Born Reciprocity and the 1/r Potential

Many structures in nature are invariant under the transformation pair, (p,r)→(b  r,−p/b), where b is some scale factor. Born’s reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We investigate this idea for atomic physics and galactic motion, where one is basically dealing with a 1/r potential and the observations are very accurate, so as to determine the scale b≡mΩ. We find that an Ω∼1.5×10⁻¹⁵ s⁻¹ has essentially no effect on atomic physics but might possibly offer an explanation for galactic rotation, without invoking dark matter.     

Semiclassical energy levels of electrons in metals with band degeneracy lines

We show that in calculating the semiclassical energy levels of electrons in metals located in a magnetic field, one must determine whether or not the corresponding electron paths in the space of wave vectors k are attached to a band degeneracy line. Calculations in the two possible cases, i.e., with and without such attachment, differ by |e|ℏ/2m*c, where e is the electron charge and m* is the cyclotron mass of the electron. This shift in the energy levels is of a topological nature, and its existence depends neither on the specific form of the electron dispersion relation ε(k) near the electron path nor on the shape or size of this path. The reason for this shift lies in the fact that the electron orbit is attached to the band degeneracy line, which is the line of singular points of the Bloch wave functions. In many respects this effect is similar to the Aharonov-Bohm effect if the band degeneracy line is considered an infinitely thin “solenoid.” This shift in energy levels should become apparent in studies of oscillation phenomena in metals. We give examples of metals in which the conditions for observing the shift is probably the most favorable. Zh. éksp. Teor. Fiz. 114, 1375–1392 (October 1998)     

Ionization of a two-electron atom in a strong electromagnetic field

A one-dimensional model of a helium atom in an intense field of a femtosecond electromagnetic pulse has been constructed using the Hartree technique. “Exact” calculations have been compared to the approximations of “frozen” and “passive” electrons. A nonmonotonic dependence of the single-electron ionization probability on the radiation intensity has been detected. Minima in the ionization probability are due to multiphoton resonances between different atomic states due to the dynamic Stark effect. We suggest that the ionization suppression is due to the interference stabilization in this case. Zh. éksp. Teor. Fiz. 112, 470–482 (August 1997)     

Optical pumping in a L-system by parametric luminescence light

We examine the optical pumping effect in an ensemble of three-level atoms with a Λ configuration of the energy sublevels excited by parametric luminescence light in the squeezed state. We derive quantum kinetic equations that describe the evolution of the density matrix of atoms irradiated by low-intensity squeezed light with a finite-width spectrum. In particular, we show that because of the quantum statistical properties of the squeezed light there can be a redistribution of atoms among the lower energy sublevels, despite the equality of the intensities of the spectral components of the light that resonantly excites optical transitions in the Λ-system. The relation of the optical pumping effect to the correlation and spatial-temporal spectral properties of squeezed light is discussed in detail. Finally, we show that the effects are closely linked to the finiteness of the width of the squeezed-light spectrum. Zh. éksp. Teor. Fiz. 112, 137–162 (July 1997)     

Sharp Lower Bounds for the Dimension of the Global Attractor of the Sabra Shell Model of Turbulence

In this work we derive lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model of turbulence in different regimes of parameters. We show that for a particular choice of the forcing term and for sufficiently small viscosity term ν, the Sabra shell model has a global attractor of large Hausdorff and fractal dimensions proportional to log  ν ⁻¹ for all values of the governing parameter ε, except for ε =1. The obtained lower bounds are sharp, matching the upper bounds for the dimension of the global attractor obtained in our previous work. Moreover, the complexity of the dynamics of the shell model increases as the viscosity ν tends to zero, and we describe a precise scenario of successive bifurcations for different parameters regimes. In the “three-dimensional” regime of parameters this scenario changes when the parameter ε becomes sufficiently close to 0 or to 1. We also show that in the “two-dimensional” regime of parameters, for a certain non-zero forcing term, the long-term dynamics of the model becomes trivial for every value of the viscosity. AMS Subject Classifications: 76F20, 76D05, 35Q30     

