# Quantum time crystals.

@article{Wilczek2012QuantumTC, title={Quantum time crystals.}, author={Frank Wilczek}, journal={Physical review letters}, year={2012}, volume={109 16}, pages={ 160401 } }

Some subtleties and apparent difficulties associated with the notion of spontaneous breaking of time-translation symmetry in quantum mechanics are identified and resolved. A model exhibiting that phenomenon is displayed. The possibility and significance of breaking of imaginary time-translation symmetry is discussed.

## 447 Citations

### Quantum physics: Time crystals

- Physics, EducationNature
- 2013

Physicists have come up with the mind-boggling concept of a time crystal based on the notion of broken time-translation symmetry, which might open up a whole new field of research.

### Existence of quantum time crystals

- Physics
- 2016

The existence of quantum time crystals is investigated and shown to be possible in pure phases defined by a state invariant under a group of space translations, as displayed by explicit examples.

### Equilibration and order in quantum Floquet matter

- Physics
- 2017

Over the past decade, remarkable progress has occurred in the physics of closed quantum systems away from equilibrium, culminating in the recent experimental realization of so-called time crystals.…

### Imaginary Time Crystal of Thermal Quantum Matter

- PhysicsChinese Physics Letters
- 2020

Spontaneous symmetry breaking is responsible for rich quantum phenomena from crystalline structures to superconductivity. This concept was boldly extended to the breaking of time translation, opening…

### Condensed-matter physics: Marching to a different quantum beat

- PhysicsNature
- 2017

Two experiments have found evidence for a Floquet time crystal, which is characterized by persistent in‐phase oscillations, and this work aims to characterize this crystal as aperiodic oscillator.

### Boundary Time Crystals.

- PhysicsPhysical review letters
- 2018

This work introduces boundary time crystals and analyzes in detail a solvable model where an accurate scaling analysis can be performed.

### Dynamical nonlocality in quantum time via modular operators

- Physics, MathematicsPhysical Review A
- 2022

We formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular…

### Nonlocality in quantum time via modular operators

- Physics, Mathematics
- 2021

The concept of the modular energy operator is formalized within the Page and Wooters timeless framework and is elevated to the same status as the more studied modular operators of position and momentum.

### The role of quantum recurrence in superconductivity, carbon nanotubes and related gauge symmetry breaking

- Physics
- 2014

Pure quantum phenomena are characterized by intrinsic recurrences in space and time. We use this intrinsic periodicity as a quantization condition to derive a heuristic description of the essential…

## References

SHOWING 1-10 OF 29 REFERENCES

### Classical time crystals.

- PhysicsPhysical review letters
- 2012

This work considers the possibility that classical dynamical systems display motion in their lowest-energy state, forming a time analogue of crystalline spatial order, and exhibits models of that kind, including a model with traveling density waves.

### Principles of condensed matter physics

- Physics
- 1995

Preface 1. Overview 2. Structure and scattering 3. Thermodynamics and statistical mechanics 4. Mean-field theory 5. Field theories, critical phenomena, and the renormalization group 6. Generalized…

### Quantum mechanics for multivalued Hamiltonians.

- MathematicsPhysical review. A, General physics
- 1987

It is shown that the path integral automatically picks up a unique combination of the branch Hamiltonians, which is a natural generalization of the Brouwer degree of the Legendre map.

### Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

- Physics
- 1996

We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition.…

### EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE

- Physics
- 1963

A gas of one-dimensional Bose particles interacting via a repulsive delta-function potential has been solved exactly. All the eigenfunctions can be found explicitly and the energies are given by the…

### Period doubling, two-color lattices, and the growth of swallowtails in Bose-Einstein condensates

- Physics
- 2005

The band structure of a Bose-Einstein condensate is studied for lattice traps of sinusoidal, Jacobi elliptic, and Kronig-Penney form, all in the context of the nonlinear Schroedinger equation. It is…

### following Letter

- Phys. Rev. Lett., 109, 160402
- 2012

### Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models

- Physics
- 1966

It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-S Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor…

### Phys

- Rev. A 72, 033602
- 2005

### Phys

- Rev. Lett. 17, 1133
- 1966