The tensor product of one-particle representations of an infinite-dimensional Lie algebra

The recently proposed infinite-dimensional Lie algebra as a model of a symmetry scheme is studied from the point of view of its representations. We construct the tensor product of two one-particle representations of this algebra and study the reduction problem. A new series of representations having non-linear mass formulas is found. Some physical consequences for two-particle states are also discussed.The authors wish to thank Prof. V. Votruba for constant interest shown throughout this work and J. Formánek for valuable discussions.     

Thermodynamic theory of finite ferroelectric crystals with surface energy

The phenomenological Landau theory of phase transition is generalized to finite ferroelectric crystals with surface energy. Restrictions of the expansion imposed by the symmetry of the surface are considered, and further analysis is devoted to a special case. The solution in the approximation of constant polarization is discussed. Single domain states of a plate are analysed in greater detail.The authors are very grateful to Dr. V.Janovec and Dr. J.Fousek of the Czechoslovak Academy of Sciences for helpful discussions. Thanks are due to Prof. L.Valenta for the valuable discussions dealing with the magnetical analogical problem.     

Rotational quantum mechanics in hyperspherical coordinates

We present a new class of quantum-mechanical problems involving the rotation of a top in a spherically symmetric torque field. The eigenvalue problem is studied for the hyperspherical rotational oscillator. We introduce a new four-dimensional parity quantum number referring to integral spin values of the excited states of a spherical top.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–7, January, 1984.The author acknowledges useful discussions with Prof. A. G. Sitenko and with I. V. Simenog.     

Some properties of bound states in the three-body problem with separable potentials

A system of three identical bosons with the pair separable S-interaction is considered. The monotonic (Yamaguchi potential) and oscillating pair potentials for the three-alpha model of¹²C have been investigated. In the case of the Yamaguchi potential many excited states (second, third, etc.) have been found.The author is thankful to Prof. V. G. Neudatchin and Prof. Yu. F. Smirnov for valuable discussions on the problems concerned.     

Splitting of the lower subband of Hubbard fermions in the Shubin–Vonsowsky model under the influence of strong intersite correlations

The diagram technique for Hubbard operators is used to investigate the influence of intersite Coulomb interactions on the energy structure and Cooper instability of strongly correlated fermions. Allowance for intersite correlations in doped Mott-Hubbard insulators is shown to lead to a splitting of the lower subband of Hubbard fermions and to the formation of a band of fluctuation states as soon as the intersite interaction energy becomes comparable to or exceeds the mean kinetic energy. The spectral intensity of the splitoff band is proportional to the root-mean-square fluctuation of the occupation numbers and increases with doping level. The predicted effect changes significantly the structure of the density of electronic states. This leads to a renormalization of the pole of the scattering amplitude in the Cooper channel and manifests itself as a nonuniform (in electron concentration) modification of the dependence of the critical superconducting transition temperature.     

Complete fourth-order calculation of correlation energy for closed-shell molecules by diagrammatic RSPT

Starting from the diagrammatic version of Wigner's (2n+1) rule the formulae for the correlation energy of closed-shell molecules are derived. This approach allows to formulate in the very compact way the correlation energy through the fourth order of perturbation theory, a repeating evaluation of the same intermediate terms is completely removed.Some part of this work has been elaborated at the Department of Chemistry, Carnegie-Mellon University, and one of us (V. K.) is very obliged to Prof. J. A. Pople and Dr. R. Krishnan for many stimulating discussions concerning the complete fourth-order evaluation of the correlation energy.     

Sharp fronts in attracting-adatom monolayers

The problem of pattern formation by adsorbates undergoing attractive lateral interactions, is described by a parabolic integrodifferential equation having the scaled inverse temperature ? and the scaled pressure α of the vapor phase as parameters. A coexistence region of high- and low-coverage stable homogeneous states has been reported in the (?, α) plane. In the small interaction-range limit an effective diffusion coefficient can be defined, which becomes however negative for a coverage range in between the stable homogeneous ones. A novel free-energy-like Lyapunov functional is found here for this problem. When evaluated on the homogeneous states, it leads to a Maxwell-like construction which selects essentially the same value α(?) as the originally posited zero front-velocity condition. Moreover, its value on static fronts at this particular α(?) coincides with those of the homogeneous states. This article is dedicated to Prof. Helmut Brand with occasion of his 60th birthday.     