Selective photoconductivity induced in PbTe(Ga) by a local phonon mode

Selective photoconductivity at frequency ω=155 cm⁻ was discovered in PbTe(Ga) narrow-gap semiconductors at liquid-nitrogen temperatures. The corresponding energy is much lower than all characteristic energies of the electronic spectrum of the semiconductor. The effect is attributed to optical excitation of a local vibrational mode of an impurity center leading to delocalization of the electrons. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 5, 342–346 (10 March 1996)     

The diffraction mechanism of electron-positron pair photoproduction

We examine a mechanism of electron-positron pair photoproduction near a giant resonance. The mechanism is based on the possibility of photons being absorbed by nuclei. Our calculations set the cross section of this process at roughly 10⁻³⁰ cm². We also discuss the feasibility of observing the effect. Zh. éksp. Teor. Fiz. 112, 1959–1965 (December 1997)     

A Dynamical Classification of the Range of Pair Interactions

We formalize a classification of pair interactions based on the convergence properties of the forces acting on particles as a function of system size. We do so by considering the behavior of the probability distribution function (PDF) P(F) of the force field F in a particle distribution in the limit that the size of the system is taken to infinity at constant particle density, i.e., in the “usual” thermodynamic limit. For a pair interaction potential V(r) with V(r→∞)∼1/r ^γ defining a bounded pair force, we show that P(F) converges continuously to a well-defined and rapidly decreasing PDF if and only if the pair force is absolutely integrable, i.e., for γ>d−1, where d is the spatial dimension. We refer to this case as dynamically short-range, because the dominant contribution to the force on a typical particle in this limit arises from particles in a finite neighborhood around it. For the dynamically long-range case, i.e., γ≤d−1, on the other hand, the dominant contribution to the force comes from the mean field due to the bulk, which becomes undefined in this limit. We discuss also how, for γ≤d−1 (and notably, for the case of gravity, γ=d−2) P(F) may, in some cases, be defined in a weaker sense. This involves a regularization of the force summation which is generalization of the procedure employed to define gravitational forces in an infinite static homogeneous universe. We explain that the relevant classification in this context is, however, that which divides pair forces with γ>d−2 (or γ<d−2), for which the PDF of the difference in forces is defined (or not defined) in the infinite system limit, without any regularization. In the former case dynamics can, as for the (marginal) case of gravity, be defined consistently in an infinite uniform system.     

High-precision measurement of separatrix splitting in a nonlinear resonance

We present the results of numerical modeling and a theoretical analysis of the splitting of a nonlinear-resonance separatrix in the intermediate asymptotic region for the standard-map model. Direct measurements of the splitting angle α(K), where K is the small parameter of the system, have been carried out over a huge range, 0.1≳α≳10⁻²⁰⁸ (1⩾K⩾0.0004), with a relative accuracy greater than one part in 10⁻²⁵ and an average accuracy of roughly one part in 10⁻³⁰. This made it possible to compare in detail our results with those of the existing asymptotic theory and to detect a number of new effects. We find a relatively simple empirical expression for the α vs. K dependence in the intermediate asymptotic region, and this region proves to be surprisingly broad: K≲10⁻². We also study the effect of noise, in particular, errors in measuring the angle, which proved to be much more significant and complicated than expected. Finally, we point out unresolved questions and possible directions of research involving this problem. Zh. éksp. Teor. Fiz. 114, 1516–1531 (October 1998)     

Photoexcitation of rare-gas neon and argon clusters doped with <Emphasis Type="Bold">H</Emphasis><Subscript><Emphasis Type="Bold">2</Emphasis></Subscript><Emphasis Type="Bold">O</Emphasis>

We have studied the fluorescence of electronically excited OH^*, H^* and H₂O^+* dissociation fragments after VUV excitation ( h ν≥11.6 eV) of rare-gas clusters (Rg = Ne, Ar) doped with H₂O molecules. In contrast to a free molecule, where Balmer H-series dominate the UV-visible spectra, only the OH ^* ( A ² Σ ⁺ ↦ X ² Π) emission band is observed in neon clusters. No emission of excited water ions has been observed. We find that while higher excitation energies (Ne vs. Ar) induce higher vibrational excitation of the OH^* ( A ) fragment, the rotational temperature is lower. This effect is attributed to the difference in the geometric position of the H₂O molecule on the surface or inside the Rg-cluster. The rotational relaxation in neon clusters is rapid while the vibrational relaxation is slow because of the coupling with the low energy matrix phonons. Received 7 March 2002 / Received in final form 27 May 2002 Published online 19 July 2002     

