Semiclassical quantum mechanics

We consider the 0 limit of the quantum dynamics generated by the HamiltonianH()=–(²/2m)+V. We prove that the evolution of certain Gaussian states is determined asymptotically as 0 by classical mechanics. For suitable potentialsV inn3 dimensions, our estimates are uniform in time and our results hold for scattering theory.Supported in part by the National Science Foundation under Grant PHY 78-08066     

Large deviations from classical paths. Hamiltonian flows as classical limits of quantum flows

We prove that in the limit0, the probability for the paths of the stochastic jump process associated to the quantum time evolution to be in a tublet around the classical trajectory is of order 1–exp{–A/}. We give some applications of this result to the study of the classical limit of Wigner functions.     

The shape resonance

For a class of Schrödinger operatorsH:=–(²/2m)+V onL ²( ⁿ ), with potentials having minima embedded in the continuum of the spectrum and non-trapping tails, we show the existence of shape resonances exponentially close to the real axis as 0. The resonant energies are given by a convergent perturbation expansion in powers of a parameter exhibiting the expected exponentially small behaviour for tunneling.     

Effects of the blackbody radiation on the harmonically bound electron-energy level shifts and consistency conditions

The influence of the vacuum radiation field on the harmonically bound electron (frequency ₀) is considered. The electron is minimally coupled to the blackbody radiation field. The dynamics of the system is exactly solvable. The high (k _B T₀) and low (k _B T₀) temperature expansions of the kinetic and potential energy are given. In the high temperature regime theT ²-dependent dynamic Stark shift is found whereas in the low temperature regime there is no temperature dependent shift. The position correlation function of the electron shows in the low temperature regime a unclassical algebraic decay (t ^–4,t/k _B T).     

Continuous quantum measurements and the action uncertainty principle

The path-integral approach to quantum theory of continuous measurements has been developed in preceding works of the author. According to this approach the measurement amplitude determining probabilities of different outputs of the measurement can be evaluated in the form of a restricted path integral (a path integral in finite limits). With the help of the measurement amplitude, maximum deviation of measurement outputs from the classical one can be easily determined. The aim of the present paper is to express this variance in a simpler and transparent form of a specific uncertainty principle (called the action uncertainty principle, AUP). The most simple (but weak) form of AUP is S, whereS is the action functional. It can be applied for simple derivation of the Bohr-Rosenfeld inequality for measurability of gravitational field. A stronger (and having wider application) form of AUP (for ideal measurements performed in the quantum regime) is | ^t (S[q]/q(t))q(t)dt|, where the paths [q] and [q] stand correspondingly for the measurement output and for the measurement error. It can also be presented in symbolic form as (Equation) (Path) . This means that deviation of the observed (measured) motion from that obeying the classical equation of motion is reciprocally proportional to the uncertainty in a path (the latter uncertainty resulting from the measurement error). The consequence of AUP is that improving the measurement precision beyond the threshold of the quantum regime leads to decreasing information resulting from the measurement.     

The role of electronic density of states in metallic Lanthanum

Observations of X-ray photoabsorption in metallic Lanthanum in the vicinity of the 3d _5/2-edge are given. Two separated absorption peaks are detected at the quantum energies =830.6eV and =834.0eV. The results are interpreted according to the model given in communication I–IV [1].     

Notes on the classical and the nonrelativistic limits in quantum mechanics

A method is presented which can be used to discuss both the classical and also the nonrelativistic limit of quantum mechanics. A one-to-one correspondence may be established between the asymptotic convergence of the resolvent and that of the timedependent solution. In so far as the question of dynamics is concerned we investigate the relation between families of nonrelativistic Hamiltonians and the corresponding Dirac-Hamiltonians when c± or when c±0. The nonrelativistic free theory formally shows the same pattern when ±0 (the classical limit) or when ±. The investigation finally shows how the asymptotic convergence of the relativistic theory can take place under some fairly general conditions of the radiation field.     

О ВЛИЯНИИ НАПЯЖЕНИЯ, ВОЗНИКАЮЩЕГО ПРИ ПРЕ ЦИПИТАЦИИ, НА КОЭРЦИТ ИВНУЮ СИЛУ ФЕРРОМАГНЕТИКО В

, . - , m. . . , , , . , , Fe₃C .     

The borderline between classical physics and quantum theory: Towards a theory of the Planck's constant

A dynamical mechanism is discussed to account for the numerical value of the Planck's constant .Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.     

ЭЛЕКТРОПРОВОД НОСТЬ И ТЕРМОЗЛЕКТРОДВИЖУ ЩАЯ СИЛА СЕРОГО ОЛОВА

, , , . .     

Beitrag zum problem der Exo-Emission von festkörpern

Zusammenfassung Es sind die Versuchsergebnisse des Studiums der Photoerscheinungen bei verschieden bearbeiteten Metallen (Au, Al, Pt) angeführt. Die Metallfolien wurden an der Luft mit UV-Licht bestrahlt und gleichmä\ig erwärmt. Die Ergebnisse wurden vom Gesichtspunkt der neueren Kenntnisse über Adsorption, Katalyse und Oxydation diskutiert. Daraus sind Folgerungen gezogen worden, die in manchen Fällen zu Bedenken über die Klärung der Exo-Emissions-Glow-Kurven zu führen scheinen.