Axiomatic restrictions on scattering amplitudes of hadrons

Problems of expsrimental verification of the quantum field theoretical principles by experimental test of any one of physical corollaries of the axiomatic quantum field theory are shortly discussed. A selective review of available axiomatic restrictions on scattering amplitudes of hadrons is given.The author is very indebted to E. P.Sabad, I. Yu.Krivsky, V. I.Kelemen, and Yu. A.Xaveri for the help offered to him during the preparation of this review. The author is especially indebted to Academician N. N.Bogolyubov for his approval of Theorem XXVIII before publishing it in Ref. [67], as well as to Prof. M. I.Podgoretsky (Dubna) and Prof. V. Ya.Fajnberg (Moscow) for numerous discussions of this theorem and Prof. Yu. M.Shirokov (Moscow) for a preciseful stimulating remark.     

AnomalousE1 conversion in octupole-deformed nuclei and muon shake-off in prompt fission

It has been shown that the coexistence of octupole and quadrupole deformation in nuclei gives rise to strong penetration effects in internal conversion for theE1 transitions. This idea has been applied for evaluating the muon shake-off probabilityW _sh. The value obtained,W _sh/–0.5% per prompt fission, is in good agreement with the experimental result. Possibilities for further experimental studies of this effect are discussed.The author would like to acknowledge fruitful discussions of the problem together with Prof. Yu.P. Gangrsky, Dr. V. Yu. Denisov and Prof. D.F. Zaretsky. He is also grateful to Prof. G.Ye. Belovitsky, Prof. P. David and Dr. Ch. Rösel for discussions of the experimental situation. This work was completed at the University of Bonn in the frame of a fellowship from the Heinrich Hertz Foundation.     

Properties of modified quantum dynamics

The general nature of the dynamics that can be described by an equation for the density matrix of nonrelativistic quantum systems previously proposed by us [1] is studied. It is shown that it leads to an experimentally observed constraint on the states of the microscopic and quasi-macroscopic systems by states that can be described by more or less localized wave packets in phase space and replaces the ordinary spreading of these packets by statistically deterministic transitions between corresponding states. This makes possible a purely dynamic solution of the problem of the classical object and of the problem of measurement in quantum mechanics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 63–67, May, 1976.I wish to express my deep appreciation to Prof. V. G. Bagrov for his interest in the study and for criticism.     

Wave functions of unstable particles

The assumptions necessary for the determination of the wave functions of unstable particles are formulated.Dedicated to Professor V. Votruba on his sixtieth birthday.On leave of absence from Charles University, Prague, Czechoslovakia.The author is indebted to Prof. V. Votruba for his support and stimulating discussions. He would further like to thank Prof. H. Leutwyler and Prof. A. Mercier for hospitality in Berne and for various suggestions.     

Motion of an electron in static and orthogonal electromagnetic fields of a special kind

Two-dimensional motion of an electron is analyzed in static and orthogonal nonuniform electromagnetic fields linearly depending (in the orbital plane) on the coordinate which determines the electric field direction. Exact solutions of relativistic equations of motion have been obtained in the form of elliptical functions. If the fields are of equal magnitudes the solutions can be expressed as elementary functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 88–92, October, 1972.The author takes the opportunity to thank Prof. A. A. Sokolov and Prof. V. G. Bagrov for their interest in this work and for useful discussions.     

High spin states in102Ag

High spin states are populated in¹⁰²Ag using the reaction¹⁶O+⁸⁹Y with projectile energies in the energy range 60–80 MeV. Gamma multipolarities are inferred from DCO ratios and coincidence relationships are established among the gamma rays assigned to¹⁰²Ag. A comprehensive level scheme is constructed with four band systems, two of positive parity and the other two of negative parity. The present study extended spins upto 19^– in the main negative parity band. A new band is populated in the present work and is similar to the one observed in¹⁰⁶Ag.The authors wish to thank and record their appreciation to Dr. S.K. Parthasaradhi, VECC, Calcutta for preparing the target used in this experiment. The authors gratefully acknowledge useful discussions with Dr. Rakhesh Popli. The authors record their grateful thanks to Prof. A.P. Patro and Prof. G.K. Mehta, former and present directors of the Nuclear Science Centre, for their interest in this work, helpful discussions and providing excellent facilities. The authors also thank Dr. S.K. Datta of the Nuclear Science Centre for his continued interest and helpful discussions and accelerator staff of N.S.C. for their efficient services in delivering the beam. Grateful thanks are also due to the University Grants Commission for providing financial support.     

