### Abstract

This paper explores the ground state energy of a system of interacting "soft core" bosons in a random Bernoulli potential in the Gross-Pitaevskii mean-field approximation. First, we prove a condition for a state to delocalize due to interaction. Using this condition, asymptotics for ground state energy per particle are derived in the large system limit for small values of the coupling constant. Our methods directly describe the shape of the ground state in a given realization of the random potential.

Original language | English (US) |
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Article number | 081902 |

Journal | Journal of Mathematical Physics |

Volume | 54 |

Issue number | 8 |

DOIs | |

State | Published - Aug 5 2013 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*54*(8), [081902]. https://doi.org/10.1063/1.4818748

**Ground state energy of mean field model of interacting bosons in Bernoulli potential.** / Bishop, M.; Wehr, Jan.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 54, no. 8, 081902. https://doi.org/10.1063/1.4818748

}

TY - JOUR

T1 - Ground state energy of mean field model of interacting bosons in Bernoulli potential

AU - Bishop, M.

AU - Wehr, Jan

PY - 2013/8/5

Y1 - 2013/8/5

N2 - This paper explores the ground state energy of a system of interacting "soft core" bosons in a random Bernoulli potential in the Gross-Pitaevskii mean-field approximation. First, we prove a condition for a state to delocalize due to interaction. Using this condition, asymptotics for ground state energy per particle are derived in the large system limit for small values of the coupling constant. Our methods directly describe the shape of the ground state in a given realization of the random potential.

AB - This paper explores the ground state energy of a system of interacting "soft core" bosons in a random Bernoulli potential in the Gross-Pitaevskii mean-field approximation. First, we prove a condition for a state to delocalize due to interaction. Using this condition, asymptotics for ground state energy per particle are derived in the large system limit for small values of the coupling constant. Our methods directly describe the shape of the ground state in a given realization of the random potential.

UR - http://www.scopus.com/inward/record.url?scp=84883433210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883433210&partnerID=8YFLogxK

U2 - 10.1063/1.4818748

DO - 10.1063/1.4818748

M3 - Article

AN - SCOPUS:84883433210

VL - 54

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 8

M1 - 081902

ER -