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The work was supported by the Belarusian National Research Program “Convergence-2020” and the Belarusian Republican Foundation for Fundamental Research (grant no. Ф20Р-301). Yurii E. Lozovik acknowledge support by the Russian Foundation of Basic Research (grant no. 20-52-00035) and the Program for Basic Research of the National Research University “Higher School of Economics”. Nguyen Ngoc Hieu acknowledge support by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant no. 103.01-2017.309. Работа поддержана Государственной программой научных исследований «Конвергенция-2020» Республики Беларусь и Белорусским республиканским фондом фундаментальных исследований (грант № Ф20Р-301). Ю. Е. Лозовик благодарит за поддержку Российский фонд фундаментальных исследований (грант № 20-52-00035) и Программу фундаментальных исследований Национального исследовательского института «Высшая школа экономики». Нгуен Нгок Хиеу благодарит за поддержку Вьетнамский национальный фонд развития науки и технологий (NAFOSTED) в рамках гранта № 103.01-2017.309.

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Zcr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z Zcr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions e0 and widths γ of quasistationary states as a function of supercriticality. The values of e0* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Zcr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.

Formation of exciton-polariton condensate due to incoherent pumping of an excitonic reservoir is considered. The condensate dynamics is governed by a system of stochastic integro-differential equations of Langevin's type corresponding to the model developed by Elistratov and Lozovik [12] . Attention is concentrated on non-Markovian interaction of the condensate with the excitonic and photonic reservoirs. It is shown that dynamical memory caused by the non-Markovian interaction qualitatively changes the condensate behavior as compared to the Markovian regime. In particular, it diminishes the threshold of pumping strength for the condensate emergence. Also, it is found that the non-Markovian regime leads to relaxation oscillations corresponding to population exchange between the condensate and the excitonic reservoir. Increasing of incoherent pumping strength leads to chaos of relaxation oscillations that is accompanied by random-like transitions between the lower and upper polaritonic states.

We propose a way to increase the lifetime of two-dimensional direct excitons and show the possibility to observe their macroscopically coherent state at temperatures much higher than that of indirect exciton condensation. For a single GaAs quantum well embedded in photonic layered heterostructures with subwavelength period, we predict the exciton radiative decay to be strongly suppressed. Quantum hydrodynamics joined with the Bogoliubov approach are used to study the Berezinskii-Kosterlitz-Thouless crossover in a finite exciton system with intermediate densities. Below the estimated critical temperatures, drastic growth of the correlation length is shown to be accompanied by a manyfold increase of the photoluminescence intensity.

A closed-form equation is derived for the critical nucleus charge at which a discrete level with the Dirac quantum number touches the lower continuum of the Dirac equation solutions. For the Coulomb potential cut off rectangularly at the short distance , , the critical nucleus charge values are obtained for several values of and . It is shown that the partial scattering matrix of elastic positron-nucleus scattering, , is also unitary for . For this range, the scattering phase is calculated as a function of the positron energy = , as are the positions and widths of quasidiscrete levels corresponding to the scattering matrix poles. The implication is that the single-particle approximation for the Dirac equation is valid not only for but also for and that there is no spontaneous creation of pairs from the vacuum.

We consider a superconducting qubit coupled to the nonstationary transmission line cavity with modulated frequency taking into account energy dissipation. Previously, it was demonstrated that in the case of a single nonadiabatical modulation of a cavity frequency there are two channels of a two-level system excitation which are due to the absorption of Casimir photons and due to the counterrotating wave processes responsible for the dynamical Lamb effect. We show that the parametric periodical modulation of the resonator frequency can increase dramatically the excitation probability. Remarkably, counterrotating wave processes under such a modulation start to play an important role even in the resonant regime. Our predictions can be used to control qubit-resonator quantum states as well as to study experimentally different channels of a parametric qubit excitation., 6 pages, 5 figures; revised version accepted in Physics Letters A

The drag effect of charge carriers in the system of two graphene layers separated by insulator that is caused by interlayer tunneling is considered. For description of interlayer tunneling the model of randomly positioned tunnel bridges is used. The dependence of transresistivity of the system on the tunnel bridge size for different mutual orientations of graphene layers (hexagonal and Bernal orientations) was calculated. We found that for the Bernal orientation, the transresistivity is sensitive to the tunneling bridge size and tends to zero in the point contact limit. For the hexagonal orientation, the transresistivity weakly depends on the tunneling bridge size. In both cases, the transresistivity of the system strongly depends on the longitudinal magnetic field strength and the difference between the Fermi energies of quasiparticles of graphene layers. This allows one to separate directly in experiments the contribution to the transresistivity caused by tunneling.

