Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process

We consider the asymmetric exclusion process (ASEP) in one dimension on sites i=1,...,N, in contact at sites i=1 and i=N with infinite particle reservoirs at densities _a and _b . As _a and _b are varied, the typical macroscopic steady state density profile ¯(x), x[a,b], obtained in the limit N=L(b–a), exhibits shocks and phase transitions. Here we derive an exact asymptotic expression for the probability of observing an arbitrary macroscopic profile , so that is the large deviation functional, a quantity similar to the free energy of equilibrium systems. We find, as in the symmetric, purely diffusive case q=1 (treated in an earlier work), that is in general a non-local functional of (x). Unlike the symmetric case, however, the asymmetric case exhibits ranges of the parameters for which is not convex and others for which has discontinuities in its second derivatives at (x)=¯(x). In the latter ranges the fluctuations of order in the density profile near ¯(x) are then non-Gaussian and cannot be calculated from the large deviation function.     

Computer simulation of shock waves in the completely asymmetric simple exclusion process

We study the evolution of the completely asymmetric simple exclusion process in one dimension, with particles moving only to the right, for initial configurations corresponding to average density _– ( ₊) left (right) of the origin, _{– +}. The microscopic shock position is identified by introducing a second-class particle. Results indicate that the shock profile is stable, and that the distribution as seen from the shock positionN(t) tends, as time increases, to a limiting distribution, which is locally close to an equilibrium distribution far from the shock. Moreover , withV=1– _–– ₊, as predicted, and the dispersion ofN(t), ²(t), behaves linearly, for not too small values of ₊– _–, i.e., , whereS is equal, up to a scaling factor, to the valueS _WA predicted in the weakly asymmetric case. For ₊= _– we find agreement with the conjecture .Dedicated to the memory of Paola Calderoni.     

Examples of Twisted Cyclic Cocycles from Covariant Differential Calculi

For two covariant differential *-calculi, the twisted cyclic cocycle associated with the volume form is represented in terms of commutators for some self-adjoint operator and some *-representation of the underlying *-algebra.     

Quenched Averages for Self-Avoiding Walks and Polygons on Deterministic Fractals

We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W _n (S), and rooted self-avoiding polygons P _n (S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P _n (S), and W _n(S) for an arbitrary point S on the lattice. These are used to compute the averages ,, and over different positions of S. We find that the connectivity constant μ, and the radius of gyration exponent are the same for the annealed and quenched averages. However, , and , where the exponents and , take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives and , to be compared with the known annealed values and .     

A Class of Generalized Gamma Functions

We study a family of holomorphic functions defined by infinite products of the form (a, r real, ar > 0) which generalize Eulers definition since . We obtain analogues of classical formulas (e.g. Gauss multiplication and complement formulas) for these functions _a,r(s)     

Generalized two-level quantum dynamics. II. Non-Hamiltonian state evolution

A theorem is derived that enables a systematic enumeration of all the linear superoperators (associated with a two-level quantum system) that generate, via the law of motion = , mappings (0) (t) restricted to the domain of statistical operators. Such dynamical evolutions include the usual Hamiltonian motion as a special case, but they also encompass more general motions, which are noncyclic and feature a destination state (t ) that is in some cases independent of (0).     

A one dimensional microscopical model for the study of the coherence in the stopping power problem. Part 2

A frictional quantum mechanical system consisting of a particle being scattered inelastically by a chain ofN infinitely heavy, equidistantly spaced two-level atoms is studied. In continuation of Part 1 of this work (G. Süßmann, P. Szilas, Z. Phys. B-Condensed Matter39, 125 (1980)) where the stationary problem has been considered the time dependent problem of a Gaussian wave packet impinging on the target atoms is treated. The reduced density matrix x| _R (t)|x of the particle is calculated. With this explicit expression the time derivative of the mean positiond<x>/dt is found in agreement with the stationary mean velocity of Part 1. As a measure of the incoherence of _R , i.e. the deviation of the state of the particle from a pure state, the quantityI:=1-Tr( _R ² ) is calculated for the quasi elastic case, and an estimate is given for the inelastic case.     

