International Journal of Modern Physics B

A complete account of the development of the method of real space Green’s function is given in this review. The emphasis is placed on the calculation of the local Green’s function in a real space representation. The discussion is centered on a list of issues particularly relevant to the study of properties of complex systems with reduced symmetry.They include:

(i) the convergence procedure for calculating the local Green’s function of infinite systems without any boundary effects associated with an arbitrary truncation of the system;

(ii) a general recursive relation which streamlines the calculation of the local Green’s function;

(iii) the calculation of the eigenvector of selected eigenvalues directly from the Green’s function.

An example of the application of the method to carry out a local analysis of dynamics of the Au(511) surface is also presented.

We study the interplay of disorder and nonlinearity in condensed matter systems modeled by the paradigmatic discrete nonlinear Schrödinger equation and focus on selftrapping and transport properties. We start by analyzing the two most simple nonlinear disordered systems, viz. a nondegenerate nonlinear dimer and a perturbed degenerate dimer. We then consider the case of few nonlinear impurities embedded in a linear host and treat the stationary problem analytically. We conclude by examining the case of a one-dimensional nonlinear random binary alloy where we find absence of quasiparticle localization, except for large nonlinearity parameter values. The transmission of plane’ waves across a disordered nonlinear segment of this type shows a power-law decay as a function of the segment size.

The nonequilibrium Statistical Operator Method, seemingly contained within the scope of Jaynes’ Predictive Statistical Mechanics, provides a foundation for irreversible thermodynamics in what is called Informational Statistical Thermodynamics, and within it a way of deriving generalized constitutive equations which contain non-localities on space. Here we present a derivation of these equations of evolution describing how memory effects are incorporated into the theory. We show that the memory kernels in the kinetic coefficients and relaxation times can be expressed in terms of an infinite series of instantaneous collisions integrals, of ever increasing order in the interaction strengths that are related to the slow relaxation processes that develop in the system. The kinetic coefficients are derived on the basis of the Hamiltonian dynamics of the system accompanied by appropriate averages over the nonequilibrium informational statistical ensemble.

The Nonequilibrium Statistical Operator Method offers a quite appropriate mechano-statistical framework to irreversible thermodynamics, providing what may be termed as Informational Statistical Thermodynamics. Such scheme, which encompasses and enlarges Extended Irreversible Thermodynamics allows for the construction, at the microscopic (molecular) level, of equations of evolution for the fluxes that replace and correct the usual phenomenological constituve equations of Classical Irreversible Thermodynamics. In the present paper we show how IST allows the retrieval of the equations of evolution of EIT (the so called Maxwell-Cattaneo-Vernotte equations) including non-linearities in the fluxes. Besides evidencing such terms, the approach allows us to derive expressions for the kinetic coefficients on the basis of averages over the nonequilibrium informational statistical ensemble that describes the macroscopic state of the system.

The wave function of two fermions, repulsively interacting in the presence of a Fermi sea, is evaluated in detail. We consider large but finite systems in order to obtain an unambiguous picture of the two-particle correlations. As recently pointed out by Anderson, in d≤2 dimensions the particles may be correlated even when situated on the Fermi surface. The “partial exclusion principle” for two particles with opposite spin on the same Fermi point is discussed, and related to results from the T-matrix approximation. Particles on different Fermi points are shown to be uncorrelated in d>1. Using the results for the two-particle correlations we find that the orthogonality effect induced by adding an extra particle to a (tentative) two-dimensional Fermi liquid is finite.