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.     

Hyperfine interactions in muonium-impurity complexes in silicon

The properties of paramagnetic complexes formed by muonium located near acceptor and donor impurities in silicon are calculated using the quantum chemical methods. The calculated data are compared to the experimentally observed characteristics of normal and anomalous muonium centers.     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

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ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

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The Micro-Canonical Point Vortex Ensemble: Beyond Equivalence

The fluid limit N is constructed for a sequence of ensembles of N classical point vortices in a finite domain ² whose ensemble densities (w.r.t. Liouville measure) are Gaussian approximations to (E-H). Letting the variance 0 after N has been taken, one recovers the special class of nonlinear stationary Euler flows that is expected from the micro-canonical ensemble. The construction improves over previous ones which either had to regularize the logarithmic singularities of the point vortex Hamiltonian or had to assume equivalence of ensembles. In particular, nonequivalence between micro-canonical and canonical ensemble prevails for certain geometries where conditionally stable configurations with negative 'global vortex pair-specific heat' can and do exist in the micro-canonical but not in the canonical ensemble.     

Определение средней величины кристаллик ов кварца И графита на основани и первичной экстинкц ии

— —10 ^–4 —10 ^–2 . , . , , , , , .     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

Stationary states of an electron in the field of a hole in an ionic crystal

An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e²/r [1+exp (–qr].

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s- , –e²/r [1+exp (–qr].

     

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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. . , 0,47 eV . , .

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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.     

BЛИЯHИE CBETA HA MOHOКPИCTAЛЛИЧECКИE ПЛACTИHКИ AgCl

The paper deals with the influence of light,=403 m, on the absorption of single-crystal plates of AgCl, grown by the capillary method. It was found that crystals with blue luminescence show no maximum in the region measured. For crystals with green luminescence a broad absorption maximum was found at – 590 m, which is partly bleached during further irradiation by light from the region of the absorption maximum. Measurements were preformed at room temperature.

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The use of the repulsive potential in the quantum theory of solids

A new method is proposed for calculating the energy in certain special points of the Brillouin zone. The wave functions of valence and conduction electrons are given in the form of the linear combination of plane waves and the orthogonality condition of these functions to the wave functions of lower states is replaced by the repulsive potential. The practical application of this very simple method is illustrated on the energy spectrum of silicon in the centre of the Brillouin zone. It is proved that the results are comparable with some other methods, e. g. the orthogonalized plane-wave method.

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The basic thesis of this paper, together with concrete calculation of the energy spectrum of diamond, was delivered at the Czechoslovak-Polish conference in Sopoty in November 1956.

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In conclusion the autor would like to thank K. Trnková for carrying out the numerical calculations.     

The problem of the imperfection of a world,itself created by a perfect god

The two main arguments concern(1) the presence of an enlightened complementarity between philosophic (including scientific) and religious (not including mystic) thought, and(2) the necessity to postulate a threefold relationship whenever one is to gain knowledge of any kind. They are both inspired by physics (from Bohr's strict complementarity, resp. from Newton's fundamental postulate).God's perfection resides at least in Symmetry in a generalized (not restrictively spatial) sense. Yet, as the argument goes, Space does not exist as a thing. Consequently, the Great Geometer (God) cannot dwell within a World He creates, and it is wrong to speak about His (God's) existence; for, existence is bound to the temporal, and Time is, together with the World, part of God's creation. Thus the only possible creation consists in God separating World and Time from Himself: This is the paradigm of Symmetry-breaking.Polytheistic mythologies all assume such and such imperfection of their deities; hence perfection is meaningful for monotheism only. A relationship of a threefold (trinitary) nature must then obtain between God, World, and Time; this is analogous to Newton's postulate relating force, momentum and time. Just as the latter and its specific generalizations must be found true by verification, the said threefold relationship must also be found true: within philosophic thoughtmore geometrico (in a generalized sense), within religious thoughtmore hymnometrico. Yet the complementarity (called enlightened) arising between the two kinds of thought is of a higher nature than Bohr's strict complementarity. While it can be understood from the role assumed by language itself, it can however only be disposed of within mystic contemplation.Dedicated to Sir KARL POPPER on the occasion of his 90th birthday.     