A Variational Principle in the Dual Pair of Reproducing Kernel Hilbert Spaces and an Application

Given a positive definite, bounded linear operator A on the Hilbert space ₀≔l ²(E), we consider a reproducing kernel Hilbert space ₊ with a reproducing kernel A(x,y). Here E is any countable set and A(x,y), x,y∊ E, is the representation of A w.r.t. the usual basis of ₀. Imposing further conditions on the operator A, we also consider another reproducing kernel Hilbert space ₋ with a kernel function B(x,y), which is the representation of the inverse of A in a sense, so that ₋⊃ ₀⊃ ₊ becomes a rigged Hilbert space. We investigate the ratios of determinants of some partial matrices of A and B. We also get a variational principle on the limit ratios of these values. We apply this relation to show the Gibbsianness of the determinantal point process (or fermion point process) defined by the operator A(I+A)⁻¹ on the set E. 2000 Mathematics Subject Classification: Primary: 46E22 Secondary: 60K35     

Surface (110) of elementary semiconductors with diamond-type structure during stratified growth from an atomic beam in a vacuum

The stratified growth of an ideal crystal with diamond structure from an atomic beam in a vacuum is investigated by using the kinetic method of the theory of crystal growth. Equations are obtained to determine the mean concentrations _n of molecules consisting of n atoms on the (110) surface of the crystal. In the stationary case, an approximate analytic solution is obtained with a nonlinear dependence of ₁, ₂, and on the atomic beam density.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 92–96, Decmeber, 1981.     

Phonon-Exchange Attraction. Optical Phonons and Type II Superconductivity, and d-Wave Cooper Pairs

The electron-pair density matrix (k ₁, k ₂; k ₃, k ₄, t) =: (1, 2; 3, 4, t) changes in time, following a quantum Liouville equation \rho (5,6;3,4,t) - < 5,6|v_c |3,4 >\rho (1,2,5,6,t)} \right]} } $$ " align="middle" border="0"> with : = 4\pi e^2 k_0 (\Omega q^2 )^{ - 1} \delta _{k_1 + k_2 ,k_3 + k_4 } \delta _{k_s - k_1 ,q} $$ " align="middle" border="0"> in the presence of a Coulomb interaction _c, where is the volume. If the virtual phonon exchange is in action, the density matrix is shown to change similarly with an effective interaction _e, \hfill \\ = |V_q |^2 \bar h\omega _q |(\varepsilon _3 - \varepsilon _1 )^2 - \bar h^2 \omega _q^2 |^{ - 1} \delta _{k_1 + k_2 ,k_3 + k_4 } \delta _{k_3 - k_1 ,q} \hfill \\ \end{gathered} $$ " align="middle" border="0"> , by using a time-dependent perturbation theory and a Markoffian approximation. The dominant longitudinal-acoustic-(optical)-phonon-exchange attraction at 0K is shown to be q-independent (-dependent). The results are used to discuss the Cooper pair size, the origin of type II superconductivity and the formation of d-wave Cooper pairs in the cuprates.     

Diffractive production of ρ-mesons and of ρπ-systems by neutrinos and antineutrinos on protons

Evidence is presented for diffractive production of -mesons and of -systems invp and chargedcurrent interactions. In the (anti-)neutrino energy range 10 GeVE _v <60 gev=" the=" cross=" sections=" for=" diffractive="> and diffractive production are found to be (0.64±0.14 (stat.)±0.08 (syst.))% and (0.28±0.08 (stat.)±0.04 (syst.))% of the charged-current cross section. The diffractive signal is consistent with being entirely due to diffractivea ₁ production. However, the data cannot distinguish between diffractivea ₁ and diffractive nonresonant production. The experimental distributions ofW, Q ²,x _Bj andy _Bj for diffractive and events are consistent with model predictions.     

Local Resolvent Estimates for <Emphasis Type="Italic">N</Emphasis>-body Stark Hamiltonians

For an N-body Stark Hamiltonian , the resolvent estimate holds uniformly in with Re and Im , where , and is a compact interval. This estimate is well known as the limiting absorption principle. In this paper, we report that by introducing the localization in the configuration space, a refined resolvent estimate holds uniformly in with Re and Im . Dedicated to Professor Hideo Tamura on the occasion of his 60th birthday     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

The role of the distribution of nucleons in finite nuclei

The total energy of many-nucleon system is expressed as a functional E[ _p(r), _n(r)] of the proton and neutron densities _p(r) and _n(r), respectively. The distribution(r) of nucleons in the nucleus, which is essential to determine the energy functional, is chosen. The energy density formalism is applied to finite nuclei, and then the binding energies per nucleon together with the mean square radii, for some medium and heavy nuclei, are obtained. Finally the achieved results are compared with the corresponding experimental values.     

