The insulating and conducting crystal states. Localization and delocalization of electronic states

An ab initio analysis is made of the localized (in Mott’s sense) and delocalized (band) states of an electron in a crystal. The criterion of a difference between these states is the behavior of the off-diagonal elements in the one-particle electronic density matrix for T=0. Localization can be related to its exponential falloff for |r−r′|→∞, and delocalization, to its power-law decay. This corresponds to the analyticity of the density matrix in k space of the Brillouin zone in the first case, and to a singularity (Fermi step) in the second. This analyticity gives rise also to a power-law decay of the correlation functions. In a normal system, localization can be identified with the insulating state, and delocalization, with the conducting state. It is shown that the above localization criterion is applicable to disordered systems as well. Electron localization in superconductors is also discussed. It is pointed out that the above criterion of localization is met also in the BCS superconducting state and in the localized-pair model. The reason for the considerable difference between the properties of the insulating and superconducting states lies in that there are no static fluctuations in the number of electrons, 〈(ΔN)²〉₀, in the ground state of an insulator whereas in a superconductor ODLRO results in nonzero fluctuations of N of a quantum nature. Fiz. Tverd. Tela (St. Petersburg) 41, 1582–1592 (September 1999)     

Nonlinear collapse of an isolated,homogeneously broadened,spectral line as a result of coherent collisions

The collisional exchange between an off-diagonal element of the density matrix and its complex conjugate results in the collapse of a homogeneously broadened spectral line. The case when such exchange is due to the polarization of the heat bath on account of two-photon absorption is studied. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 599–603 (10 November 1996)     

Nonelectrical method of pumping solid-state lasers

An alternative, nonelectrical method for obtaining a dense radiating plasma and the possibilities of using this method to pump solid-state lasers are investigated. The plasma was obtained experimentally by heating the working gas in a two-stage ballistic plasmatron. A new device — a vortex chamber — is proposed for transferring energy into the plasmatron-laser system. Zh. Tekh. Fiz. 68, 67–70 (September 1998)     

Quantum cryptography based on homodyne detection (vacuum-state cryptosystem)

A new protocol is proposed for quantum cryptography. The protocol is based on the use of a set of measurements which make it possible to reconstruct completely the density matrix — the information carrier — of a physical system. Such a protocol can be implemented by means of homodyne detection (well known in quantum optics) of an electromagnetic field. An example is given of a quantum cryptosystem in which the vacuum state of the photon field is used as one of two information states. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 1, 64–68 (10 July 1997)     

Vortex stretching and reconnection in a compressible fluid

Vortex stretching in a compressible fluid is considered. Two-dimensional (2D) and axisymmetric cases are considered separately. The flows associated with the vortices are perpendicular to the plane of the uniform straining flows. Externally-imposed density build-up near the axis leads to enhanced compactness of the vortices — “dressed" vortices (in analogy to “dressed" charged particles in a dielectric system). The compressible vortex flow solutions in the 2D as well as axisymmetric cases identify a length scale relevant for the compressible case which leads to the Kadomtsev-Petviashvili spectrum for compressible turbulence. Vortex reconnection process in a compressible fluid is shown to be possible even in the inviscid case — compressibility leads to defreezing of vortex lines in the fluid.     

Kinetics of photoluminescence decay of KCl-Yb

We have investigated the kinetics of the luminescence decay of a KCl-Yb crystal excited in one of the long-wavelength absorption bands of the Yb²⁺ ion by nitrogen laser radiation with a power density less than 10³ W/cm². We found that, in both luminescence bands, both the one associated with the allowed transition (399 nm) and the one associated with the forbidden transition (430 nm), there are two stages of decay—an initial exponential stage that gives way to a hyperbolic stage. Non-exponential decay due to the optical electron tunneling back to the luminescence center is treated as evidence of delocalization of the electron upon intracenter excitation and is explained by the formation of an excimer-like molecular bond upon photoexcitation of the crystal. Fiz. Tverd. Tela (St. Petersburg) 41, 1763–1765 (October 1999)     