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Au, Al, Pt . , . , . , .

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Ich möchte auch an dieser Stelle meinen besten Dank Frau K. Listoová aussprechen für die mit gro\er Sorgfältigkeit durchgeführten Versuchsreihen und K. Huml für die Hilfe bei der Bearbeitung der Versuchsergebnisse.     

Сцинтилляционный сп ектрометр с сложение м импулъсов от двух кри сталлов

, . , .     

The distribution of dislocations in silicon iron single-crystals grown from the melt

The distribution of dislocations in a crystal of an Fe-4.2% Si alloy prepared from the melt is studied microscopically and, by X-ray diffraction after rendering them visible by anodic dissolving. The dislocations are also studied inside the crystal by successively grinding the surface. The density of the dislocations inside the blocks is determined by calculation from microphotos, the density of the dislocations forming the boundaries between the blocks by measuring the angles between the lattices of neighbouring blocks. It is found that the dislocations are distributed very unevenly in the crystal and most of them form complicated boundaries of blocks, similarly as with ionic crystals. The distribution of dislocations is also discussed from the point of view of their formation and conclusions are reached as to the preparation of single crystals having a smaller number of dislocations.

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Fe-Si,

- Fe-4,2%Si, , . . , , — . , , . .

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The author is indebted to Candidates of Mathematics and Physics, F. Kroupa and J. Kaczér, for careful reading and advice whereby they helped to give greater depth and accuracy to this paper. He thanks Z. Tahal and M. Honegrová for initiative shown in helping to prepare the single crystals and during exacting experimental work, and S. Kadeková for aid in adjusting the spectrometer.     

Quantum hair and quantum gravity

A black hole may carry quantum numbers that arenot associated with massless gauge fields, contrary to the spirit of the no-hair theorems. The quantum hair is invisible in the classical limit, but measurable via quantum interference experiments. Quantum hair alters the temperature of the radiation emitted by a black hole. It also induces non-zero expectation values for fields outside the event horizon; these expectation values are non-perturbative in , and decay exponentially far from the hole. The existence of quantum hair demonstrates that a black hole can have an intricate quantum-mechanical structure that is completely missed by standard semiclassical theory.Based on an essay which received second award from the Gravity Research Foundation, 1991     

Photo-piezoelectric effect in semiconductors

A new photo-voltaic effect was observed which is caused by inhomogeneous distribution of the pressure in a semiconductor. Its production can be explained by the dependence of the energy gap on the pressure.

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Der Einfluss der Plastischen Verformung durch Kaltwalzen auf die Koerzitivkraft

Zusammenfassung Es werden die Ergebnisse der Messungen der Koerzitivkraft von Eisen, Nickel und einiger Fe-Ni-Legierungen in Abhängigkeit von der plastischen Verformung durch Kaltwalzen angegeben. Gemessen wurde in Richtung parallel und senkrecht zur Walzrichtung. Die Ergebnisse werden insbesondere vom Gesichtspunkt des Einflusses der Versetzungen und der einachsigen induzierten Anisotropie diskutiert.

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Für die wertvollen Diskussionen und das Durchlesen der Arbeit danken wir den Kollegen J. Kaczér und V. Janovec, für die wirkungsvolle Hilfe bei den Messungen Koll. J. Grolmus.     

Probability Backflow for a Dirac Particle

The phenomenon of probability backflow, previously quantified for a free nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is shown that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist positive-energy states in which the particle certainly has a positive momentum in a given direction, but for which the component of the probability flux vector in that direction is negative. It is shown that the maximum possible amount of probability that can flow backwards, over a given time interval of duration T, depends on the dimensionless parameter = (4/mc²T)^1/2, where m is the mass of the particle and c is the speed of light. At = 0, the nonrelativistic value of approximately 0.039 for this maximum is recovered. Numerical studies suggest that the maximum decreases monotonically as increases from 0, and show that it depends on the size of m, , and T, unlike the nonrelativistic case.     

СПЕКТРАЛЬНЫЙ СОСТАВ И ИНТЕНСИВНОСТЬ ЛЮМИНЕСЦЕНТНОГО СВЕ ЧЕНИЯ ФОТОГРАФИЧЕСК ОЙ ЭМУЛЬСИИ

- - .     

Determination op energy gap width in some semi-conductors

The formula derived by the author for the width of the energy gap is compared with experiment for GaSb, InAs, InSb, and InSb. GaSb semi-conductors. The agreement is good.

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GaSb, InAs, InSb, InSb. GaSb. o.

     

ССЛЕДОВАНИЕ РАСПАДА Dy155 → Tb155

The gamma-spectrum and coincidences of gamma-rays appearing in Dy¹⁵⁵ Tb¹⁵⁵ decay have been measured with the aid of a scintillation gamma-spectrometer. The Dy¹⁵⁵ source has been obtained by a repeated chromatographic separation from Ho fraction produced by a spallations reaction Ta+p(E _p=660 MeV). Dy¹⁵⁵ appears as a decay product of Ho¹⁵⁵ (T _1/2= =45 min). In the gamma-spectrum new transitions in the energy range of 1170–2000 keV have been observed. As a result of- coincidence measurements we get a new energy level (1820±15 keV) of Tb¹⁵⁵.

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, Dy¹⁵⁵ . . .