Asymptotically abelian systems

We study pairs { , } for which is aC*-algebra and is a homomorphism of a locally compact, non-compact groupG into the group of *-automorphisms of . We examine, especially, those systems { , } which are (weakly) asymptotically abelian with respect to their invariant states (i.e. |A _g (B) — _g (B)A 0 asg for those states such that ( _g (A)) = (A) for allg inG andA in ). For concrete systems (those with -acting on a Hilbert space andg _g implemented by a unitary representationg U _g on this space) we prove, among other results, that the operators commuting with and {U _g } form a commuting family when there is a vector cyclic under and invariant under {U _g }. We characterize the extremal invariant states, in this case, in terms of weak clustering properties and also in terms of factor and irreducibility properties of { ,U _g }. Specializing to amenable groups, we describe operator means arising from invariant group means; and we study systems which are asymptotically abelian in mean. Our interest in these structures resides in their appearance in the infinite system approach to quantum statistical mechanics.     

Ion Mobility Measurements and Ion Chemical Reaction Studies at Heavy Elements in a Buffer Gas Cell

Drift time measurements of ions in a buffer gas cell filled with argon have been performed from which changes of the ion mobility and ionic radii for various heavy elements and their compounds were determined. The ionic radius of americium shrinks by (3.1 1.3)% with respect to that of plutonium, and an increase of the radius by (28 2)% of plutonium oxide with respect to plutonium was found. Ion chemical reactions of erbium ions were studied online in an argon buffer gas cell to which the reaction gases oxygen (O) and methane (CH) were added. The erbium ions were implanted into the buffer gas cell with an energy of 50 MeV. The online measured reaction constant = (3.2 0.4) 10 cm/(molecule s) for the reaction Er + O ErO + O agrees with a reference measurement = (3.6 0.4) 10 cm/(molecule s), performed with a Fourier-Transform-Mass-Spectrometer.     

Why is \mathcal{CPT} Fundamental?

Lüders and Pauli proved the theorem based on Lagrangian quantum field theory almost half a century ago. Jost gave a more general proof based on “axiomatic” field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why is fundamental—because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the transform of any relativistic field without calculating , and separately and then multiplying them. The purpose of this pedagogical paper is to “deaxiomatize” the theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary.     

The decays of theρ′1 andω′1 mesons

New measurements of the reactione ⁺ e ^– confirm previous evidence for the decay₁ and provide a strong constraint on the mass of the₁. The results from a detailed analysis of these data are compared with those from a corresponding analysis of new data on the reactione ⁺ e ^–. It is shown that in accord with expectation. This identification of a strong₁ decay supports a previous claim that the₁ and theC(1480), observed in the channel, cannot be different manifestations of the same particle.     

Electron-electron interaction and magnon scattering in the d-electron dominated resistivity of Ni80−xFe x Si8B12 glasses

Our investigation of the electrical resistivity (T) betweenT=0.1 K and 295 K revealed for all Fe-concentrations, 2.4x16, a minimum of betweenT _min=7 K and 15 K. Above the minimum, scattering from structural disorder prevails in the paramagnetic alloy (x=2.4), while in the ferromagnetic glasses (x5.6) coherent magnon scattering appears to dominate. With one exception, (TT _min) increases as down to the lowest temperatures for all investigated Fe-contents (x10.4) in zero magnetic field as well as in applied 6 T. The value of the slopes, 6.3(6) ( cm)^–1 K^–1/2, agrees with the universal scaling behaviour reported recently by Cochrane and Strom-Olsen for systems with strong electron-electron interaction. A large, linear rise of (T<T _min,B=0) observed in the most diluted sample (x=2.4) is tentatively attributed to quantum localization in the non-reentrant spin glass phase. The magnitude of the temperature effects on (T) above as well as belowT _min indicates significantd-band contributions to the conductivity.     

Symmetries and Modular Intersections of Von Neumann Algebras

Let be von Neumann algebras acting on a Hilbert space and let be a common cyclic and separating vector. We say that have the modular intersection property with respect to if(1) -half-sided modular inclusions,(2) (If (1) holds the strong limit exists.) We show that under these conditions the modular groups of and generate a 2-dim. Lie group.This observation is the basis for obtaining group representations of Sl(2, )/Z ₂ generated by modular groups.