Fluctuation of inverse compressibility for electronic systems with random capacitive matrices

This article is concerned with the statistics of the addition spectra of ce rtain many-body systems of identical particles. In the first part, the pert inent system consists of N identical particles distributed among K < N inde pendent subsystems, such that the energy of each Subsystem is a quadratic f unction of the number of particles residing on it with random coefficients. On a large scale, the ground-state energy E(N) of the whole system grows q uadratically 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) chi(N) = E(N + 1) - 2E(N) + E(N - 1) is a fluctuating quantity. Regarding the numbers chi(N) as values assumed by a certain random variable chi, we obtain a closed-for m expression for its distribution F(chi). Its main feature is that the corr esponding density P(chi) = dF(chi)/d chi has a maximum at the point chi = o . As K --> infinity the density is Poissonian, namely, P(chi) --> e(-chi). This result serves as a starting point for the second part, in which coupli ng between subsystems is included. More generally, a classical model is sug gested in order to study fluctuations of Coulomb blockade peak spacings in large two-dimensional semiconductor quantum dots. It is based on the electr ostatics of several electron islands among which there are random inductive and capacitive couplings. Each island can accommodate electrons on quantum orbitals whose energy depends also on an external magnetic field. In contr ast to a single-island quantum dot, where the spacing distribution between conductance peaks is close to Gaussian, here the distribution has a peak at small spacing value. The fluctuations are mainly due to charging effects. The model can explain the occasional occurrence of couples or even triples of closely spaced Coulomb blockade peaks, as well as the qualitative behavi our of peak positions with the applied magnetic field.