Transquantum Dynamics

Segal proposed transquantum commutation relations with two transquantum constants , besides Planck's quantum constant and with a variable i. The Heisenberg quantum algebra is a contraction—in a more general sense than that of Inönü and Wigner—of the Segal transquantum algebra. The usual constant i arises as a vacuum order-parameter in the quantum limit ,0. One physical consequence is a discrete spectrum for canonical variables and space-time coordinates. Another is an interconversion of time and energy accompanying space-time meltdown (disorder), with a fundamental conversion factor of some kilograms of energy per second.     

On the pointwise behavior of semi-classical measures

In this paper we concern ourselves with the small asymptotics of the inner products of the eigenfunctions of a Schrödinger-type operator with a coherent state. More precisely, let _j and E _j denote the eigenfunctions and eigenvalues of a Schrödinger-type operator H with discrete spectrum. Let _(x,) be a coherent state centered at the point (x, ) in phase space. We estimate as 0 the averages of the squares of the inner products ( _a ^(x,) , _j ) over an energy interval of size around a fixed energy, E. This follows from asymptotic expansions of the form for certain test function and Schwartz amplitudes a of the coherent state. We compute the leading coefficient in the expansion, which depends on whether the classical trajectory through (x, ) is periodic or not. In the periodic case the iterates of the trajectory contribute to the leading coefficient. We also discuss the case of the Laplacian on a compact Riemannian manifold.Research supported in part by NSF grant DMS-9303778     

On the failure of the time-energy uncertainty principle

We establish, for the quantum system made up of a single free particle, the formula E t(v/c) , where E is the precision to whichE can be ascertained in time t. The measurement can be carried out with zero disturbance inE itself.     

Electronic structure and optical spectra of YBa2Cu3O7−δ thin films in the infrared and UV region

Optical reflectance of YBa₂Cu₃O_7- thin films grown by laser ablation is measured within photon energies of 0.1 eV to 3.5 eV at room temperature. The spectra can be fit congruently with the anisotropic dielectric constants which take account of the intraband free carrier transition and interband transition. The anisotropic plasma frequencies are simulated to be _pl=2.18 eV and _ch=2.80 eV contributed from free carriers on the plane and in the chain, respectively. The interband transition occurs near 2.5 eV and is pertinent to a rather broad line width.     

Smoothed Wigner functions: a tool to resolve semiclassical structures

The Wigner and Husimi distributions are the usual phase space representations of a quantum state. The Wigner distribution has structures of order 2. On the other hand, the Husimi distribution is a Gaussian smearing of the Wigner function on an area of size and then, it only displays structures of size . We have developed a phase space representation which results a Gaussian smearing of the Wigner function on an area of size , with 1. Within this representation, the Husimi and Wigner functions are recovered when =1 and respectively. We treat the application of this intermediate representation to explore the semiclassical limit of quantum mechanics. In particular we show how this representation uncover semiclassical hyperbolic structures of chaotic eigenstates.     

ИССЛЕДОВАНИЕ ЭРОЗИЙ НОГО ДЕЙСТВИЯ ИМПУЛЬ СНЯХ ЭЛЕКТРИЧЕСКИХ РАЗРЯ ДОВ С СЛАБЫМ ТОКОМ

50–100 , 1–2 1–10 . - . - . , , - . -.     

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 .     

Twisted Lie Group C*-Algebras as Strict Quantization

A nonzero 2-cocycle Z2(g, R) on the Lie algebra g of a compact Lie group G defines a twisted version of the Lie–Poisson structure on the dual Lie algebra g*, leading to a Poisson algebra C (g*()). Similarly, a multiplier c Z2(G, U(1)) on G which is smooth near the identity defines a twist in the convolution product on G, encoded by the twisted group C-algebra C*(G,c). Further to some superficial yet enlightening analogies between C (g*()) and C*(G,c), it is shown that the latter is a strict quantization of the former, where Plancks constant assumes values in (Z\{0})-1. This means that there exists a continuous field of C*-algebras, indexed by 0 (Z\{0})-1, for which A0= C0(g*) and A=C*(G,c) for 0, along with a cross-section of the field satisfying Diracs condition asymptotically relating the commutator in A to the Poisson bracket on C(g*()). Note that the quantization of does not occur for =0.     

The elastic coupling between longitudinal and transversal vibrations оf isotropic rods II. Rods of circular cross-section

The new approximative method for calculating the frequencies of longitudinal vibrations of isotropic homogeneous rods described in part I. is used for rods of circular crosssection. Similarly to the rods of rectangular cross-section there does not exist any dead zone of frequencies.

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II.

, I. (. . 366), . , , .

     

On the photo-electroluminescence of ZnS-Cu

The influence of weak ultra-violet irradiation on the brightness waves of electroluminescence is investigated for two types of ZnS-Cuphosphors. The observed effects (increase in brightness in the primary peak and its phase shift, the disappearance of the secondary peak) are explained on the basis of present-day conceptions on electroluminescence.

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ZnS-Cu

ZnS-Cu. ( , ) .

     

The Phase of a Quantum Mechanical Particle in Curved Spacetime

We investigate the quantum mechanical wave equations for free particles of spin 0, 1/2, 1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is S/ = p dx /, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple manageable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has exactly the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin 1 wave equations yield the above phase only to lowest order in . We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in . For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations.     

Short-time propagator on curved spaces

It is shown that the standard WKB-approximation (the approximation of the first order in) to the propagator is not sufficient for the construction of the short-time propagator on curved spaces. The proper short-time propagator can be obtained by means of the second order (in) WKB-approximation and then no subtraction of a quantum correction proportional to ² from the original Lagrangian is necessary.The authors are indebted to J. Tolar for valuable critical comments and advices.     

