Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical lattices

Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical lattices Within the emergent eigenstate solution to quantum dynamics [Phys. Rev. X 7, 021012 (2017)2160-330810.1103/PhysRevX.7.021012], one can construct a local operator (an emergent Hamiltonian) of which the time-evolving state is an eigenstate. Here we show that such a solution exists for the expansion dynamics of Tonks-Girardeau gases in optical lattices after turning off power-law (e.g., harmonic or quartic) confining potentials, which are geometric quenches that do not involve the boost operator. For systems that are initially in the ground state and undergo dynamical fermionization during the expansion, we show that they remain in the ground state of the emergent local Hamiltonian at all times. On the other hand, for systems at nonzero initial temperatures, the expansion dynamics can be described constructing a Gibbs ensemble for the emergent local Hamiltonian (an emergent Gibbs ensemble). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical lattices

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Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical lattices

Abstract

Within the emergent eigenstate solution to quantum dynamics [Phys. Rev. X 7, 021012 (2017)2160-330810.1103/PhysRevX.7.021012], one can construct a local operator (an emergent Hamiltonian) of which the time-evolving state is an eigenstate. Here we show that such a solution exists for the expansion dynamics of Tonks-Girardeau gases in optical lattices after turning off power-law (e.g., harmonic or quartic) confining potentials, which are geometric quenches that do not involve the boost operator. For systems that are initially in the ground state and undergo dynamical fermionization during the expansion, we show that they remain in the ground state of the emergent local Hamiltonian at all times. On the other hand, for systems at nonzero initial temperatures, the expansion dynamics can be described constructing a Gibbs ensemble for the emergent local Hamiltonian (an emergent Gibbs ensemble).
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.013608
Publisher site
See Article on Publisher Site

Abstract

Within the emergent eigenstate solution to quantum dynamics [Phys. Rev. X 7, 021012 (2017)2160-330810.1103/PhysRevX.7.021012], one can construct a local operator (an emergent Hamiltonian) of which the time-evolving state is an eigenstate. Here we show that such a solution exists for the expansion dynamics of Tonks-Girardeau gases in optical lattices after turning off power-law (e.g., harmonic or quartic) confining potentials, which are geometric quenches that do not involve the boost operator. For systems that are initially in the ground state and undergo dynamical fermionization during the expansion, we show that they remain in the ground state of the emergent local Hamiltonian at all times. On the other hand, for systems at nonzero initial temperatures, the expansion dynamics can be described constructing a Gibbs ensemble for the emergent local Hamiltonian (an emergent Gibbs ensemble).

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jul 6, 2017

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