Pier A. Mello

Macroscopic approach to multichannel disordered conductors

We present a theory of multichannel disordered conductors by directly studying the statistical distribution of the transfer matrix for the full system. The theory is based on the general properties of the scattering system: flux conservation, time-reversal invariance, and the appropriate combination requirement when two wires are put together. The distribution associated with systems of very small length is then selected on the basis of a maximum-entropy criterion; a fixed value is assumed for the diffusion coefficient that characterizes the evolution of the distribution as the length increases. We obtain a diffusion equation for the probability distribution and compute the average of a few relevant quantities.

Mesoscopic transport through chaotic cavities: A random S-matrix theory approach.

We deduce the effects of quantum interference on the conductance of chaotic cavities by using a statistical ansatz for the S matrix. Assuming that the circular ensembles describe the S matrix, we find that the conductance fluctuation and weak-localization magnitudes are universal: they are independent of the size and shape of the cavity if the number of incoming modes, N, is large. The limit of small N is more relevant experimentally; here we calculate the full distribution of the conductance and find striking differences as N changes or a magnetic field is applied.

Information theory and statistical nuclear reactions. I. General theory and applications to few-channel problems☆

Abstract Ensembles of scattering S-matrices have been used in the past to describe the statistical fluctuations exhibited by many nuclear-reaction cross sections as a function of energy. In recent years, there have been attempts to construct these ensembles explicitly in terms of S, by directly proposing a statistical law for S. In the present paper, it is shown that, for an arbitrary number of channels, one can incorporate, in the ensemble of S-matrices, the conditions of flux conservation, time-reversal invariance, causality, ergodicity, and the requirement that the ensemble average 〈S〉 coincide with the optical scattering matrix. Since these conditions do not specify the ensemble uniquely, the ensemble that has maximum information-entropy is dealt with among those that satisfy the above requirements. Some applications to few-channel problems and comparisons to Monte-Carlo calculations are presented.

Mesoscopic Capacitors: A Statistical Analysis.

The capacitance of mesoscopic samples depends on their geometry and physical properties, described in terms of characteristic times scales. The resulting ac admittance shows sample to sample fluctuations. Their distribution is studied here -through a random-matrix model- for a chaotic cavity capacitively coupled to a backgate: it is observed from the distribution of scattering time delays for the cavity, which is found analytically for the orthogonal, unitary, and symplectic universality classes, one mode in the lead connecting the cavity to the reservoir and no direct scattering. The results agree with numerical simulations.

Statistical properties of many-particle spectra. II. Two-point correlations and fluctuations☆

Abstract The two-point correlation function for complex spectra described by the Gaussian Orthogonal Ensemble (GOE) is calculated, and its essential simplicity displayed, by an elementary procedure which derives from orthogonal invariance and the dominance of intrinsic binary correlations. The resultant function is used for an approximate calculation of the standard fluctuation measures. Good agreements are found with exact results where these are available, this incidentally demonstrating that the measures are, for the most part, two-point measures. It is shown that they vary slowly over the spectrum, a result which is in agreement both with experiment and with Monte Carlo calculations. The same technique can be used for higher-order correlation functions, and possibly also for more complicated ensembles in which case the results would be relevant to the question why GOE fluctuations give a good account of experimental results.

EFFECT OF PHASE BREAKING ON QUANTUM TRANSPORT THROUGH CHAOTIC CAVITIES

We investigate the effects of phase-breaking events on electronic transport through ballistic chaotic cavities. We simulate phase-breaking by a fictitious lead connecting the cavity to a phase-randomizing reservoir and introduce a statistical description for the total scattering matrix, including the additional lead. For strong phase-breaking, the average and variance of the conductance are calculated analytically. Combining these results with those in the absence of phase-breaking, we propose an interpolation formula, show that it is an excellent description of random-matrix numerical calculations, and obtain good agreement with several recent experiments.

The time-energy uncertainty relation

Abstract A discussion is presented of the formulations of the time and energy uncertainty principle given by Mandelstam, Tamm, Wigner, and the one proposed recently by the present authors, based on the concept of the equivalent width. In the case of the free particle, all three formulations give essentially the same result, while in the problem of the lifetime-width relation for a decaying state, only the one based on the equivalent width concept is applicable. This is also the case in the energy-measurement process, when it is formulated as a transition produced by an external interaction of finite duration.

Time delay in nuclear reactions

The time delays involved under different circumstances in nuclear reactions, e.g., isolated or overlapping resonances, are analysed from the unified point of view of unitarity and of the statistical and analytical properties of theS-matrix. A general theorem is proved which says that the average over then open channels of the time delay of a wave packet covering many resonances (whose average separation isD) is given byħ/(nD). The case of an incoherent superposition of monochromatic beams is also studied and the corresponding time delay is evaluated in the statistical model of Ericson.

The statistical distribution of theS-matrix in the one-channel case

It is shown that the statistical distribution of an ensemble of one-channelS-matrices is uniquely determined by requiring that:1)S has poles only in the lower half of the energy plane and2) the functionS(E) is ergodic in a sense to be defined. A Monte Carlo calculation was performed to illustrate numerically the above statement.

Studies on the problem of small metallic particles. I. — Spectrum fluctuations in a two-dimensional model and the associated specific heat

Abstract It is shown that the qualitative arguments given up to now in the literature, are not enough to justify the applications of Random Matrix Theory to the small metallic particle problem. Using a two-dimensional model we show that the spacing distributions approach Poissons law, as originally assumed by Kubo, who computed the specific heat for this case. By means of a numerical calculation we show, however, that Kubos result is only valid for kBT:δ ≲ 0.025, where δ is the mean spacing and kB is Boltzmanns constant.