Low-T Asymptotic Expansion of the Solution to the Yang–Yang Equation

We prove that the unique solution to the Yang–Yang equation arising in the context of the thermodynamics of the so-called non-linear Schrödinger model admits a low-temperature expansion to all orders. Our approach provides a rigorous justification, for a certain class of non-linear integral equations, of the low-temperature asymptotic expansions that were argued previously in various works related to the low-temperature behaviour of integrable models.     

Analysis of the Liquid–Cluster State of Melts near the Melting Point

Technical Physics - We have analyzed the available data on the transition from equilibrium crystallization of melts of various substances to nonequilibrium explosive crystallization depending on...     

Spectral–Dynamic Model of the Hot Plasma Layer Expansion

Journal of Experimental and Theoretical Physics - We propose a theoretical model describing the expansion of a plasma layer into vacuum for an arbitrary electron plasma component temperature....     

Anisotropy of the Thermal Expansion of a Polycrystalline Ni–Mn–Ga Alloy Subjected to Plastic Deformation by Forging

The formation of a sharp crystallographic texture in a Ni–Mn–Ga Heusler alloy by the multiple isothermal forging has been studied. An analysis of the thermal expansion near the martensitic transformation temperatures in the as-cast and forged states of the alloy shows that the thermomechanical treatment leads to an increase in the anisotropy of the sample geometric size changing during the phase transformation, which favors an increase in the functional characteristics of the alloy. The structural studies show that the alloy structure after multiple isothermal forging has the bimodal distribution of grain sizes. The formation of the bimodal structure by forging is assumed to make it possible to enhance the stability of the functional properties of the alloy during repeated cycles of the phase transformation.     

A Method to Calculate Correlation Functions for β=1 Random Matrices of Odd Size

The calculation of correlation functions for β=1 random matrix ensembles, which can be carried out using Pfaffians, has the peculiar feature of requiring a separate calculation depending on the parity of the matrix size N. This same complication is present in the calculation of the correlations for the Ginibre Orthogonal Ensemble of real Gaussian matrices. In fact the methods used to compute the β=1, N odd, correlations break down in the case of N odd real Ginibre matrices, necessitating a new approach to both problems. The new approach taken in this work is to deduce the β=1, N odd correlations as limiting cases of their N even counterparts, when one of the particles is removed towards infinity. This method is shown to yield the correlations for N odd real Gaussian matrices. The work of P.J.F. was supported by the Australian Research Council, and A.M. was supported by an Australian Postgraduate Award.     

On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

We consider the coupling from the past implementation of the random–cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector’s problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process.     

A Generalization of the Stone–Von Neumann Theorem to Nonregular Representations of the CCR-Algebra

We give a classification, up to unitary equivalence, of the representations of the C*-algebra of the Canonical Commutation Relations which generalizes the classical Stone–von Neumann Theorem to the case of representations which are strongly measurable, but not necessarily strongly continuous. The classification includes all the (nonregular) representations which have been considered in physical models.     

A New Approach to the Lenard–Magri Scheme of Integrability

We develop a new approach to the Lenard–Magri scheme of integrability of bi-Hamiltonian PDEs, when one of the Poisson structures is a strongly skew-adjoint differential operator.     

A II1 Factor Approach to the Kadison–Singer Problem

We show that the Kadison–Singer problem, asking whether the pure states of the diagonal subalgebra \({\ell^\infty\mathbb{N}\subset \mathcal{B}(\ell^2\mathbb{N})}\) have unique state extensions to \({\mathcal{B}(\ell^2\mathbb{N})}\) , is equivalent to a similar statement in II₁ factor framework, concerning the ultrapower inclusion \({D^\omega \subset R^\omega}\) , where D is the Cartan subalgebra of the hyperfinite II₁ factor R (i.e., a maximal abelian *-subalgebra of R whose normalizer generates R, e.g. \({D=L^\infty([0, 1]^{\mathbb{Z}}) \subset L^\infty([0,1]^{\mathbb{Z}} \rtimes \mathbb{Z} = R)}\) , and ω is a free ultrafilter. Instead, we prove here that if A is any singular maximal abelian *-subalgebra of R (i.e., whose normalizer consists of the unitary group of A, e.g. \({A=L(\mathbb{Z})\subset L^\infty([0,1]^\mathbb{Z})\rtimes \mathbb{Z}=R}\) ), then the inclusion \({A^\omega \subset R^\omega}\) does satisfy the Kadison–Singer property.     