Electron-hole pairing due to the Coulomb interaction in the system of two graphene sheets has been considered. The critical transition temperature has been determined as a function of both the distance between the electron and hole Fermi lines and the triangular distortion of their spectrum. It has been shown that when the distance between Fermi lines is longer than a critical value, the temperature of the transition to a state with nonzero momentum of Cooper pairs (Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state) is higher than the temperature of the transition to the Bardeen-Cooper-Schrieffer state. The Josephson effect for the FFLO state has been analyzed, which is due to the tunneling of charge carriers between the graphene sheets. It has been shown that the spatial structure of the order parameter of the system in this state can be reconstructed, i.e., the FFLO state can be identified from the dependence of the tunneling current on the magnetic field parallel to the graphene sheets. Other experimental methods for studying the phase diagram of the system have been discussed.

The energy spectra and transport of electronic excitations in one-dimensional aperiodic sequences of quantum dots of Thue-Morse and double-periodic type are studied. The influence of external magnetic and electric fields on the energy spectra and transport is considered. For aperiodic sequences of quantum dots, in contrast to aperiodic sequences of atoms, the influence of relatively small magnetic and electric fields is essential, but localization occurs at finite values of the perturbations. The transmission coefficient is determined using the quasiclassical approximation with the Coulomb blockade taken into account. The resonance tunneling is studied.

Plasmon polaritons in a new system, a monolayer doped graphene embedded in optical microcavity, are studied here. The dispersion law for lower and upper cavity plasmon polaritons is obtained. Peculiarities of Rabi splitting for the system are analyzed; particularly, role of Dirac-like spinor (envelope) wave functions in graphene and corresponding angle factors are considered. Typical Rabi frequencies for maximal (acceptable for Dirac-like electron spectra) Fermi energy and frequencies of polaritons near polariton gap are estimated. The plasmon polaritons in considered system can be used for high-speed information transfer in the THz region.

The thermodynamic properties of a cluster of point Coulomb charges on a sphere have been analyzed using the Monte Carlo method for the number of charges 20 ≤ N ≤ 90. The ground state of the system of charges is described in the model of a closed quasi-two-dimensional triangular lattice with topological defects. We have determined the dependence of the Lindeman parameter δL of this system on N and on the dimensionless parameter $$ \tilde T $$ , which is proportional to the temperature T and to the radius R of the cluster: $$ \tilde T = {{k_B T\varepsilon R} \mathord{\left/ {\vphantom {{k_B T\varepsilon R} {e^2 }}} \right. \kern-\nulldelimiterspace} {e^2 }} $$ , where ∈ is the dielectric constant of the medium and e is the charge of a particle. The “magic numbers,” i.e., the N values, for which the melting point of the closed triangular lattice of charges is much higher than those for neighboring N values, have been found. The evolution of the lattice-melting mechanisms with an increase in the number of charges N in a mesoscopic cluster has been analyzed. For N ≤ 32, the melting of the lattice does not involve dislocations (nontopological melting); this behavior of the mesoscopic system of charges on the sphere differs from the behavior of the extended planar two-dimensional system. At N ≳ 50, melting is accompanied by the formation of dislocations. The mechanism of dislocation-free non-topological melting of a closed lattice, which occurs at small N values and is associated with the cooperative rotational motion of “rings” of particles, has been analyzed. The model has various implementations in the mesoscopic region; in particular, it describes the system of electrons over the liquid-helium cluster, the liquid-helium cluster with incorporated charged particles, a multielectron bubble in liquid helium, a charged quantum dot, etc.