Influence ofp-shell nuclei structure on the formation of hypernuclear resonances

In the translationally invariant shell model the supermultiplet structure of the 1 states ofp-shell hypernuclei is studied. Fragmentation of the strangeness analogue state is discussed and the spectroscopic amplitudes for all decay channels are estimated.Presented at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Oscillation correction to the electron density of an atom

The oscillation correction to the electron density of an atom in the Thomas-Fermi model is calculated with the help of the method of Green's functions and continuous integration. This correction has a nonanalytic dependence on Planck's constant and cannot be obtained by the usual methods, which employ an expansion in terms of a small parameter proportional to .The author is deeply grateful to L. Ya. Kobelev for suggesting this subject and supervising the work.     

Higher approximations for quasiclassical trajectory-coherent states of a nonrelativistic particle

A scheme is developed for constructing higher approximations for quasiclassical trajectory-coherent states of a nonrelativistic particle. The basic property of these states is that the quantum-mechanical mean of the coordinate and momentum operators in these states are accurate solutions of the Hamiltonian system in the limit as 0. The quantum-mechanical means of the energy, coordinate and momentum operators and the mean square deviations from the classical trajectory are calculated with an accuracy of order 0(²). Higher approximations are obtained by the Maslov complexgrowth method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 14–18, October, 1987.     

тЕМпЕРАтУРНАь жАВИс ИМОсть ЁФФЕктА ДЕМБЕ РА НА AgCl

AgCl . –190C +20C. –60C . T–130°C, . .

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The temperature dependence of the Dember effect on AgCl

The condenser method was used to study the temperature dependence of the Dember effect on monocrystalline plates of AgCl when illuminating with ultra-violet light. The dependence was studied from –190C up to room temperature. At approximately –60C a change in the effect from negative to positive was found. At temperatures around –130C there was a maximum the magnitude of which changed when the measurement was repeated. A possible interpretation of the experiments is put forward.

     

Low-energy elementary surface excitations of symmetric films of liquid4He atT=0 K

It is known that low-energy elementary excitations of symmetric films of liquid⁴He atT=0 K are characterized by a momentum q parallel to the surface and may be described by bound states. We have evaluated wave functions and energies of these states for both best short-ranged and optimal long-ranged correlations. Quantities of physical interest may be expressed in terms of these eigenstates and, in particular, for very small momenta (q<0.2 Å^–1) they are mainly determined by the contribution due to the lowest-lying one. We propose analytic expressions for the lowest-lying excitations and fluctuations in the long-wavelength limit. It is proved that in this limiting case, the excitation energy _LW(q) and the averaged static structure functionS _LW(q) should go linearly to zero asq0, whereas the averaged direct correlationX _LW ^Dg (q) should diverge at the origin as 1/q. It is shown that numerical solutions exhibit the expected long-wavelength behavior provided that optimal correlations are used. All these results are displayed in a series of figures and are discussed in detail.     

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.     

Models of optical absorption in amorphous semiconductors at the absorption edge — A review and re-evaluation

Davis-Mott and Tauc models of optical absorption at the absorption edge in the high absorption coefficient region (10⁴cm^–1) are carefully reviewed with regard to their theoretical foundations, assumptions, mathematical derivations, and results. The full implications of these models are exploited, and it is found that the Davis-Mott model for negligible matrix elements between localised states could account for the cubic power law behaviour of with photon energy of some amorphous semiconductors such as a-Si. A fractional power law to find the optical band gapE _opt, of the form [ (–E _opt)^r; 2r3] based on Davis-Mott model is proposed in which the indexr can be a function of disorder. The Tauc model has further been extended to the case of negligible matrix elements between localised states, in which the same square power law for vs. with the same meaning of the optical gap as in the original Tauc model has resulted. A consideration of the case of unequal matrix elements for those transitions between localised states and those between extended states is also included. The meaning ofE _opt has been re-assessed and it is emphasized that it is an extrapolation of delocalised states to the zero of the density of states rather than a threshold energy for the onset of some kind of optical transitions.This paper is cordially dedicated to Professor C. A. Hogarth who taught us the Physics of amorphous materials.     

тРЕхлУЧЕВыЕ ВжАИМОД ЕИстВИь π−-МЕжОНОВ с ИМпУльсОМ 4 GeV/c В пРОпАНОВОИ пУжыРь кОВОИ кАМЕРЕ

Altogether 1648 cases of three-prong interaction of ^–-mesons with a 4 GeV/c impulse were found on 90 000 pictures from a propane bubble chamber 55 × 28 × 14 cm³ in size; all three secondary particles were pions, two having a negative and one a positive charge. Analysis of these cases showed that at an impulse of 4 GeV/c of primary ^–-mesons the process of the coherent production of pions was not observed. On the other hand, this analysis led to an interesting result: (19 ± 9) % of the total number of (⁺, ^–) pairs in A interactions is due to the decay of the meson ^{0 +} + ^–. A value of = (764 ± 36) MeV was obtained for the mass of mesons and = (166 ± 55) MeV fort he width of its resonance curve. Investigation of the distribution of masses in the case in question gave no answer due to the insufficiently determined course of the background curve.

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On leave from:Institute of Physics, Czechosl. Acad. Sci., Lumumbova 1, Praha 8, Czechoslovakia.

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Joint Institute of Nuclear Research, Dubna, USSR.

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Institute of Physics, Czechosl. Acad. Sci., Lumumbova 1, Praha 8, Czechoslovakia.

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Faculty of Mathematics and Physics, Charles University, Brehová 7, Praha 1, Czechoslovakia.

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