On the indistinguishability of classical particles

If no property of a system of many particles discriminates among the particles, they are said to be indistinguishable. This indistinguishability is equivalent to the requirement that the many-particle distribution function and all of the dynamic functions for the system be symmetric. The indistinguishability defined in terms of the discrete symmetry of many-particle functions cannot change in the continuous classical statistical limit in which the number density n and the reciprocal temperature become small. Thus, microscopic particles like electrons must remain indistinguishable in the classical statistical limit although their behavior can be calculated as if they move following the classical laws of motion. In the classical mechanical limit in which quantum cells of volume (2)³ are reduced to points in the phase space, the partition functionTr{exp(–) for N identical bosons (fermions) approaches (2)^–3N(N!) ... d³r₁ d³p₁ ... d³r_N d³p_N exp(–H). The two factors, (2)^–3N and (N!)^–1, which are often added in anad hoc manner in many books on statistical mechanics, are thus derived from the first principles. The criterion of the classical statistical approximation is that the thermal de Broglie wavelength be much shorter than the interparticle distance irrespective of any translation-invariant interparticle interaction. A new derivation of the Maxwell velocity distribution from Boltzmann's principle is given with the assumption of indistinguishable classical particles.     

Rate equations in the hopping transport

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limitsN, 0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limitsN, 0 and c) the same boundary conditions but reversed order of limiting processes 0,N typical of e.g. numerical and percolation treatments. (N and are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes 0,N+ andn+ (N–n+) for local shifts of the chemical potential _n in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of _r.     

Random surfaces with two-sided constraints: An application of the theory of dominant ground states

We consider some models of classical statistical mechanics which admit an investigation by means of the theory of dominant ground states. Our models are related to the Gibbs ensemble for the multidimensional SOS model with symmetric constraints _x m/2. The main result is that for ₀, where ₀ does not depend onm, the structure of thermodynamic phases in the model is determined by dominant ground states: for an evenm a Gibbs state is unique and for an oddm the number of space-periodic pure Gibbs states is two.     

Effect of radiation on hydromagnetic vertical channel flow

The effect of radiation on the combined free and forced convection flow of an electrical conducting viscous fluid through an open-ended vertical channel in slip flow regime and permeated by a constant magnetic field in transverse direction has been considered. The temperature on the walls has been supposed to vary linearly with distance. On the assumption of optically thin limit, the expressions for velocity, induced magnetic field, temperature, flow rate and the heat transfer coefficient due to thermal conduction are obtained and the influence of radiation on these solutions are shown either graphically or in tabulated forms.Notation x, y, z cartesian coordinates - v velocity - 2L distance between the channel walls - B ₀ applied magnetic field - B induced magnetic field - T temperature - p pressure - density - magnetic permeability - v kinematic coefficient of viscosity - conductivity of the fluid - g acceleration due to gravity - coefficient of volume expansion - thermal diffusivity of the fluid - c _p specific heat at constant pressure - q_R radiative heat flux - k absorption coefficient - e _b Plank function - T 0 reference temperature - N vertical temperature gradient - M= B₀L[/(v)]^1/2 Hartmann number - R _a=gNL⁴/(v) Rayleigh number - P_m = magnetic Prandtl number - 2d₁, 2d₂ thickness of the walls - ₁, ₂ conductivities of the walls     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Harmonic maps with defects

Two problems concerning maps with point singularities from a domain C ³ toS ² are solved. The first is to determine the minimum energy of when the location and topological degree of the singularities are prescribed. In the second problem is the unit ball and =g is given on ; we show that the only cases in whichg(x/|x|) minimizes the energy isg=const org(x)=±Rx withR a rotation. Extensions of these problems are also solved, e.g. points are replaced by holes, ³,S ² is replaced by ^N ,S ^N–1 or by ^N , P ^N–1, the latter being appropriate for the theory of liquid crystals.Work partially supported by U.S. National Science Foundation grant PHY 85-15288-A02     

On the ferromagnetism of thin films

In this paper the magnetic properties of ferromagnetic thin layers are studied by calculating the partition function for the magnetic system inKirkwood's approximation of the second order. The results obtained for the Curie temperature and the magnetization are in somewhat better agreement with the experiment than those obtained by Valenta.