Physics of the amplification of vortex disturbances in shear flows

The physics of the linear mechanism of the amplification of vortex disturbances in shear flows, which is due to the nonorthogonality of the eigenfunctions of the problem in the linear dynamics, is described. To obtain the clearest and simplest picture, a parallel flow with a linear velocity shear is studied, and the vortex disturbances are represented in the form of plane waves — spatial Fourier harmonics. On this level our physical approach is consonant with the nonmodal mathematical analysis of linear processes in shear flows, which has been actively cultivated in the last few years. The physics presented explains the non-monotonic growth of vortex disturbances in time at the linear stage of evolution. Moreover, being universal, the “language” employed in this work can also be used to describe the amplification of potential (acoustic) disturbances. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 517–522 (10 April 1996)     

Off-specular neutron reflection from magnetic media with nondiagonal reflectivity matrices

The reflection of neutrons from magnetic substances is described using a reflection matrix including (in general) the off-diagonal matrix elements responsible for neutron spin reversal. In an external field the spin reversal is accompanied by changes in the neutron kinetic energy and, as a result, the reflection angle. An experiment to observe this new effect is described and the results are reported. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 900–905 (25 June 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Dynamics of collective decoherence and thermalization

We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N², while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.     

Vortex dynamics in classical non-Abelian spin models

We discuss the Abelian vortex dynamics in the Abelian projection approach to non-Abelian spin models. We show numerically that in the three-dimensional SU(2) spin model in the maximal Abelian projection the Abelian off-diagonal vortices, unlike the diagonal vortices, are not responsible for the phase transition. A generalization of the Abelian projection approach to SU(N) spin models is briefly discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 526–530 (25 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.     

A new type of local polariton at the interface of gyrotropic enantiomorphic crystals

It is shown that a new type of local polariton can propagate at the interface of enantiomorphic twins—gyrotropic crystals with left-handed and right-handed rotation of the polarization plane. The wave function of these local polaritons oscillates strongly, with changes of sign, over lengths of the order of the lattice constant near the interface, and the period of the spatial oscillations grows with increasing distance from the interface. The local polariton term is detached from the band of delocalized states toward higher frequencies. Calculations of the radiation broadening of this term show that, for a local polariton, the effect of a giant increase of the decay (“superradiance”) is possible. The magnitude of the polarization rotation due to a local polariton has been found. Fiz. Tverd. Tela (St. Petersburg) 41, 337–340 (February 1999)     

Critical fields and currents in a weakly nonlinear medium near the percolation threshold

For fields above a critical value the expansion of the conductivity in powers of the field ceases to be valid and the weak-nonlinearity approximation no longer works. The density behavior of the critical fields in strongly inhomogeneous media near the percolation threshold is found on the basis of two criteria—an average criterion and a local criterion. The parameter values of the medium for which crossover—a change of the critical behavior—occurs are determined. Similar calculations are performed for the critical currents. Zh. Tekh. Fiz. 68, 5–8 (June 1998)     

Exciton-exciton collisions and conversion of interwell excitons in GaAs/AlGaAs superlattices

The ratio of the densities of intra-and interwell excitons in a symmetric system of coupled quantum wells — a superlattice based on a GaAs/AlGaAs heterostructure — is investigated over a wide range of optical excitation power densities. Conversion of interwell excitons into intrawell excitons as a result of exciton-exciton collisions is observed at high exciton densities. Direct evidence for such a conversion mechanism is the square-root dependence of the interwell exciton density on the optical excitation level. The decrease in the lifetime of interwell excitons with increasing excitation density, as measured directly by time-resolved spectroscopy methods, confirms the explanation proposed for the effect. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 623–628 (25 April 1997)     

Cooperative population dynamics of an ensemble of Λ atoms in a bichromatic field

Equations are derived which describe the dynamics of three-level atoms with a Λ level scheme, interacting with two coherent resonance fields under conditions such that cooperative relaxation predominates over incoherent spontaneous emission. A numerical calculation of the temporal dynamics of the values of the atomic populations is performed. It is shown that coherent population trapping in the presence of cooperative decay is possible. The quantities characterizing this phenomenon are calculated—the width of the black line and the transition time to coherent trapping in this scheme. Zh. Tekh. Fiz. 68, 19–24 (June 1998)     