Numerical simulation using the layered Korringa-Kohn-Rostoker (LKKR) method is applied to calculate the reflection and absorption spectra of an s-polarized electromagnetic wave incident on a faced-centered cubic photonic crystal (PC) with opal structure whose sites are occupied by two-layer metal-dielectric spheres. The reflection and absorption coefficients of the PC are analyzed as a function of the angle of incidence of the electromagnetic wave on the crystal surface. A range of wavelengths λ and angles of inclination θ to the normal is found in which the absorption experiences a sharp change under small variations of the above parameters. The appearance of peaks in the absorption spectrum of the PC is analyzed, and the spectrum is compared with the behavior of the reduced density of states. By the finite difference time domain (FDTD) method applied to the Maxwell equations, the spatial distribution of the energy density of electromagnetic field inside each of five layers of the PC is obtained at angles of incidence of 23° and 30° for a wave-length of 455 nm. It is demonstrated that the sharp maxima of the density of electromagnetic-field energy that are localized on the surfaces of absorbing metal spheres correspond to the absorption maximum. At the same time, at the absorption minimum, the maxima of the field energy density in each of the five layers are localized mainly between the lattice sites of the PC. An analogy between this phenomenon and the Borrmann effect, which is known in X-ray spectroscopy of ordinary crystals, is analyzed.

Phonon-exchange-induced superconducting pairing of effectively ultrarelativistic electrons in graphene is investigated. The Eliashberg equation obtained for describing pairing in the Cooper channel with allowance for delayed interaction are matrix equations with indices corresponding to the valence and conduction bands. The equations are solved in the high doping limit, in which pairing is effectively a single-band process, and in the vicinity of a critical quantum point of underdoped graphene for a value of the coupling constant for which pairing is an essentially multiband process. For such cases, analytic estimates are obtained for the superconducting transition temperature of the system. It is shown that the inclusion of dynamic effects makes it possible to determine the superconducting transition temperature, as well as the critical coupling constant for underdoped graphene, more accurately than in the static approximation of the BCS type. Estimates of the constants of electron interaction with the scalar optical phonon mode in graphene indicate that an appreciable superconducting transition temperature can be attained under a high chemical doping level of graphene.

Multi-band pairing of effectively ultrarelativistic electrons and holes in asymmetrically biased graphene bilayer in strong coupling regime is considered. In this regime, the pairing affects both conduction and valence bands of the both graphene layers, and the order parameter is a matrix, which indices correspond to the bands. For band-diagonal s-wave pairing, we derive the system of multi-band gap equations for the gaps in the valence and conduction bands and solve it in the approximation of constant gaps and in the approximation of separable pairing potential. For a characteristic width of the pairing region of order of magnitude of the chemical potential, the gap values are not much different from single-band BCS estimations. However, if the pairing region is wider, then the gaps can be much larger and depend exponentially on its energy width. We also predict gapped and soliton-like oscillations of a relative phase of the gaps and unpairing of quarter-vortices at Kosterlitz–Thouless transition.

The optical properties of textured surfaces of silicon solar cells are investigated by computer modeling. In calculations, the finite difference time-domain (FDTD) method is used to solve the Maxwell equations. Optimal sizes and shape of the textured surface are determined for which the reflection coefficient reaches its minimum. A comparison with the experimental data available from the literature is performed.

A method of predictive simulation of the optical properties of photonic crystals has been developed. Firstprinciple calculations of the optical properties have been performed for various materials over a wide temperature range. Absorption spectra have been calculated for tungsten opals with various geometric parameters. The influence of imperfections of a photonic crystal on its optical characteristics has been investigated. The calculation results agree with experimental data.

