STATISTICS OF ADDITION SPECTRA OF INDEPENDENT QUANTUM-SYSTEMS

Motivated by recent experiments on large quantum dots, we consider the energy spectrum in a system consisting of N particles distributed amo ng K < N independent subsystems, such that the energy of each subsyste m is a quadratic function of the number of particles residing on it. O n a large scale, the ground-state energy E(N) of such a system grows q uadratically with N, but in general there is no simple relation such a s E(N) = aN + bN(2). The deviation of E(N) from exact quadratic behavi our implies that its second difference (the inverse compressibility) c hi N = E(N + 1) - 2E(N) + E(N - 1) is a fluctuating quantity. Regardin g the numbers chi N as values assumed by a certain random variable chi , we obtain a closed-form expression for its distribution F(chi). Its main feature is that the corresponding density P(chi) = dF(chi)/d chi has a maximum at the point chi = 0. As K --> infinity the density is P oissonian, namely, P(chi) --> e(-chi).