Existence of free energy for models with long-range random Hamiltonians

Classical lattice systems with random Hamiltonians $$\frac{1}{2}\sum\limits_{x_1 \ne x_2 } {\frac{{\varepsilon (x_1 ,x_2 )\varphi (x_1 )\varphi (x_2 )}}{{\left| {x_1 - x_2 } \right|^{\alpha d} }}}$$ are considered, whered is the dimension, andε(x ₁,x ₂) are independent random variables for different pairs (x ₁,x ₂),Eε(x ₁,x ₂) = 0. It is shown that the free energy for such a system exiists with probability 1 and does not depend on the boundary conditions, providedα > 1/2.     

Universal estimates for critical circle mappings

A thermodynamic formalism is constructed for critical circle mappings. It is used to prove universal estimates for the asymptotic behavior of renormalized mappings. Certain applications of statistical mechanics to research on the ergodic properties of critical homeomorphisms of a circle are also discussed.     

Continued Fractions and the d-Dimensional Gauss Transformation

In this paper we study a multidimensional continued fraction algorithm which is related to the Modified Jacobi–Perron algorithm considered by Podsypanin and Schweiger. We demonstrate that this algorithm has many important properties which are natural generalisations of properties of one-dimensional continued fractions. For this reason, we call the transformation associated to the algorithm the d-dimensional Gauss transformation. We construct a coordinate system for the natural extension which reveals its symmetries and allows one to give an explicit formula for the density of its invariant measure. We also discuss the ergodic properties of this invariant measure. Received: 4 February 2000 / Accepted: 23 May 2000     

Observation of the low-temperature peak in the interlayer tunneling conductance in bilayer electron systems in the absence of the magnetic field

A high narrow peak in the interlayer differential tunnel conductance has been observed in heterostructures with two closely located electron layers at low temperatures. Analysis of the experimental results suggests that this peak is due to the interlayer phase coherence, which appears in the system under investigation owing to the Bose condensation of indirect excitons, i.e., pairs of electrons and holes from different layers in the absence of the magnetic field.     

Transmission and Conversion of Electromagnetic Radiation by Photonic Crystal Metal–Dielectric Systems Based on Opals

Optics and Spectroscopy - An experimental study of the optical properties of two types of metal–dielectric composites based on opal matrices has been carried out: (1) layered structures,...     

Topological shocks in Burgers turbulence

The dynamics of the multidimensional randomly forced Burgers equation is studied in the limit of vanishing viscosity. It is shown both theoretically and numerically that the shocks have a universal global structure which is determined by the topology of the configuration space. This structure is shown to be particularly rigid for the case of periodic boundary conditions.     

Fractal properties of critical invariant curves

We examine the dimension of the invariant measure for some singular circle homeomorphisms for a variety of rotation numbers, through both the thermodynamic formalism and numerical computation. The maps we consider include those induced by the action of the standard map on an invariant curve at the critical parameter value beyond which the curve is destroyed. Our results indicate that the dimension is universal for a given type of singularity and rotation number, and that among all rotation numbers, the golden mean produces the largest dimension.     

Resonant tunneling of electrons through virtual interference states formed as a result of reflection from the boundary of strongly doped region of GaAs

The paper is devoted to analysis of the electron transport through one-barrier GaAs/AlAs/GaAs heterostructures. The oscillating component of transport characteristics of symmetric one-barrier GaAs/AlAs/GaAs heterostructures with spacers, which is associated with resonance tunneling of electrons via virtual states formed in the spacer region of the structures due to reflection of electrons from the n^?-GaAs/n⁺-GaAs interface and their subsequent interference. It is shown that electrons are predominantly reflected coherently from the boundary of the strongly doped region as in the case of one-dimensional averaged potential of randomly arranged (beginning from this boundary) impurities. It is shown that low-energy virtual resonances are suppressed due to electron scattering as a result of their interaction with longitudinal optical (LO) phonons in the spacer region.