The structure and elastic properties of (5,5) and (10,10) nanotubes, as well as barriers for relative rotation of the walls and their relative sliding along the axis in a double-walled (5,5)@(10,10) carbon nanotube, are calculated using the density functional method. The results of these calculations are the basis for estimating the following physical quantities: shear strengths and diffusion coefficients for relative sliding along the axis and rotation of the walls, as well as frequencies of relative rotational and translational oscillations of the walls. The commensurability-incommensurability phase transition is analyzed. The length of the incommensurability defect is estimated on the basis of ab initio calculations. It is proposed that (5,5)@(10,10) double-walled carbon nanotube be used as a plain bearing. The possibility of experimental verification of the results is discussed., Comment: 14 pages

A new method is proposed for controlling the motion of nanoelectromechanical systems based on carbon nanotubes. In this method, a single-walled nanotube acquires an electric dipole moment owing to the chemical adsorption of atoms or molecules at open ends of the nanotube. The electric dipole moments of carbon nanotubes with chemically modified ends are calculated by the molecular orbital method. These nanotubes can be set in motion under the effect of a nonuniform electric field. The possibility of controlling the motion of nanoelectromechanical systems with the proposed method is demonstrated using a nanotube-based gigahertz oscillator as an example. The operating characteristics of the gigahertz oscillator are analyzed, and its operation is simulated by the molecular dynamics method. The controlling parameters and characteristics corresponding to the controlled operating conditions at a constant frequency for the system under investigation are determined.

The Bose condensation of two-dimensional dipolar excitons in quantum wells is numerically studied by the diffusion Monte Carlo simulation method. The correlation, microscopic, thermodynamic, and spectral characteristics are calculated. It is shown that, in structures of coupled quantum wells, in which low-temperature features of exciton luminescence have presently been observed, dipolar excitons form a strongly correlated system.

A system of like (positive or negative) charges forming “snowballs” or “bubbles” in a three-dimensional liquid helium cluster is investigated. The charges are confined inside the cluster by an “image potential” produced by the polarization of liquid helium. The stability of a multiply charged helium cluster is considered. Computer simulations are used to investigate the crystallization and melting of the system of charges depending on the dimensionless parameter T* = k B TeR/e 2, where k B is the Boltzmann constant, T is the temperature, e is the dielectric constant of liquid helium, R is the cluster radius, and e is a unit charge. Various characteristics, including symmetry groups and moments, have been found for equilibrium configurations of charges in a cluster with N = 1–100 charges. At small N ∼ 10, Thomson’s model of successive filling of “belts” of charges can be used to describe the structure of equilibrium configurations of charges. At large N, the description of the structure formed by charges using the idea of a quasi-two-dimensional “closed triangular lattice” with topological defects is more adequate. Formally, this description is valid starting from N = 4. The melting of a “lattice” of charges is described. A number of our conclusions can be generalized to clusters of other noble gases.

Crystal phase of indirect excitons formed by spatially separated electrons and holes in coupled quantum wells is analyzed. The collective mode spectrum of the exciton crystal at zero and nonzero agnetic fields is found. The spectrum consists of two optical and two acoustical modes (transverse and longitudinal in each case). We also study changes of the dipole crystal collective excitations at the transition exciton crystal-electron-hole plasma.

We investigate a one random variable tomography map, describing quantum state of a multipartite system. The random variable is analogous to center of mass considered in rotated and scaled reference frames in the phase space. Starting from the star product formalism, we construct the map, investigate its properties (including the symmetry properties in respect to identical particles permutations), derive the evolution equation, and consider a multimode oscillator as an example. The physical meaning of the map is analyzed in detail.

Screening and rearrangement of excitonic states in double layer systems were considered. Binding energy changes as a result of screening by spatially separated electrons were calculated for both direct and spatially indirect excitons. The critical electron concentrations at which screening effects cause a sharp decrease in the exciton binding energy and an increase in the exciton radius depending on the interlayer distance were determined. For a spatially indirect exciton, this dependence had a maximum caused by the competition of two effects as the interlayer distance grew, namely, a decrease in the seed interaction between electrons and holes and a weakening of the effect of hole screening by spatially separated electrons. The effect of spatially separated electron-exciton drag in a double layer system was studied in the Debye-Huckel approximation taking into account screening of interlayer electron-exciton interaction.

A new method is proposed for ab initio calculations of nonstationary quantum processes on the basis of a probability representation of quantum mechanics with the help of a positive definite function (quantum tomogram). The essence of the method is that an ensemble of trajectories associated with the characteristics of the evolution equation for the quantum tomogram is considered in the space where the quantum tomogram is defined. The method is applied for detailed analysis of transient tunneling of a wave packet. The results are in good agreement with the exact numerical solution to the Schrodinger equation for this system. The probability density distributions are obtained in the coordinate and momentum spaces at consecutive instances. For transient tunneling of a wave packet, the probability of penetration behind the barrier and the time of tunneling are calculated as functions of the initial energy.

