### Abstract

Boundary effects in quantum mechanics are examined by considering a partition wall inserted at the centre of a harmonic oscillator system. We put an equal number of particles on both sides of the impenetrable wall keeping the system under finite temperatures. When the wall admits distinct boundary conditions on the two sides, then a net force is induced on the wall. We study the temperature behaviour of the induced force both analytically and numerically under the combination of the Dirichlet and the Neumann conditions, and determine its scaling property for two statistical cases of the particles: fermions and bosons. We find that the force has a nonvanishing limit at zero temperature T = 0 and exhibits scalings characteristic to the statistics of the particles. We also see that for higher temperatures the force decreases according to 1/T , in sharp contrast to the case of the infinite potential well where it diverges according to T. The results suggest that, if such a nontrivial partition wall can be realized, it may be used as a probe to examine the profile of the potentials and the statistics of the particles involved.

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

Article number | 475301 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 47 |

DOIs | |

Publication status | Published - 2009 |

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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*,

*42*(47), [475301]. https://doi.org/10.1088/1751-8113/42/47/475301

**Quantum force induced on a partition wall in a harmonic potential.** / Fülöp, T.; Tsutsui, I.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 42, no. 47, 475301. https://doi.org/10.1088/1751-8113/42/47/475301

}

TY - JOUR

T1 - Quantum force induced on a partition wall in a harmonic potential

AU - Fülöp, T.

AU - Tsutsui, I.

PY - 2009

Y1 - 2009

N2 - Boundary effects in quantum mechanics are examined by considering a partition wall inserted at the centre of a harmonic oscillator system. We put an equal number of particles on both sides of the impenetrable wall keeping the system under finite temperatures. When the wall admits distinct boundary conditions on the two sides, then a net force is induced on the wall. We study the temperature behaviour of the induced force both analytically and numerically under the combination of the Dirichlet and the Neumann conditions, and determine its scaling property for two statistical cases of the particles: fermions and bosons. We find that the force has a nonvanishing limit at zero temperature T = 0 and exhibits scalings characteristic to the statistics of the particles. We also see that for higher temperatures the force decreases according to 1/T , in sharp contrast to the case of the infinite potential well where it diverges according to T. The results suggest that, if such a nontrivial partition wall can be realized, it may be used as a probe to examine the profile of the potentials and the statistics of the particles involved.

AB - Boundary effects in quantum mechanics are examined by considering a partition wall inserted at the centre of a harmonic oscillator system. We put an equal number of particles on both sides of the impenetrable wall keeping the system under finite temperatures. When the wall admits distinct boundary conditions on the two sides, then a net force is induced on the wall. We study the temperature behaviour of the induced force both analytically and numerically under the combination of the Dirichlet and the Neumann conditions, and determine its scaling property for two statistical cases of the particles: fermions and bosons. We find that the force has a nonvanishing limit at zero temperature T = 0 and exhibits scalings characteristic to the statistics of the particles. We also see that for higher temperatures the force decreases according to 1/T , in sharp contrast to the case of the infinite potential well where it diverges according to T. The results suggest that, if such a nontrivial partition wall can be realized, it may be used as a probe to examine the profile of the potentials and the statistics of the particles involved.

UR - http://www.scopus.com/inward/record.url?scp=70649096233&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70649096233&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/42/47/475301

DO - 10.1088/1751-8113/42/47/475301

M3 - Article

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 47

M1 - 475301

ER -