ЕСТЕСТВЕННЫЙ ФОН ПРИ ИЗМЕРЕНИИ РАДИОАКТИ ВНЫХ АЭРОЗОЛЕЙ

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Wave chaos in quantum systems with point interaction

We study perturbations of the quantized version ₀ of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of ₀ are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf     

Inertial frames of reference: Mass coupling to space and time

We consider a new expression for the dependence of mass on velocity, more general than the corresponding law of the special theory of relativity (STR). The deviations from the STR become large with increasing rest mass. One should therefore measure the dependence of mass on velocity for objects with a large rest mass. The theory predicts that particles with real mass can travel with hyperlight velocities. The space-time picture discussed here is close to Mach's conception: It is assumed that the dynamical behavior of a particle in uniform translational motion is due to the action of all the other masses in the universe. Space-time is eliminated as an active cause and, in contrast to the STR, is not absolute within the theory discussed here. It turns out that effects based on the new transformation formulas (from the coordinates and time in a stationary frame to the coordinates and time in a moving frame) are identical to those expected from the Lorentz transformations. For example, it is known that rapidly moving mesons decay with a longer half-life than stationary mesons and the STR describes this effect quantitatively. However, there is no strong evidence for the validity of the STR because the theory given in this paper predicts the same result.     

МОДЕЛИРОВАНИЕ ЭЛЕКТ РОННО-ОПТИЧЕСКИХ СИС ТЕМ С ОСЕВОЙ СИММЕТРИЕЙ П РИ ПОМОЩИ СЕТИ СОПРОТИВЛЕНИЙ

The paper explains the theory of modelling electrostatic fields by a resistance network. The conditions, which the resistance network must satisfy, are derived and the question of modelling electrodes of different shapes is solved. The finished network and the results obtained on it when modelling a jet for a linear h-f accelerator of electrons are described. Particular attention is paid to the influence of a space charge, the modelling of which is an advantage of this method.

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Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (electron) in a classical fluid (of protons) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form atomic bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the cell model of a fluid. We find that when the system is at low density the spectrum of the electron-proton pair density matrix has, in addition to a continuous part, a discrete part that is associated with atomic bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.     

The use of time-dependent projection operators in the derivation of master equations

In this paper we generalize our previous work on the use of time-dependent projection operators for the derivation of master equations for general systems. Previously we had generalized the usual time-independent projection operator approach to include time-dependent projection operators, in which the relevant part of the full density operator is considered to be the uncorrelated part of the full density operator. The irrelevant part of the density operator was then the part describing the correlations between the coupled systems. In the present work we present new time-dependent projections operators which have the property that some correlations between the interacting subsystems are placed in the relevant part of the distribution function and the remaining correlations are placed in the irrelevant part of the distribution function.     

Observables in a noncommutative approach to the unification of quanta and gravity: a finite model

We further develop a noncommutative model unifying quantum mechanics and general relativity proposed in Gen. Rel. Grav. (36, 111–126 (2004)). Generalized symmetries of the model are defined by a groupoid given by the action of a finite group on a space E. The geometry of the model is constructed in terms of suitable (noncommutative) algebras on . We investigate observables of the model, especially its position and momentum observables. This is not a trivial thing since the model is based on a noncommutative geometry and has strong nonlocal properties. We show that, in the position representation of the model, the position observable is a coderivation of a corresponding coalgebra, coparallelly to the well-known fact that the momentum observable is a derivation of the algebra. We also study the momentum representation of the model. It turns out that, in the case of the algebra of smooth, quickly decreasing functions on , the model in its quantum sector is nonlocal, i.e., there are no nontrivial coderivations of the corresponding coalgebra, whereas in its gravity sector such coderivations do exist. They are investigated.This revised version was published online in April 2005. The publishing date was inserted.