Classification scheme for double-wall carbon nanotubes (DWCNT) based on their symmetry is proposed. According to the scheme each DWCNT ascribes to a family of DWCNTs with the same geometrical parameters: interwall distance, nanotube unit cell length and difference of wall chirality angles. This geometrical parameters, the barriers for the relative rotation of the wall, sliding along the nanotube axis and helical line of ‘thread’ and threshold forces causing the relative motion of the walls are calculated for a set of DWCNTs. The results of calculations allow to select DWCNTs that can be used in mechanical nanodevices such as nanobearings and of bolt-and-nut pairs. Possibility of orientational melting of DWCNTs with commensurate walls is discussed.

We propose a new method to simulate the quantum dynamics, based on the tomography representation. In its framework the quantum state is described by real nonnegative distribution function. We demonstrate the method applying it to the wave packet tunneling of one and two interacting particles.

We present a first-principles path integral Monte Carlo study of a finite number of strongly correlated electron–hole pairs in two symmetric vertically coupled quantum dots. In this system, the intra- and interdot correlations depend on the distance d between the dots, the density n (strength of confinement potential) and temperature T .F or fi xedd and T> 0, increasing n leads to four qualitatively different states: an exciton ‘liquid’, an exciton ‘crystal’, orientationally decoupled electron and hole ‘crystals’ and an electron (hole) liquid.

A new method is proposed for calculating the energy spectrum and the wave functions of N-electron quantum dots with an arbitrary confining potential. The method consists in expansion with respect to a dimensionless quantum parameter 1/Q, which is expressed in terms of the ratio of the characteristic Coulomb energy of electron-electron interaction to the characteristic energy of one-particle transition in a confining potential. Two-electron quantum dots with a parabolic confining potential in an external magnetic field are considered. Strongly correlated states of the system and the spin rearrangement in a strong magnetic field are analyzed. Analytic expressions are obtained for the energy and the wave functions of the system. It is shown that restriction of the analysis only to the first three terms in the quantum-parameter expansion gives an accuracy of one percent when calculating the energy even for values of Q on the order of unity, i.e., for the presently implementable GaAs quantum dots. The expressions for energy obtained are in a good agreement with the experimental data for quantum dots in a perpendicular magnetic field.

A rearrangement of the ground state of a Wannier-Mott exciton upon an increase in its momentum is considered. The phase diagram of the electron and the hole experiencing the Coulomb interaction on the magnetic momentum-external magnetic field plane is investigated. A jumplike exciton-magnetoexciton “phase” transition is observed upon an increase in the momentum in fields B weaker than a certain value B 0 even for B→0. At the point of transition, the exciton energy-momentum relation changes jumpwise from a quadratic law to a relation virtually independent of the momentum. For B

We theoretically analyze exciton-photon oscillatory dynamics within a homogenous polariton gas in presence of energy detuning between the cavity and quantum well modes. Whereas pure Rabi oscillations consist of the particle exchange between the photon and excitons states in the polariton system without any oscillations of the phases of the two sub-condensates, we demonstrate that any non-zero detuning results in oscillations of the relative phase of the photon and exciton macroscopic wave functions. Different initial conditions reveal a variety of behaviors of the relative phase between the two condensates, and a crossover from Rabi-like to Josephson-like oscillations is predicted., Comment: 6 pages, 3 figures

The changes in binding energy and oscillator strength of the exciton state due to the screening by a quasi-two-dimensional electron gas are calculated self-consistently in the approximation of noninteracting electrons and in the local field approximation. It is shown that the collapse of the bound state occurs at very low concentrations, Ns≈5×109 cm−2, which is a consequence of the inclusion of the nonlinearity of the response of the system to a Coulomb perturbation. The temperature dependence of the exciton collapse is investigated. The phase diagram of the dissociation of the given bound state is constructed, and the region in which it is possible to observe experimentally the temperature dependence of the exciton collapse is indicated.