Stimulated scattering and wavefront conjugation in an inhomogeneous plasma

In the context of the problem of stimulated scattering we discuss the mechanism of wavefront conjugation in an inhomogeneous plasma proposed relatively recently, associated with a difference in suppression of scattering (due to inhomogeneities) for the inverted and uninverted components. We analyze the solutions of the integro-differential equations describing this process both numerically and analytically for different sound attenuation lengths (v ⁻¹). It is shown that for this effect to exist it is necessary that n not be too small. We also consider extinction of the inverted wave in terms of this mechanism. Zh. éksp. Teor. Fiz. 113, 168–180 (January 1998)     

Large-scale amplification of a magnetic field by turbulent helicity fluctuations

In this paper the procedure of large-scale averaging of the magnetic-field diffusion equation with the α-term curlα(r,t)B(r,t) is used to show that a nonuniform distribution of the turbulent helicity fluctuations (more precisely, the fluctuations of the coefficient α) with a zero average value gives rise to large-scale amplification of the initial magnetic field. A detailed study is carried out of the dependence of the resulting large-scale α effect on the characteristics of the correlator 〈〈α(r, t)α(r″,t″)〉〉 in a rotating medium with a nonuniform distribution of the angular velocity ω=ω(ρ,z) (ρ is the distance for the rotation axis z). The effect of helicity fluctuations and the diffusion coefficient on the turbulent diffusion process is also investigated. Zh. éksp. Teor. Fiz. 116, 85–104 (July 1999)     

Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation

This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators ${\bf Q}_{\pm}(\lambda)$ which act in the highest weight Virasoro module and commute for different values of the parameter λ. These operators appear to be the CFT analogs of the Q - matrix of Baxter [2], in particular they satisfy Baxter's famous T- Q equation. We also show that under natural assumptions about analytic properties of the operators as the functions of λ the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV) [3] for the eigenvalues of the Q-operators. We then use the DDV equation to obtain the asymptotic expansions of the Q - operators at large λ; it is remarkable that unlike the expansions of the T operators of [1], the asymptotic series for Q(λ) contains the “dual” nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the vacuum eigenvalues of the Q - operators and the stationary transport properties in the boundary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum Hall system. Received: 2 December 1996 / Accepted: 11 March 1997     

Influence of magnetic scattering centers in the insulator component of the composite HTSC+Cu1−x NixO on its resistive properties

We present results of an experimental study of the effect of magnetic scattering centers (nickel) in the insulator component (cuprous oxide) of the composite HTSC+Cu_1−x Ni_xO on its transport properties. A suppression of the superconducting properties of this system is observed to take place with increasing nickel content. The results are analyzed within the framework of the model of strong electron correlations. Fiz. Tverd. Tela (St. Petersburg) 40, 1599–1603 (September 1998)     

Restoration of selection rules in nonadiabatic resonant inelastic x-ray scattering

Recently a new effect in the Raman scattering of x-ray radiation has been predicted theoretically and discovered in experiments, the effect of restoration of the selection rules for the scattering tensor under strong electron-vibrational interaction. We propose a fairly simple model for describing this effect, a model that allows for an exact solution and takes into account the real vibrational structure of the molecule and electron-vibrational interaction. Zh. éksp. Teor. Fiz. 112, 37–49 (July 1997)     

Molecular Stark effect spectroscopy of diflavonol and inhomogeneous broadening of its electronic spectra in erythrocyte membranes

