Quantum creation of the universe with a minimum scalar-field energy

The quantum creation of a closed Friedmann universe is studied on the basis of a Wheeler-DeWitt equation with two arguments — a scale factor and a scalar-field potential. In the quasiclassical approximation the wave function of the universe (WF) starts to evolve at a zero scalar field. A near-Planckian energy density of the field arises as a result of tunneling through a potential barrier. In our opinion, this variant of the scenario most closely resembles creation ex nihilo. The only parameter controlling quantum evolution is the mass of a quantum of the scalar field. In the paper by Khalatnikov and Schiller [JETP Lett. 57,1 (1993)], tunneling through the classically inaccessible region of the superpotential U(a,φ) is calculated by the instanton method. However, this method requires that the potential U(a,φ) satisfy special conditions in the space (a,φ). For this reason, in the present paper the tunneling calculation is performed by the method of characteristics for the quasiclassical approximation of the Wheeler-DeWitt equation under the barrier. The WKB theory, which has been well-developed for one-dimensional problems, is employed along each characteristic. It is shown that the corresponding turning points are also points where U(a, φ)=0. The total barrier penetrability is obtained by averaging over a bundle of characteristics. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 305–308 (10 September 1996)     

Surface electron scattering in d-wave superconductors

A theoretical model of a rough surface in a d-wave superconductor is studied for the general case of arbitrary strength of electron scattering by an impurity layer covering the surface. Boundary conditions for quasiclassical Eilenberger equations are derived at the interface between the impurity layer and the d-wave superconductor. The model is applied to the self-consistent calculation of the surface density of states and the critical current in d-wave Josephson junctions. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 242–246 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Equation of state of matter at high pressures and temperatures by the modified hartree-fock-slater model

Abstract

The equation of state of matter at extremely high pressures P～ 10–100 Mbars and temperatures T～ 5–50 eV has been very intensively investigated^1,2. The experimental determination of the matter properties in this region of parameters is very expensive, while the theory meets with grave difficulties because the matter under these conditions represents a strongly coupled multicomponent nonideal plasma. In practice, for calculations of the equation of state quasiclassical models are used, as those by Thomas-Fermi (TF) and Thomas-Fenni with corrections3. However, they do not include the shell effects. Most consistently these effects can be taken into account by quantomechanical self-consistent models^4–7     

Exact function of the equations of quantum mechanics in an electromagnetic field. II

The zero term of the quasiclassical asymptotic (?→ 0) of the Klein-Gordon-Fock equation as symmetrized by Feynman (V. V. Belov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 11, 45 (1975)), giving the exact Green's function of the Cauchy problem in arbitrary (nonparallel) steady homogeneous electric and magnetic fields, is constructed. The exact Green's function for the Dirae equation in an arbitrary, steady electromagnetic field and for the Pauli equation (semirelativistic Schrödinger equation) in the nonsteady-state case is constructed in an analogous manner.     

Quantum Dynamics in the Fermi–Pasta–Ulam Problem

We study a quantum chain of oscillators with nonlinear quartic interactions, under the “narrow packet” approximation. We analyse the dynamics of quantum corrections and the conditions at which the quantum solution for average complex amplitude converges to the corresponding classical unstable solution which describes the four-wave decay processes of phonons. We develop an asymptotic theory by using a small quasiclassical parameter, and determine the characteristic time scale for which the evolution of decay processes is essentially specified by quantum effects. AMS Subject classification: Primary: 35F10 Secondary: 35Q40, 35B40     

Topological quantum characteristics observed in the investigation of the conductivity in normal metals

It is shown that the investigation of the conductivity in a single crystal of a normal metal with a complicated Fermi surface in strong magnetic fields B can reveal integral topological characteristics which are determined by the topology of open-ended quasiclassical electron trajectories. Specifically, in the case of open-ended trajectories of the general position there always exists a direction η orthogonal to B in which the conductivity approaches zero for large B, and this direction lies in some integral (i.e., generated by two reciprocal-lattice vectors) plane that remains stationary for small variations of the direction of B. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 809–813 (25 May 1996)     

