Quantum thermostatted disordered systems and sensitivity under compression

Abstract

A one-dimensional quantum system with off diagonal disorder, consisting of a sample of conducting regions randomly interspersed within potential barriers is considered. Results mainly concerning the large N limit are presented. In particular, the effect of compression on the transmission coefficient is investigated. A numerical method to simulate such a system, for a physically relevant number of barriers, is proposed. It is shown that the disordered model converges to the periodic case as N increases, with a rate of convergence which depends on the disorder degree. Compression always leads to a decrease of the transmission coefficient which may be exploited to design nano-technological sensors. Effective choices for the physical parameters to improve the sensitivity are provided. Eventually large fluctuations and rate functions are analysed.

Transport in Quantum Multi-barrier Systems as Random Walks on a Lattice

“…This reinforces the results of Refs. [11,12,25], showing convergence with growing N of the transmission coefficients of the random systems to the regular case values. The correspondence highlighted in Figs.…”

“…As in Refs. [10][11][12]25], the total length L, and the fraction γ of insulating to conducting material are fixed, while the number of barriers N can be varied to represent more or less finely structured media. Therefore, the width of the conducting regions is given by…”

“…Unlike the tight-binding model introduced by Anderson, the one of Refs. [11,12,25] enjoys a purely off-diagonal disorder that affects the tunneling couplings among the wells, but not the energies of the bound states within the wells. In Refs.…”

“…In Ref. [25], the transmission coefficient has been investigated for physically relevant numbers of potential barriers, referring to the scales of nano-structured sensors. In particular, the effect of compression has been numerically investigated, for different compression rules, finding that the rate of convergence to the behavior of the Kronig-Penney model [10,18] strongly depends on the disorder degree; that compression induces a decrease of the transmission coefficient; and that a moderate number of barriers together with strong disorder imply high sensitivity to compression, which can be used for pressure sensors.…”

“…In search for a more detailed treatment of the model of Refs. [11,12,25], the present paper investigates the possibility of adopting an effective description, that replaces the original one with models that behave in an equivalent fashion, while being better suited for analytical treatment. The first case that ought to be investigated, in this respect, is the regular one, corresponding to the finite Kronig-Penney model.…”