The Lyapunov Exponent of Products of Random 2×2 Matrices Close to the Identity

We study products of arbitrary random real 2×2 matrices that are close to the identity matrix. Using the Iwasawa decomposition of SL(2,?), we identify a continuum regime where the mean values and the covariances of the three Iwasawa parameters are simultaneously small. In this regime, the Lyapunov exponent of the product is shown to assume a scaling form. In the general case, the corresponding scaling function is expressed in terms of Gauss’ hypergeometric function. A number of particular cases are also considered, where the scaling function of the Lyapunov exponent involves other special functions (Airy, Bessel, Whittaker, elliptic). The general solution thus obtained allows us, among other things, to recover in a unified framework many results known previously from exactly solvable models of one-dimensional disordered systems.     

Dipole–Dipole Polarizability of the Cadmium 1S0 State Revisited

Optics and Spectroscopy - Experimental results and high-level quantum chemical ab initio calculations of the static polarizability α0 = α(ω = 0) of the cadmium 1S0 state are still in...     

A New Approach to the Justification of the Wolkenstein–Ptitsyn Formula for the Parameter of the Vitrification Equation

Technical Physics - An extended interpretation of the Wolkenstein–Ptitsyn formula for temperature band δTg, characterizing a range of transition from liquid to glass, is considered using...     

A Bohmian approach to the perturbations of non-linear Klein–Gordon equation

In the framework of Bohmian quantum mechanics, the Klein–Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave ?(x) in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein–Gordon equation? We examine this approach for ?⁴(x) and sine-Gordon potentials. It turns out that this method leads to equations for quantum states which are identical to those derived by field theoretical methods used for quantum solitons. Moreover, the quantum force exerted on the particle can be determined. This method can be used for other non-linear potentials as well.     

A topological way of finding solutions to the Yang–Mills equation

We propose a systematic way of finding solutions to the classical Yang–Mills equation with nontrivial topology. This approach is based on one of the Wightman axioms for quantum field theory, which is referred to as the form invariance condition in this paper. For a given gauge group and a spacetime with certain isometries, thanks to this axiom that imposes strong constraints on the general ansatz, a systematic way of solving the Yang–Mills equation can be obtained in both flat and curved spacetimes. In order to demonstrate this method, we recover various known solutions as special cases, as well as producing new solutions not previously reported in the literature.     

New bound to the probability of 76Ge ββ decay to the 0 1 + 76Se level

Measurements were carried out at the underground low-background laboratory of the Baksan Neutrino Observatory using a detection system involving four ultrapure germanium detectors made from enriched ⁷⁶Ge. The sensitivity of the experiment to the detection of a ⁷⁶Ge double beta decay to the excited levels of the ⁷⁶Se nucleus was determined. As a result of 228-day measurements, the new bound to the time of ⁷⁶Ge half-decay to the ⁷⁶Se 0 ₁ ⁺ excited level is found to be T _1/2(2ν2β)≥6.2×10²¹ years (90% confidence level).     

In the Land of the Dinosaurs,How to Survive Experience with Building of Midrange Computing Cluster

This paper discusses how to put into operation a midrange computing cluster for the Nuclear Chemistry Group(NCG) of the State University of New York at STONY Brook(SUNY-SB).The NCG is part and one of the collaborators within the RHIC/Phenix experiment located at the Brookhaven National Laboratory(BNL).The Phenix detector system produces about half a PB(or 500 TB) of data a year and our goal was to provide to this remote collaborating facility the means to be part of the analysis process.The computing installation was put into operation at the beginning of the year 2000.The cluster consists of 32 peripheral machines running under Linux and central server Alpha 4100 under DIgital Unix 4.of (formally True Unix 64),In the paper the realization process is under discussion.     

Adsorption kinetics of the Cs–O activation layer on GaAs(1 0 0)

In this work, we study the adsorption of (molecular) oxygen on Cs-covered GaAs(1 0 0) surfaces at RT. The study took place in a multi-method UHV system using the techniques such as low energy electron diffraction (LEED), Auger electron spectroscopy (AES), work function measurements (WF), thermal desorption spectroscopy (TDS), secondary ion mass spectroscopy (SIMS) and electron stimulated desorption (ESD) spectroscopy in correlation with the photocurrent measurements. It is shown that the oxygen burrows under the Cs overlayer and interacts at low exposures with the GaAs substrate, whereas at higher exposures oxygen interacts also with Cs leading to Cs oxides. The maximum photocurrent appears after the WF minimum and before the oxidation of Cs. Our results support the dipolar model for the explanation of the negative electron affinity effect.