## Abstract

Motivated by recent experiments on large quantum dots, we consider the energy spectrum in a system consisting of N particles distributed among K < N independent subsystems, such that the energy of each subsystem is a quadratic function of the number of particles residing on it. On a large scale, the ground-state energy E(N) of such a system grows quadratically with N, but in general there is no simple relation such as E(N) = aN + bN^{2}. The deviation of E(N) from exact quadratic behaviour implies that its second difference (the inverse compressibility) XN ≡ E(N + 1) - 2E(N) + E(N - 1) is a fluctuating quantity. Regarding the numbers XN as values assumed by a certain random variable X, we obtain a closed-form expression for its distribution F(X). Its main feature is that the corresponding density P(X) = dF(X)/dX has a maximum at the point X = 0. As K → ∞ the density is Poissonian, namely, P(X) → ^{e-X}.

Original language | English |
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Pages (from-to) | 8063-8072 |

Number of pages | 10 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 31 |

Issue number | 40 |

DOIs | |

State | Published - 9 Oct 1998 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy (all)