# Superfluidity and space-time translation symmetry breaking.

@article{Wilczek2013SuperfluidityAS, title={Superfluidity and space-time translation symmetry breaking.}, author={Frank Wilczek}, journal={Physical review letters}, year={2013}, volume={111 25}, pages={ 250402 } }

I present a simple model that exhibits a temporal analogue of superconducting crystalline (Larkin-Ovchinnikov-Ferrell-Fulde) ordering, with a time-dependent order parameter. I sketch designs for minimally dissipative ac circuits, all based on time translation symmetry (τ) invariant dynamics, exploiting weak links (Josephson effects). These systems violate τ spontaneously. I also discuss effective theories of that phenomenon, and space-time generalizations.

## 61 Citations

### Higgs time crystal in a high- Tc superconductor

- PhysicsPhysical Review Research
- 2020

We propose to induce a time crystalline state in a high-$T_c$ superconductor, by optically driving a sum resonance of the Higgs mode and a Josephson plasma mode. The generic cubic process that…

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

- PhysicsPhysical Review B
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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…

### 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…

### Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems.

- PhysicsPhysical review letters
- 2019

A semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role.

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

- PhysicsPhysical 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…

### Quantum Time Crystals from Hamiltonians with Long-Range Interactions.

- PhysicsPhysical review letters
- 2019

This study proposes a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous TTS, based on a spin-1/2 many-body Hamiltonian which has long-range multispin interactions in the form of spin strings, thus bypassing previously known no-go theorems.

### Absence of Quantum Time Crystals.

- PhysicsPhysical 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.

### Thermodynamic quantum time-space crystal and pseudogap state in superconducting cuprates

- Physics
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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…

### Clean Floquet Time Crystals: Models and Realizations in Cold Atoms.

- PhysicsPhysical review letters
- 2018

It is pointed out that time crystals can generally exist in systems without disorder, and a series of clean quasi-one-dimensional models under Floquet driving are proposed to demonstrate this unexpected result in principle.

### Ju l 2 01 9 Continuous time crystals from static Hamiltonians with long-range interactions

- Physics
- 2019

Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where external drive allows to break…

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