Parametric excitation of atom moving parallel to corrugated (or artificially structured) metallic surface due to nonadiabatic variation of image forces is considered. It is shown that the excitation can be accompanied by photon radiation. Selection rules of the process are considered.

Two schemes for steady stimulated phonon generation (saser, i.e., phonon laser ) are proposed. The first scheme exploits a narrow-gap indirect semiconductor or analogous indirect gap semiconductor heterostructure where the tuning into resonance of one-phonon transition of electron–hole recombination can be carried out by external pressure, magnetic or electric fields. The second scheme uses one-phonon transition between direct and indirect exciton levels in coupled quantum wells. The tuning into the resonance of this transition can be accomplished by engineering of dispersion of indirect exciton by external in-plane magnetic and normal electric fields. In the second scheme the magnitude of phonon wave vector is determined by magnitude of in-plane magnetic field and, therefore, such a saser is tunable. Both schemes are analyzed and estimated numerically.

Spectral dependences of charge carrier relaxation rates, γe-e(ħω) and γ e-ph(ħω), were observed in Au and Cu films and YBa2Cu3O7-δ high-Tc superconductor films. The relaxation rates decreased substantially in the spectral region corresponding to interband transitions to the Fermi level region (ħωAu = 2.45 eV, ħωCu = 2.15 eV, and ħ ω1 = 1.89 eV and ħω2 = 2.08 eV for YBa2Cu3O7-δ). This relaxation deceleration opens up possibilities for developing a new method, based on the spectral dependences of relaxation rates, for the determination of the Fermi level position and the parameters of electron-electron and electron-phonon interactions on the one hand and for studying deviations from the Fermi-liquid behavior in strongly correlated electronic systems. The linear γe-e (ħω) ∝ |ħω− EF| spectral dependence was observed for a YBa2Cu3O7-δ film near ħω2 = 2.08 eV, which may be evidence of a non-Fermi-liquid behavior of the electronic subsystem.

This paper discusses two-dimensional mesoscopic clusters of particles that repel according to dipole, Coulomb, and logarithmic laws and are confined by an external parabolic potential. These models describe a number of physical systems, in particular, electrons in semiconductor structures or on a liquid-helium surface allowing for image forces, indirect excitons in coupled semi-conductor dots, and a small number of vortices in an island of a second-order superconductor or in superfluid helium. Two competing forms of ordering are detected in the particles in the mesoscopic clusters-the formation of a triangular lattice or of a shell structure. The temperature dependences of the potential energy, the mean-square radial and angular deviations, the radial and angular distributions of the particles, and the distribution of the particles over the local minima are studied. Melting in mesoscopic clusters occurs in two stages: at lower temperatures, there is orientation melting, from the frozen phase into a phase with rotational reorientation of “crystalline” shells with respect to each other; subsequently, a transition occurs in which the radial order disappears. Melting in dipole macroclusters occurs in a single stage. However, in Coulomb and logarithmic macroclusters, orientation melting occurs only for the outer pairs of shells. Orientation melting is also detected in three-dimensional Coulomb clusters. A connection is established between the character of the melting and the ratio of the energy barriers that describe the breakdown of the orientational and radial structure of a cluster.

The symmetry, energy, dipole and quadrupole moments of the ground states in `Thomson's problem' of point Coulomb charges on a sphere are found and analized for the number of charges N=2–100. The equilibrium configurations are considered as closed quasi-2D triangular lattices with topological defects (disclinations of various charge). An appropriate classification of the structures is proposed. The approach is compared with the description of the configurations in terms of `ring structures on sphere'. The problem has a number of physical and chemical realizations.

A two-dimensional mesoscopic cluster of “dusty plasma” particles, which can be interpreted as a system of microparticles in an rf gas discharge, is investigated. The ground-state configurations and corresponding eigenfrequencies and eigenvectors are found for clusters of N=22–40 particles in a harmonic confining potential. It is shown that a change in the Debye screening length R of the particle charge in the plasma can cause structural transformations of the ground state of the system, manifested as first-order or second-order phase transitions with respect to the parameter R. The disorder (“melting”) of the clusters is analyzed in detail by Monte Carlo simulation and molecular dynamics. By varying the characteristic range of particle interaction in a cluster, it is possible to modulate its thermodynamic properties and the character of the phase transitions, thereby causing a controlled transition of the system into the fully ordered, orientationally disordered, or fully disordered state. The possibility of dusty plasma clusters coexisting in different states is discussed.