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The author extends his thanks to the group of research workers who performed the numerical calculation of the Curie temperatures on the computer CIFA 1, as well as gratitude to Dr. l. Valenta for so kindly supplying information on the results of his investigations on the same subject.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids

In a Coulomb fluid confined to a domain V, the dielectric susceptibility tensor _V depends on the shape of V, even in the thermodynamic V limit. This paper deals with the classical two-dimensional one-component plasma formulated in an elliptic V-domain, equilibrium statistical mechanics is used. For the dimensionless coupling constant =even positive integer, the mapping of the plasma onto a discrete one-dimensional anticommuting-field theory provides a new sum rule. This sum rule confirms the limiting value of _V predicted by macroscopic electrostatics and gives a finite-size correction term to _V.     

Химическая сенсиБил изация фотографичес кой эмульсии

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Chemical sensiblilisation of photographic emulsion

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, 7. V. 1953 .     

The quantum efficiency of the internal photo-electric effect in indium antimonide

A method is described for measuring the relative quantum efficiency of the internal photo-electric effect in semi-conductors by simultaneously measuring the photo-magnetoelectric and photo-conductive effect. The results of measurements on indium antimonide are given. The quantum efficiency begins to increase if the energy of the photon exceeds 0·47 eVat room temperature. The quantum efficiency as a function of the energy of the photon is analysed on the basis of the conception of impact ionization and it is shown that a study of the structure of this curve can supply information on the, band structure of a semi-conductor in the region of high energies of electrons and holes.

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The authors thank M. Závtová and M. Vantuchová for efficient help with the measurements, K. mirous and V. Vrchovská for preparing the material, E. Antoník for critical remarks and M. Matyá and A. Müller for determining the constants of the material.     

Temperature Dependence of the Gibbs State in the Random Energy Model

We consider the problem of temperature dependence of the Gibbs states in two spin-glass models: Derrida's Random Energy Model and its analogue, where the random variables in the Hamiltonian are replaced by independent standard Brownian motions. For both of them we compute in the thermodynamic limit the overlap distribution ^N _{i=1 i i} /N[–1,1] of two spin configurations , under the product of two Gibbs measures, which are taken at temperatures T,T respectively. If TT are fixed, then at low temperature phase the results are different for these models: for the first one this distribution is D _{0 0}+D _{1 1}, with random weights D ₀, D ₁, while for the second one it is ₀. We compute consequently the overlap distribution for the second model whenever T–T0 at different speeds as N.     

Kinetics of random sequential parking on a line

We study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line. For the simplest fixed-length parking distribution the model reduces to the known car-parking problem and we present an alternate solution to this problem. We also consider the general homogeneous case when the parking distribution varies asx ^–1 atx 1 with the lengthx of the filling interval. We develop a scaling theory describing such mixture-deposition processes and show that the scaled hole-size distribution(), with =xt ^z a scaling variable, decays with the scaled mass as ^–exp(—const·¹⁺) as . We determine scaling exponentsz and, and find that at large times the coverage(t) has a power-law form 1 – (t)t ^–v with nonuniversal exponent =(2–)/(1+) depending on the homogeneity index .     

Über den Einfluss von Stickstopf auf die Exoelektronenemission von Germanium

Zusammenfassung Es wurde der Einfluß eines Bombardements mit Stickstoffionen vor der Erregung untersucht und gezeigt, daß die Stiekstoffatome eine große Rolle bei der Entstehung des Emissionsmaximums bei 150° spielen.

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, 150°C.

     

Characteristics analysis of metal-clad and absorptive dielectric waveguides by a simple and accurate perturbation method

We present a simple and accurate method for characteristic analysis of metal-clad dielectric waveguides and absorptive waveguides. The real partN of the complex modal indexN=N + iN is obtained by solving the corresponding real eigenvalue equation, and the imaginary partN is given by (n/), where= + i is the complex dielectric constant of the absorptive layer, and N/ is obtained by numerical differentiation. The method is straightforward, and the cumbersome solution of complex transcendental equations is completely eliminated. Results for simple structures are in good agreement with those obtained by exact analysis.     