Spectrum of the supersymmetric Liouville theory

The problem of the monopole infinite moments of inertia, and the related degeneracies in the dyon spectrum of a grand unified theory in the absence of light fermions is considered. A careful application to gauge theories of the method of collective coordinates is given in two different classes of gauges. A basic defect in the earlier treatments of the subject is pointed out. It is shown that the commonly accepted method, while giving reasonable qualitative results for the dyon spectrum in the SO(3) model, fails completely when applied to grand unified theories. The reason is simply that there is a contribution to the monopole moments of inertia that has so far been overlooked. This contribution is of the same order of magnitude as the already known one. The sum of the two contributions vanishes for these moments of inertia that have been thought to be infinite. This means that, in a grand unified theory without light fermions, dyon states transforming as definite color representations (chromodyons) do not exist if we believe this lowest-order analysis (which is almost all what one can do to show their existence). It is shown that applying the Bohr-Sommerfeld method to the classical dyon solutions leads to the same result.     

Generation of massless fermions in cosmological models of first Bianchi type

Generation of massless fermions in a general case of the anisotropic metric of first Bianchi type is considered. A regularized energy-momentum tensor of the generated particles is constructed. The absence of a conformal anomaly is shown for the initially massless quantum theory of a spinor field in an external gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 35–40, January, 1984.The author thanks A. A. Grib and A. V. Nesteruk for useful discussions.     

Theory of magnetic oscillations in Weyl semimetals

Weyl semimetals are a new class of Dirac material that possesses bulk energy nodes in three dimensions, in contrast to two dimensional graphene. In this paper, we study a Weyl semimetal subject to an applied magnetic field. We find distinct behavior that can be used to identify materials containing three dimensional Dirac fermions. We derive expressions for the density of states, electronic specific heat, and the magnetization. We focus our attention on the quantum oscillations in the magnetization. We find phase shifts in the quantum oscillations that distinguish the Weyl semimetal from conventional three dimensional Schrödinger fermions, as well as from two dimensional Dirac fermions. The density of states as a function of energy displays a sawtooth pattern which has its origin in the dispersion of the three dimensional Landau levels. At the same time, the spacing in energy of the sawtooth spike goes like the square root of the applied magnetic field which reflects the Dirac nature of the fermions. These features are reflected in the specific heat and magnetization. Finally, we apply a simple model for disorder and show that this tends to damp out the magnetic oscillations in the magnetization at small fields.     

Superfluid-insulator transitions of the fermi gas with near-unitary interactions in a periodic potential

We consider spin-1/2 fermions of mass m with interactions near the unitary limit. In an applied periodic potential of amplitude V and period a_{L}, and with a density of an even integer number of fermions per unit cell, there is a second-order quantum phase transition between superfluid and insulating ground states at a critical V=V_{c}. We compute the universal ratio V_{c}ma_{L};{2}/variant Planck's over 2pi;{2} at N=infinity in a model with Sp(2N) spin symmetry. The insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs. We discuss implications for recent experiments.     

Resonance absorption of terahertz radiation in nanoperforated graphene

Recent measurements of the conductivity of nanoperforated graphene are interpreted in terms of edges states existing near the edge of each nanohole. The perimetric quantization of edge states should result in the formation of a quasi-equidistant ladder of quasistationary energy levels. Dirac fermions filling this ladder rotate about each nanohole in the direction determined by the valley index. It is shown that the irradiation of this system by circularly polarized terahertz radiation leads to a resonance in absorption in one of the valleys. The magnitude of absorption at the resonance frequency can be controlled by means of gate voltage.     

Particle with anomalous moments in an axial magnetic field

The exact solutions of the generalized phenomenological Dirac equation in an axisymmetrical time-invariant magnetic field are discussed. The influence of an anomalous magnetic and a postulated electric moment on the spectrum of fermions moving in that field is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 36–39, May, 1981.The author is grateful to Prof. V. G. Bagrov for interest and useful consultations.