Attempt at a gauge-theory-based explanation of the mass spectrum and number of light neutrinos

The symplectic group Sp(n/2) of invariance of flavors of n Majorana states (n is even) does not admit the existence of invariant Majorana masses. Only a specific mass matrix involving diagonal and off-diagonal elements is possible. A mass matrix as a result of spontaneous flavor- and chiral-symmetry breaking may appear here only in the case where the number of flavors is n = 6 and only together with spontaneous R- and L-symmetry violation—that is, parity violation. As a result, three light and three heavy Dirac particles (neutrinos) are present if the seesaw mechanism is operative. Special features of the observed spectrum of light neutrinos—in particular, the fact that two states are far off the third one—can be explained by simple properties of the mass matrices arising in Sp(3). The arrangement of states corresponds to an ordinary mass hierarchy. The mixing angles for physical neutrinos cannot be determined without understanding the mechanisms responsible for the formation of the charged-lepton spectrum and the weak current of Majorana states.     

The wideband attenuation of short radio waves on mid-latitude paths during X-ray flares in January 2005

We present the results of the ionosphere oblique chirp sounding on the Cyprus—Nizhny Novgorod, Cyprus—Rostov-on-Don, and Moscow—Rostov-on-Don mid-latitude paths during X-ray flares in January 17, 19, and 20, 2005. It is found that during strong flares the blackout of short radio waves was observed over the entire frequency range of chirp sounding on the Cyprus—Nizhny Novgorod and Cyprus—Rostov-on-Don paths. Modeling of the electron-density profiles in the lower ionosphere based on absorption of short radio waves on the Moscow—Rostov-on-Don path at different stages of the decay of the X-ray radiation intensity is carried out. It is shown that at the instant corresponding to the maximum value of the flare radiation flux, the electron density in the lower ionosphere at altitudes 60–80 km increased by a factor of about 10 and 100 for flares with radiation flux densities 5·10⁻² and 3·10⁻¹ erg/(cm ²·s) in the wavelength range 0.5–4.0 Å which took place in January 19 and 20, respectively. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 1, pp. 1–8, January 2007.     

Luminescence of short-lived color centers induced in LiF crystals by a pulsed microwave discharge

A new phenomenon — intense luminescence of noncolored lithium fluoride (LiF) crystals excited by an electrodeless pulsed microwave discharge at the prebreakdown stage of development — is observed. This luminescence consists of the luminescence of short-lived aggregate F₂ and F ₃ ⁺ color centers at room temperature. It is shown that the density of short-lived color centers induced in the surface layer of LiF crystals by a microsecond microwave discharge reaches values of ∼10¹⁹−10²⁰ cm⁻³. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 163–167 (10 August 1997)     

Magnetic phase diagrams of ferrimagnets having two magnetically unstable subsystems

The molecular field approximation is used to construct magnetic phase diagrams along with magnetization curves for ferrimagnets having two magnetically unstable subsystems. Diverse sequences of phase transitions of various kinds—first order (metamagnetic) and second order (via a noncollinear phase)—are realized in the course of magnetizing such ferrimagnets. Analysis reveals how the magnetization curves depend on the relative values of parameters of the two subsystems, e.g., sublattice magnetizations in weak and strong states, critical fields, and values of the exchange interaction between sublattices. Fiz. Tverd. Tela (St. Petersburg) 40, 280–284 (February 1998)     

Vortex mass in BCS systems: Kopnin and Baym-Chandler contributions

The Kopnin mass and the Baym-Chandler mass of a vortex have the same origin. Both represent the mass of the normal component trapped by the vortex. The Kopnin mass of a vortex is formed by quasiparticles localized in the vicinity of the vortex. In the superclean limit it is calculated as a linear response, in exactly the same way as the density of the normal component is calculated in a homogeneous superfluid. The Baym-Chandler mass is the hydrodynamic (associated) mass trapped by a vortex. It is analogous to the normal component formed by inhomogeneities, such as pores and impurities. Both contributions are calculated for a generic model of a continuous vortex core. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 502–506 (10 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.