The distribution of neutron density in the vicinity of a partly inserted black rod in two-group approximation

The neutron density in the vicinity of a black cylindrical rod partly inserted in a bare reactor is calculated and illustrated by a numerical example. The starting point is a two-group diffusion theory approximation. While the dependence of the effect of the rod on the insertion depth can be calculated simply by means of perturbation theory, the question of the neutron density estimate in the vicinity of the rod is considerably more difficult and in some considerations the estimate of the neutron density caused by the presence of the rod is indispensable. The method makes it possible to determine the reactivity value of the rod in dependence on the insertion depth and especially the neutron density deformation in the vicinity of the rod.

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In conclusion the author thanks J. Svato for help in carrying out the numerical calculations.     

Phonon assisted quantum diffusion in a periodic potential

We study the diffusion of a quantum heavy particle moving in a one dimensional strongly corrugated periodic potential, and interacting with a phonon bath.By integrating out the phonons degrees of freedom we derive an effective action functional for the particle, which includes a non-local self-interacting term whose strength is proved to be the classical friction coefficient .Using an instanton approach we express the velocity-velocity correlation function, and thus the mobility, of the brownian particle in terms of the charge density-density correlation function of a classical Coulomb gas, which in the strong corrugation limit has a very low fugacity.By making a virial expansion in the gas fugacity we evaluate the static mobility of the brownian particle as a function of the temperature, and we find two different behaviours: a diffusive behaviour at low friction, where decreases withT, and a localised behaviour at high friction, where increases withT.The cross-over between the two régimes takes place at a critical friction ₀, corresponding to the Kosterlitz-Thouless transition for the Coulomb gas.     

Спектралъный метод о пределения изотопно го состава свинца. Частъ II

, . , [1]. 1–4 mg PbJ₂, . (c. m. c.) PbI 4058 Å. , , - , 5–7%. 3–4% –183 °C. , . 10% . , .     

The Schrödinger equation and canonical perturbation theory

LetT ₀(, )+V be the Schrödinger operator corresponding to the classical HamiltonianH ₀()+V, whereH ₀() is thed-dimensional harmonic oscillator with non-resonant frequencies =(₁, ... , _d ) and the potentialV(q ₁, ... ,q _d) is an entire function of order (d+1)^–1. We prove that the algorithm of classical, canonical perturbation theory can be applied to the Schrödinger equation in the Bargmann representation. As a consequence, each term of the Rayleigh-Schrödinger series near any eigenvalue ofT ₀(, ) admits a convergent expansion in powers of of initial point the corresponding term of the classical Birkhoff expansion. Moreover ifV is an even polynomial, the above result and the KAM theorem show that all eigenvalues _n (, ) ofT ₀+V such thatn coincides with a KAM torus are given, up to order , by a quantization formula which reduces to the Bohr-Sommerfeld one up to first order terms in .     

Particle-like configurations of the electromagnetic field: An extension of de Broglie's ideas

Localised configurations of the free electromagnetic field are constructed, possessing properties of massive, spinning, relativistic particles. In an inertial frame, each configuration travels in a straight line at constant speed, less than the speed of lightc, while slowly spreading. It eventually decays into pulses of radiation travelling at speedc. Each configuration has a definite rest mass and internal angular momentum, or spin. Each can be of electric or magnetic type, according as the radial component of the magnetic or electric field vanishes in the rest frame, and each has an antiparticle. Any such configuration, of electric or magnetic type, is characterized in part by a set of labels (, ₀, ,l, m), where ₀ is the mean of the angular frequencies of the plane waves making up the configuration, is the variance of those frequencies, is a positive constant with dimensions of action, andl, m are angular momentum quantum numbers withl a positive integer andm an integer such that ml. The rest energy of the particle is ₀, its spin is m, and its lifetime is of the order of 1/. Its antiparticle has ₀ replaced by –₀.