Scaling at the chaos threshold for interacting electrons in a quantum Dot

The chaotic mixing by random two-body interactions of many-electron Fock states in a confined geometry is investigated. Two regimes are distinguished in the dependence of the typical number of Fock states that are mixed into an eigenstate on the interaction strength V, the excitation energy varepsilon, and the level spacing Delta. In both regimes the number is large (indicating delocalization in Fock space). However, only the large- V regime is described by the golden rule (indicating chaotic mixing). The crossover region is characterized by a maximum in a scaling function that becomes more pronounced with increasing excitation energy. The scaling parameter that governs the transition is (varepsilonV/Delta(2))ln(Delta/V).     

Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 1

Methodology and Computing in Applied Probability - New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite...     

Graded quasi-lie algebras of witt type

In this article, we introduce a new class of graded algebras called quasi-Lie algebras of Witt type. These algebras can be seen as a generalization of other Witt-type algebras like Lie algebras of Witt type and their colored version, Lie color algebras of Witt type.     

Estimation of Parameters for the Multi-peaked AEF Current Functions

An examination of how the analytically extended function (AEF) can be used to approximate multi-peaked lightning current waveforms, is presented in the paper. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks is presented. This framework is used to find parameters for some common waveforms with a single peak, such as Standard IEC 62305 lightning currents. Illustration of fitting a p-peak AEF to recorded lightning current data is also presented.     

On rings generalizing commutativity

A class of rings is introduced and shown to be useful for obtaining deformation invariant equalities and commutativity results for some important algebras.     

Canonical involutions in three-dimensional generalised Lie algebras

All involutions in complex three-dimensional generalised Lie algebras with one-dimensional or zero-dimensional homogeneous components are described up to isomorphism.     

Quasi-deformations of sl2 (F) with base ℝ[t,t −1]

In this paper we construct quasi-deformations of sl₂(?) with the Laurent polynomials over the reals as base algebra and general vector fields for sl₂(?) in the base of the quasideformation.     

Adiabatic quantization of Andreev quantum billiard levels

We identify the time T between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent lambda), coupled to a superconductor by an N-mode constriction. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods T(n), which in turn generate a ladder of excited states epsilon (nm)=(m+1/2)pi(h) /T(n). The largest quantized period is the Ehrenfest time T(0)=lambda(-1)ln(N). Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension W/sqrt[N], much below the width W of the constriction.