Squeezed states and quantum chaos

We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of a quantum rotator excited by a periodic sequence of kicks. This model is the main model of quantum chaos and allows for a transition from regular behavior to chaotic in the classical limit. By doing a numerical experiment we study the generation of squeezed states in quasiclassical conditions and in a time interval when quantum-classical correspondence is well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov classical stochasticity parameter. We also discuss the dependence of the degree of squeezing on the initial width of the packet, the problem of stability and observability of squeezed states in the transition to quantum chaos, and the dynamics of disintegration of wave packets in quantum chaos. Zh. éksp. Teor. Fiz. 113, 111–127 (January 1998)     

Algebraically Self-Consistent Quasiclassical Approximation on Phase Space

The Wigner–Weyl mapping of quantum operators to classical phase space functions preserves the algebra, when operator multiplication is mapped to the binary * operation. However, this isomorphism is destroyed under the quasiclassical substitution of * with conventional multiplication; consequently, an approximate mapping is required if algebraic relations are to be preserved. Such a mapping is uniquely determined by the fundamental relations of quantum mechanics, as is shown in this paper. The resultant quasiclassical approximation leads to an algebraic derivation of Thomas–Fermi theory, and a new quantization rule which—unlike semiclassical quantization—is non-invariant under action transformations of the Hamiltonian, in the same qualitative manner as the true eigenvalues. The quasiclassical eigenvalues are shown to be significantly more accurate than the corresponding semiclassical values, for a variety of 1D and 2D systems. In addition, certain standard refinements of semiclassical theory are shown to be easily incorporated into the quasiclassical formalism.     

Excited hydrogenic atom in a strong low-frequency electromagnetic field

The multiphoton ionization of a bound electron state which is twofold degenerate with respect to its orbital angular momentum is considered in a quasiclassical approximation. It is shown that the ionization probability increases strongly in an intense electromagnetic field, in which nonresonant mixing of the levels forming the degenerate state is significant, in comparison to the case described by the Keldysh formula. It is also shown that such degeneracy leads to a sharp increase in the intensity of the radiation scattered by the bound electron, and the high-frequency cutoff of the emission spectrum is shifted to higher frequencies. Zh. Tekh. Fiz. 69, 15–20 (August 1999)     

Magnetopolaron states of a spin-correlated antiferromagnet in the neighborhood of the spin-glass transition

The problem of the spectrum of magnetopolaron states of a strongly correlated conducting canted antiferromagnet is solved. The approach used to study the spectrum is based on an atomic representation and a diagram technique for Hubbard operators. This approach makes it possible to include strong intra-ion interactions in a first-principles way, and to obtain the dispersion equation for the magnetopolaron spectrum for arbitrary values of the magnitude of the spin, temperature, and magnetic field. In the vicinity of the spin-flip transition an analytic expression is obtained for the spectrum of magnetopolaron states that goes beyond the framework of the quasiclassical approximation. Fiz. Tverd. Tela (St. Petersburg) 40, 310–314 (February 1998)     

Anomalous behavior of the electrical conductivity tensor in strong magnetic fields

The behavior of the electrical conductivity tensor in strong magnetic fields in the presence of unclosed quasiclassical electron trajectories of complex form near the Fermi surface is considered. It is shown that the asymptotic behavior of the conductivity tensor in the limit B→∞ differs in this case from the picture previously described for trajectories of simpler form. The possibility of blocking the longitudinal conductivity in strong magnetic fields at low temperatures in the case of a Fermi surface of special form is also treated theoretically. Zh. éksp. Teor. Fiz. 112, 1710–1726 (November 1997)     

Phase Space Optimization of Quantum Representations: Non-Cartesian Coordinate Spaces

In an earlier article [Found. Phys. 30, 1191 (2000)], a quasiclassical phase space approximation for quantum projection operators was presented, whose accuracy increases in the limit of large basis size (projection subspace dimensionality). In a second paper [J. Chem. Phys. 111, 4869 (1999)], this approximation was used to generate a nearly optimal direct-product basis for representing an arbitrary (Cartesian) quantum Hamiltonian, within a given energy range of interest. From a few reduced-dimensional integrals, the method determines the optimal 1D marginal Hamiltonians, whose eigenstates comprise the direct-product basis. In the present paper, this phase space optimized direct-product basis method is generalized to incorporate non-Cartesian coordinate spaces, composed of radii and angles, that arise in molecular applications. Analytical results are presented for certain standard systems, including rigid rotors, and three-body vibrators.     