Using spectroscopy of the molecular Stark effect and fluorescence spectroscopy, we study the characteristics of diflavonol 3,7-dihydroxy-2,8-di(4-dimethylaminophenyl)-4H,6H-pyrano[3,2-g]chromene-4,6-dione (DFME), which demonstrates intramolecular charge and proton phototransfer. In the ground state, this dye has only one form and, in the excited state, it has two forms, i.e., normal and phototautomeric. We found that, for the normal form of DFME, the transition dipole moment that is responsible for the absorption (m _a ), the dipole moment in the equilibrium ground state (μ _g ), and the change of the dipole moment upon transition of the molecule in the excited Franck-Condon state (Δ ^a μ) are parallel. In the ground equilibrium state, the dipole moments in 1,4-dioxane and cyclohexane are equal to μg = 12.2 × 10⁻³⁰ C m and μ _g = 11.0 × 10⁻³⁰ C m, respectively. Upon excitation, they increase by Δ ^a μ = 61 × 10⁻³⁰ C m and Δ ^a μ = 50.2 × 10⁻³⁰ C m in these solvents. We study the spectral characteristics of DFME in organic solvents and erythrocyte membranes. A spectral inhomogeneity of DFME in erythrocyte ghosts is found. The inhomogeneous broadening of fluorescence spectra is manifested as a long-wavelength shift of the band of the normal form of DFME by 1640 cm⁻¹ upon excitation at the red edge of the absorption spectrum.     

Capacitance spectroscopy investigation of the spin polarization of two-dimensional electronic systems

It is shown that capacitance spectroscopy can be used to investigate the spin polarization of two-dimensional electronic systems (2DESs). We employed this method to investigate the spin polarization of 2DESs in a GaAs/AlGaAs heterojunction for filling factors of the magneticquantization levels 0.28<ν<0.9. It is proved that in the presence of states of the fractional quantum Hall effect with ν _f =1/3 and 2/3 the ground state of a 2DES with ν>2/3 is incompletely spin-polarized. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 102–107 (10 January 1997)     

Out-of-equilibrium quantum field dynamics in external fields

The quantum dynamics of the symmetry-broken λ(Φ ²)² scalar-field theory in the presence of an homogeneous external field is investigated in the large-N limit. We consider an initial thermal state of temperature T for a constant external field J. A subsequent sign flip of the external field, J→ - J, gives rise to an out-of-equilibrium nonperturbative quantum field dynamics. We review here the dynamics for the symmetry-broken λ(Φ ²)² scalar N component field theory in the large-N limit, with particular stress in the comparison between the results when the initial temperature is zero and when it is finite. The presence of a finite temperature modifies the dynamical effective potential for the expectation value, and also makes that the transition between the two regimes of the early dynamics occurs for lower values of the external field. The two regimes are characterized by the presence or absence of a temporal trapping close to the metastable equilibrium position of the potential. In the cases when the trapping occurs it is shorter for larger initial temperatures.     

Projective Invariance in Cosmological Models and Dark Energy

We study theories of gravitation that are based on the Einstein – Hilbert action that are not projectively invariant and can therefore completely determine their connections. We are thus lead to the conclusion that the geometry is necessarily Riemann – Cartan and at least the trace part of a torsion field must be present. We examine the consequence of including these torsion fields in cosmological models. Our results differ from those obtained earlier in the Einstein – Cartan – Sciama – Kibble theory. We also consider a model that includes a series of quadratic torsion terms. This series leads to a potential function that has the effect of “turning on” the cosmological constant. This potential function then acts like dark energy. This model also shows that the torsion field can produce an inflationary period. PACS: 04.02 Cv, 95.30 Sf, 98.80-k     

Ground state energy calculations of the ν=1/2 and the ν=5/2 FQHE system

We reconsider energy calculations of the spin polarized ν = 1/2 Chern-Simons theory. We show that one has to be careful in the definition of the Chern-Simons path integral in order to avoid an IR divergent magnetic ground state energy in RPA as in [J. Dietel et al, Eur. Phys. J. B 5, 439 (1998)]. We correct the path integral and get a well behaved magnetic energy by considering the energy of the maximal divergent graphs as well as the Hartree-Fock graphs. Furthermore, we consider the ν = 1/2 and the ν = 5/2 system with spin degrees of freedom. In doing this we formulate a Chern-Simons theory of the ν = 5/2 system by transforming the interaction operator to the next lower Landau level. We calculate the Coulomb energy of the spin polarized as well as the spin unpolarized ν = 1/2 and the ν = 5/2 system as a function of the interaction strength in RPA. These energies are in good agreement with numerical simulations of interacting electrons in the first as well as in the second Landau level. Furthermore, we calculate the compressibility, the effective mass and the excitations of the spin polarized ν = 2 + 1/ systems where is an even number. Received 13 June 2000