It has been shown that effective lowering of dimension underlies ground-state space structure and properties of two-dimensional lattice systems with a long-range interparticle repulsion. On the basis of this fact a rigorous general procedure has been developed to describe the ground state of the systems.PACS number(s): 64.60. Cn,

We consider an electron system under conditions of strong Anderson localization, taking into account interelectron long-range Coulomb repulsion. We have established that with the electron density going to zero the Coulomb interaction brings the arrangement of the Anderson localized electrons closer and closer to an ideal (Wigner) crystal lattice, provided the temperature is sufficiently low and the dimension of the system is > 1. The ordering occurs despite the fact that a random spread of the energy levels of the localized one-electron states, exceeding the mean Coulomb energy per electron, renders it impossible the electrons to be self-localized due to their mutual Coulomb repulsion This differs principally the Coulomb ordered Anderson localized electron system (COALES) from Wigner crystal, Wigner glass, and any other ordered electron or hole system that results from the Coulomb self-localization of electrons/holes. The residual disorder inherent to COALES is found to bring about a multi-valley ground-state degeneration akin to that in spin glass. With the electron density increasing, COALES is revealed to turn into Wigner glass or a glassy state of a Fermi-glass type depending on the width of the random spread of the electron levels.PACS number(s): 72.15.Rn, a. Introduction. As was shown by Wigner long ago 1 , slow decrease in the Coulomb electron-electron interaction potential v(r) = e 2 /κr (e is the free electron charge, r is a distance between the interacting electrons, κ is the permittivity) with an increase in the interelectron distance inevitably causes the Coulomb energy of free electron gas to exceed its kinetic energy at sufficiently low electron densities with the resulting transition of the gas into an electron crystal (Wigner crystal). In the wake of Wigner's prediction a natural question was raised whether long-range (weakly screened) Coulomb forces can lead to ordering of charge carrier ensembles in conductors. However, a strong evidence of "Wignercrystal-in-crystal" existence has not been found yet. This suggests that the Wigner crystallization, at least in the convential conductors, is very difficult (if at all possible) to observe in pure form. Therefore, seeking mechanisms of charge carrier Coulomb ordering that are beyond the above Wigner's scenario is of great interest.At present much attention is being given to an electron/hole Coulomb self-localization in lattice systems with so small overlap intergal t that tunnelling of charge carriers is supressed by their mutual Coulomb interaction. The self-localization brings about electron/hole ordering in two cases: i/the host lattice is regular (generally an incommensurate electron/hole structure is formed 2,3 ), ii/the host lattice is disordered, but the mean separation of its sites is much less than that of the charge carriersr (the so-called Wigner glass is formed, whose space structure, though disordered, is close to a Wigner crystal lattice (WCL) 4 in a sense 5 ). Ordered self-localized charge carrier lattice systems (OSLCCLS) of both type...

We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time, x n ∼ t µn , where µ < 1 is dimensionless mean drift. We employ a method originated in quantum diffusion which is based on the exact mapping of the problem to an imaginary-time Schrödinger equation. For nonzero drift such an equation has an isolated lowest eigenvalue separated by a gap from quasi-continuous excited states, and the eigenstate corresponding to the former governs the long-time asymptotic behavior. The Sinai model [1] is one of the simplest models for transport in classical disordered systems where physical behavior of various disorder-averaged quantities is interesting and non-trivial and yet amenable to analytical calculations. The model describes random walks under the influence of a spatially homogeneous thermal white noise in the presence of spatial disorder represented by a Gaussian quenched random-drift field v(x). In one dimension (1D) such a disorder strongly suppresses diffusion so that the mean random-walk displacement in the absence of the mean drift is given by x 2 (t) ∝ ln 4 t [1, 2]. In higher dimensions, where the properly generalized Sinai model describes various physical applications like hopping transport in the presence of charged or magnetic impurities, dynamics of dislocations in glasses, 1/f -noise etc., diffusion can be either suppressed (sub-diffusion) for potential random drifts or enhanced (super-diffusion) for solenoidal ones [2][3][4]. The model also exhibits mesoscopic fluctuations [4] within the ensemble of realizations similar to the mesoscopic fluctuations [5] in quantum diffusion in the Anderson model. In such a situation, any exact analytical result for the Sinai model can be potentially of a wide interest and applicability. Naturally, the 1D case is most promising for finding exact solutions.The exact analytic results for the most generic quantity in the 1D Sinai model, the random walks probability distribution function (PDF), has been presented by Kesten [6] but only in the limit of zero mean drift while the extension of this method to the case of an arbitrary drift is not known. Although some exact results for the 1D Sinai model with an arbitrary drift have been obtained -e.g. return probability [2], mean first-passage time [7], or persistence [8] -none of the methods used for these quantities has been generalized for the PDF.In the present publication we close this gap by applying the method developed [9] in the context of quantum diffusion in the presence of losses (non-Hermiticity) to obtain exact asymptotic (long-time) results for the PDF of the 1D Sinai model in the presence of a finite drift.The essence of the method is the following. First we obtain a formally exact solution for the Laplace image of the PDF, P ε (x, x ), for a given realization of the quenched random drift field v(x). We represent this solution in terms of ...

We study what happens to generalized Wigner crystal, GWC (a regular structure formed by narrow-band electrons on a one-dimensional periodic host lattice), when there is a host lattice random distortion that does not break the host-lattice long-range order. We show that an arbitrarily weak distortion of the kind gives rise to soliton-like GWC defects (discrete solitons, DS) in the ground state, and thereby converts the ordered GWC into a new disordered macroscopic statelattice Wigner glass (LWG). The ground-state DS concentration is found to be proportional to l 4 (l is the typical host-lattice strain). We show that the low-temperature LWG thermodynamics and kinetics are fully described in DS terms. A new phenomenon of a super-slow logarithmic relaxation in the LWG is revealed. Its time turns out to be tens orders of magnitude greater than the microscopic ones. Analytical dependences of LWG thermodynamic quantities on temperature and l are obtained for an arbitrary relationship between the relevant Coulomb energies and the electron bandwidth.