Quantum time crystals.

@article{Wilczek2012QuantumTC,
  title={Quantum time crystals.},
  author={Frank Wilczek},
  journal={Physical review letters},
  year={2012},
  volume={109 16},
  pages={
          160401
        }
}
  • F. Wilczek
  • Published 12 February 2012
  • Physics
  • Physical review letters
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. 
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References

SHOWING 1-10 OF 29 REFERENCES
Classical time crystals.
TLDR
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
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.
TLDR
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.
Period doubling, two-color lattices, and the growth of swallowtails in Bose-Einstein condensates
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
EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE
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
Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
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
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
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.
Phys
  • Rev. A 72, 033602
  • 2005
Phys
  • Rev. Lett. 17, 1133
  • 1966
...
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