxation times: the relaxation time τQ of…

## Figures from this paper

## 22 Citations

Mean-field thermodynamic quantum time-space crystal: Spontaneous breaking of time-translation symmetry in a macroscopic fermion system

- Physics
- 2019

A model demonstrating existence of a thermodynamically stable quantum time-space crystal has been proposed and studied. This state is characterized by an order parameter periodic in both real and…

Pre-thermal phases of matter protected by time-translation symmetry

- Physics, Mathematics
- 2016

In a periodically driven (Floquet) system, there is the possibility for new phases of matter, not present in stationary systems, protected by discrete time-translation symmetry. This includes…

Classical discrete time crystals

- Physics
- 2018

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective…

Quantum many-body scars from magnon condensation

- Physics
- 2019

We study the eigenstate properties of a nonintegrable spin chain that was recently realized experimentally in a Rydberg-atom quantum simulator. In the experiment, long-lived coherent many-body…

Observation of a Time Quasicrystal and Its Transition to a Superfluid Time Crystal.

- Physics, MedicinePhysical review letters
- 2018

We report experimental realization of a quantum time quasicrystal and its transformation to a quantum time crystal. We study Bose-Einstein condensation of magnons, associated with coherent spin…

Effective Minkowski-to-Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar 3He

- Physics
- 2017

We discuss the effective metric experienced by the Nambu–Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode…

Spontaneous Symmetry Breaking in Nonrelativistic Systems

- Physics
- 2015

The subject of condensed matter physics is very rich — there are an infinite number of parameters producing a diversity of exciting phenomena. As a theorist, my goal is to distill general principles…

Isolated Heisenberg magnet as a quantum time crystal

- Physics
- 2020

Local observables of closed many-body quantum systems are generally believed to quickly equilibrate after a quench, according to the eigenstate thermalization hypothesis. Here, the authors show that…

Absence of Quantum Time Crystals.

- Physics, MedicinePhysical review letters
- 2015

A no-go theorem is proved that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.

Floquet time crystals in clock models

- PhysicsPhysical Review B
- 2019

We construct a class of period-$n$-tupling discrete time crystals based on $\mathbb{Z}_n$ clock variables, for all the integers $n$. We consider two classes of systems where this phenomenology…

## References

SHOWING 1-10 OF 21 REFERENCES

Self-trapping of magnon Bose-Einstein condensates in the ground state and on excited levels: from harmonic to box confinement.

- Physics, MedicinePhysical review letters
- 2012

This is the first experimental example of Bose condensation in a box and the orbital texture reorients under the influence of the spin-orbit interaction and the profile of the trap gradually changes from harmonic to a square well, with walls almost impenetrable to magnons.

Superfluidity and space-time translation symmetry breaking.

- Medicine, PhysicsPhysical review letters
- 2013

A simple model is presented that exhibits a temporal analogue of superconducting crystalline ordering, with a time-dependent order parameter, based on time translation symmetry (τ) invariant dynamics, exploiting weak links (Josephson effects).

A theoretical description of the new phases of liquid He-3

- Physics
- 1975

This paper reviews the theory of anisotropic superfluid phases and its application to the new A and B phases of liquid $^{3}\mathrm{He}$. It is tutorial in nature and advanced formal techniques are…

Spin Superfluidity and Magnon BEC

- Physics
- 2010

The superfluid current of spins – spin supercurrent – is one more representative of superfluid currents, such as the superfluid current of mass and atoms in superfluid 4 He; superfluid current of…

The role of the Josephson-Anderson equation in superfluid helium

- Physics
- 1998

This article explains how a simple equation describing the time evolution of a superfluid’s quantum phase can be used as a powerful tool to rapidly deduce exact magnitudes of physical observables in…

Precession of a single vortex line in superfluid 3He-B.

- Physics, MedicinePhysical review letters
- 1992

The discovery of a new vortex phenomenon in superfluid {sup 3}He-{ital B}.

Dynamic vacuum variable and equilibrium approach in cosmology

- Physics
- 2008

A modified-gravity theory is considered with a four-form field strength F, a variable gravitational coupling parameter G(F), and a standard matter action. This theory provides a concrete realization…

Dynamically broken Lorentz invariance from the Higgs sector

- Physics
- 2012

The original Abelian U(1) Higgs model in flat spacetime is enlarged by the addition of one real scalar with a particular potential. It is then shown that, while maintaining the original masses of the…

Superfluid vortex front at T→0: decoupling from the reference frame.

- Physics, MedicinePhysical review letters
- 2011

The first measurements on the thermal signal from dissipation as a function of time, recorded at 0.2T(c) during the front motion, are presented, first evidence for the decoupling of the superfluid from the container reference frame in the zero-temperature limit.

Impossibility of spontaneously rotating time crystals: a no-go theorem.

- Physics, MedicinePhysical review letters
- 2013

A "no-go theorem" is proved, rigorously ruling out the possibility of spontaneous ground-state rotation for a broad class of systems.