Contribution to the theory of Lorentzian ionization

The probability w _L of Lorentzian ionization, which arises when an atom or ion moves in a constant magnetic field, is calculated in the quasiclassical approximation. The nonrelativistic (v≲e ²/ℏ=1, v is the velocity of the atom) and ultrarelativistic (v→c=137) cases are examined and the stabilization factor S, which takes account of the effect of the magnetic field on tunneling of an electron, is found. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 391–396 (10 March 1997)     

Global Well-Posedness for the KP-I Equation on the Background of a Non-Localized Solution

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in x and y periodic or conversely).     

Quasiclassical boundary conditions for Fermi liquids at surfaces

The general boundary conditions at surfaces are derived within the quasiclassical theory of superfluidity in Fermi liquids (superconductors, superfluid³He). These conditions supplement the transport-like equations first introduced into the theory of superconductivity by G. Eilenberger, and allow a quantitative analysis of superfluids near a wall.     

Motion of a particle in a static magnetic field and in the field of a electromagnetic plane wave

The solutions of the equations of motion of a charged particle in an external electromagnetic field consisting of a superposition of a constant uniform magnetic field and the field of a circularly polarized electromagnetic plane wave are presented as solutions of the Cauchy problem. The resonance case is studied. Zh. Tekh. Fiz. 67, 94–99 (February 1997)     

Ballistic transport and spin-orbit interaction of two-dimensional electrons on a cylindrical surface

The components of the ballistic magnetoconductance tensor of a two-dimensional electron gas placed on a cylindrical sector are calculated for various geometries. For a quasiclassical system a method is proposed for finding the conductance based only on the Bohr-Sommerfeld quantization condition and not requiring a knowledge of the matrix elements of the velocity. The effect of curvature of the surface on the spin-orbit interaction in a two-dimensional electron gas is investigated. As examples, the microwave absorption and longitudinal conductance of a hollow cylindrical wire are calculated, and also the conductance of a cylindrical sector. There are qualitative differences from planar systems, in particular the relative sign of the curvature and the spin-orbit coupling constant becomes important. Zh. éksp. Teor. Fiz. 113, 1411–1428 (April 1998)     

Bose-Einstein condensation in a static scalar field from the standpoint of the Goursat problem

The Goursat problem, developed by the present authors in previous papers [Ukr. Fiz. Zh. (Russ. Ed.) 27, 1602 (1982); Differentsial’nye Uravneniya 20, 302 (1984); J. Math. Phys. 33, 233 (1996)], is used to study the energy spectrum of a scalar relativistic particle in a static axisymmetric external scalar field of an attractive nature. This is obviously a model. It is shown that the problem formulated in this way has no unstable solutions, i.e., solutions increasing with time, in contrast to the Cauchy problem, where such solutions appear when the square of the particle frequency (energy) vanishes (in other words, in a Bose-Einstein condensation) Zh. éksp. Teor. Fiz. 112, 1167–1175 (October 1997)     

Causality and Cauchy horizons

LetS be a partial Cauchy surface for (M, go) which remains a partial Cauchy surface under small metric perturbations. In general, the Cauchy horizon H⁺(go, S) may be unstable to small changes in the metric. Points of the horizon may move by large amounts and even the topological type of the horizon may change under arbitrarily small changes in the metric tensor. In this paper, we investigate sufficient conditions for existential, locational, and topological stability of Cauchy horizons under metric changes which perturb the light cones by small amounts.     

Motion of a particle in a static magnetic field and the field of a monochromatic electromagnetic plane wave

A solution of the equation of motion of a charged particle in an external electromagnetic field comprising a superposition of a uniform static magnetic field and the field of a monochromatic, elliptically polarized electromagnetic plane wave is obtained as the solution of a Cauchy problem. The resonance case is investigated. An analysis of the resulting solution is given. Zh. Tekh. Fiz. 69, 106–110 (May 1999)