### Abstract

We consider a quantum gas of noninteracting particles confined in the expanding cavity and investigate the nature of the nonadiabatic force which is generated from the gas and acts on the cavity wall. First, with use of the time-dependent canonical transformation, which transforms the expanding cavity to the nonexpanding one, we can define the force operator. Second, applying the perturbative theory, which works when the cavity wall begins to move at time origin, we find that the nonadiabatic force is quadratic in the wall velocity and thereby does not break the time-reversal symmetry, in contrast with general belief. Finally, using an assembly of the transitionless quantum states, we obtain the nonadiabatic force exactly. The exact result justifies the validity of both the definition of the force operator and the issue of the perturbative theory. The mysterious mechanism of nonadiabatic transition with the use of transitionless quantum states is also explained. The study is done for both cases of the hard- and soft-wall confinement with the time-dependent confining length.

Original language | English |
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Article number | 041133 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 83 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2011 Apr 28 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*83*(4), [041133]. https://doi.org/10.1103/PhysRevE.83.041133

**Ideal quantum gas in an expanding cavity : Nature of nonadiabatic force.** / Nakamura, K.; Avazbaev, S. K.; Sobirov, Z. A.; Matrasulov, D. U.; Monnai, T.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 83, no. 4, 041133. https://doi.org/10.1103/PhysRevE.83.041133

}

TY - JOUR

T1 - Ideal quantum gas in an expanding cavity

T2 - Nature of nonadiabatic force

AU - Nakamura, K.

AU - Avazbaev, S. K.

AU - Sobirov, Z. A.

AU - Matrasulov, D. U.

AU - Monnai, T.

PY - 2011/4/28

Y1 - 2011/4/28

N2 - We consider a quantum gas of noninteracting particles confined in the expanding cavity and investigate the nature of the nonadiabatic force which is generated from the gas and acts on the cavity wall. First, with use of the time-dependent canonical transformation, which transforms the expanding cavity to the nonexpanding one, we can define the force operator. Second, applying the perturbative theory, which works when the cavity wall begins to move at time origin, we find that the nonadiabatic force is quadratic in the wall velocity and thereby does not break the time-reversal symmetry, in contrast with general belief. Finally, using an assembly of the transitionless quantum states, we obtain the nonadiabatic force exactly. The exact result justifies the validity of both the definition of the force operator and the issue of the perturbative theory. The mysterious mechanism of nonadiabatic transition with the use of transitionless quantum states is also explained. The study is done for both cases of the hard- and soft-wall confinement with the time-dependent confining length.

AB - We consider a quantum gas of noninteracting particles confined in the expanding cavity and investigate the nature of the nonadiabatic force which is generated from the gas and acts on the cavity wall. First, with use of the time-dependent canonical transformation, which transforms the expanding cavity to the nonexpanding one, we can define the force operator. Second, applying the perturbative theory, which works when the cavity wall begins to move at time origin, we find that the nonadiabatic force is quadratic in the wall velocity and thereby does not break the time-reversal symmetry, in contrast with general belief. Finally, using an assembly of the transitionless quantum states, we obtain the nonadiabatic force exactly. The exact result justifies the validity of both the definition of the force operator and the issue of the perturbative theory. The mysterious mechanism of nonadiabatic transition with the use of transitionless quantum states is also explained. The study is done for both cases of the hard- and soft-wall confinement with the time-dependent confining length.

UR - http://www.scopus.com/inward/record.url?scp=79961091487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79961091487&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.83.041133

DO - 10.1103/PhysRevE.83.041133

M3 - Article

AN - SCOPUS:79961091487

VL - 83

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 4

M1 - 041133

ER -