### Abstract

The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one-dimensional potential well that is divided into two halves by a thin separating wall. The two half wells are populated by the same type and number of particles and are kept at the same temperature. The only difference is in the boundary condition imposed at the two sides of the separating wall, which is the Dirichlet condition from the left and the Neumann condition from the right. The resulting different energy spectra cause a difference in the quantum statistically emerging pressure on the two sides. The net force acting on the separating wall proves to be nonzero at any temperature and, after a weak decrease in the low-temperature domain, to increase and diverge with a square-root-of-temperature asymptotics for high temperatures. These observations hold for both bosonic and fermionic type particles, but with quantitative differences. We work out several analytic approximations to explain these differences and the various aspects of the found unexpectedly complex picture.

Original language | English |
---|---|

Pages (from-to) | 4585-4608 |

Number of pages | 24 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 40 |

Issue number | 17 |

DOIs | |

Publication status | Published - Apr 27 2007 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*40*(17), 4585-4608. https://doi.org/10.1088/1751-8113/40/17/013

**Boundary effect of a partition in a quantum well.** / Fülöp, T.; Tsutsui, I.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 40, no. 17, pp. 4585-4608. https://doi.org/10.1088/1751-8113/40/17/013

}

TY - JOUR

T1 - Boundary effect of a partition in a quantum well

AU - Fülöp, T.

AU - Tsutsui, I.

PY - 2007/4/27

Y1 - 2007/4/27

N2 - The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one-dimensional potential well that is divided into two halves by a thin separating wall. The two half wells are populated by the same type and number of particles and are kept at the same temperature. The only difference is in the boundary condition imposed at the two sides of the separating wall, which is the Dirichlet condition from the left and the Neumann condition from the right. The resulting different energy spectra cause a difference in the quantum statistically emerging pressure on the two sides. The net force acting on the separating wall proves to be nonzero at any temperature and, after a weak decrease in the low-temperature domain, to increase and diverge with a square-root-of-temperature asymptotics for high temperatures. These observations hold for both bosonic and fermionic type particles, but with quantitative differences. We work out several analytic approximations to explain these differences and the various aspects of the found unexpectedly complex picture.

AB - The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one-dimensional potential well that is divided into two halves by a thin separating wall. The two half wells are populated by the same type and number of particles and are kept at the same temperature. The only difference is in the boundary condition imposed at the two sides of the separating wall, which is the Dirichlet condition from the left and the Neumann condition from the right. The resulting different energy spectra cause a difference in the quantum statistically emerging pressure on the two sides. The net force acting on the separating wall proves to be nonzero at any temperature and, after a weak decrease in the low-temperature domain, to increase and diverge with a square-root-of-temperature asymptotics for high temperatures. These observations hold for both bosonic and fermionic type particles, but with quantitative differences. We work out several analytic approximations to explain these differences and the various aspects of the found unexpectedly complex picture.

UR - http://www.scopus.com/inward/record.url?scp=70649110808&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70649110808&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/40/17/013

DO - 10.1088/1751-8113/40/17/013

M3 - Article

VL - 40

SP - 4585

EP - 4608

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 17

ER -