# Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons

## Abstract

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)].

- Authors:

- Physics Department, University of California, Davis, California 95616 (United States)
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089 (United States)
- (United States)
- School of Chemistry, Tel Aviv University, Tel Aviv 69978 (Israel)

- Publication Date:

- OSTI Identifier:
- 20955408

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevLett.98.050405; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSONS; EQUILIBRIUM; EXCITED STATES; HARMONIC POTENTIAL; INTEGRAL CALCULUS; MANY-BODY PROBLEM; ONE-DIMENSIONAL CALCULATIONS; RELAXATION

### Citation Formats

```
Rigol, Marcos, Dunjko, Vanja, Olshanii, Maxim, Institute for Theoretical Atomic and Molecular Physics, Cambridge, Massachusetts 02138, and Yurovsky, Vladimir.
```*Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVLETT.98.050405.

```
Rigol, Marcos, Dunjko, Vanja, Olshanii, Maxim, Institute for Theoretical Atomic and Molecular Physics, Cambridge, Massachusetts 02138, & Yurovsky, Vladimir.
```*Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons*. United States. doi:10.1103/PHYSREVLETT.98.050405.

```
Rigol, Marcos, Dunjko, Vanja, Olshanii, Maxim, Institute for Theoretical Atomic and Molecular Physics, Cambridge, Massachusetts 02138, and Yurovsky, Vladimir. Fri .
"Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons". United States.
doi:10.1103/PHYSREVLETT.98.050405.
```

```
@article{osti_20955408,
```

title = {Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons},

author = {Rigol, Marcos and Dunjko, Vanja and Olshanii, Maxim and Institute for Theoretical Atomic and Molecular Physics, Cambridge, Massachusetts 02138 and Yurovsky, Vladimir},

abstractNote = {In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)].},

doi = {10.1103/PHYSREVLETT.98.050405},

journal = {Physical Review Letters},

number = 5,

volume = 98,

place = {United States},

year = {Fri Feb 02 00:00:00 EST 2007},

month = {Fri Feb 02 00:00:00 EST 2007}

}