A system of interacting, spatially separated excitons and electrons is examined in the presence of a Bose condensate of excitons. The kinetic properties of the system that are governed by the interaction of excitations in the exciton subsystem with electrons are investigated. It is shown that a nonequilibrium distribution of excitations in the exciton subsystem gives rise to an induced electron current. Experimental observation of the kinetic phenomena described can provide new information on the exciton phase state.

The transmission of wave packets through tunneling barriers is studied in detail by the method of quantum molecular dynamics. The distribution function of the times describing the arrival of a tunneling packet in front of and behind a barrier and the momentum distribution function of the packet are calculated. The behavior of the average coordinate of a packet, the average momentum, and their variances is investigated. It is found that under the barrier a part of the packet is reflected and a Gaussian barrier increases the average momentum of the transmitted packet and its variance in momentum space.

Instability in a system of interacting quasi-two-dimensional excitons in a type II superlattice of a finite thickness due to attraction between oppositely-directed excitonic dipoles in neighboring layers has been discovered. A stable system is that of indirect quasi-two-dimensional biexcitons formed by indirect excitons with dipole moments oriented in opposite directions. The radius and binding energy of indirect biexcitons has been calculated. A collective spectrum of a system of such biexcitons with a weak quadrupole interaction between them has been studied. Feasibility of Bose condensation, the density n s(T) of the superfluid component, and a phase transition to the superfliud state in a low-density system of indirect biexcitons have been analyzed.

The relaxation of nonequilibrium charge carriers in ZnSe films on metal substrates has been investigated by the femtosecond spectroscopic pump-supercontinuum probe method. Upon subgap and overgap excitations of ZnSe, red and blue photoinduced frequency shifts for the interference cavity modes in ZnSe films on chromium have been revealed. Such shifts and features of the relaxation times are explained by photoinduced changes in the boundary conditions and optical thickness of the microcavity.

The problem of exciton light absorption in quasi-two-dimensional inhomogeneous systems in a strong transverse magnetic field H is analyzed. We assume that a random Gaussian field (“white noise”) acting separately on an electron and a hole is due to (1) fluctuations in the quantum well thickness or (2) fluctuations in the concentrations of the solid solution components. The problem of a magnetoexciton in a random Gaussian white noise field has been reduced to the problem of the motion in an H-dependent effective field of a single particle with the effective magnetic mass of the exciton, which is a function of the magnetic field and parameters of the quantum wells, in a field characterized by “colored noise,” whose correlation function is different from that of the white noise field. In this approximation, the problem of a magnetoexciton in isolated and coupled quantum dots is considered. In the coherent-potential approximation, the exciton absorption in random fields of the first and second type in single and coupled quantum wells has been calculated. The absorption decreases as H increases in the range of strong magnetic fields, which is in agreement with experimental data.

Two-dimensional microclusters made up of particles repelled by the dipole law and confined by an external quadratic potential are considered. The model describes a number of physical systems, in particular, electrons in semiconductor structures near a metallic electrode, indirect excitons in coupled semiconductor dots etc. Two competing types of particle ordering in clusters have been revealed: formation of a triangular lattice and of a shell structure. Equilibrium configurations of clusters with N=1–40 particles are calculated. Temperature dependences of the structure, potential energy, and mean-square radial and angular displacements are studied. These characteristics are used to investigate cluster melting. Melting occurs in one or two stages, depending on N. Melting of a two-shell microcluster takes place in two stages: at low temperatures—from the frozen phase to a state with rotationally reoriented “crystalline” shells with respect to one another, followed by a transition involving breakdown of radial order. Melting in a cluster made up of a larger number of shells occurs in one stage. This is due to the fact that the potential barrier to intershell rotation is substantially lower than that to particle jumping from one shell to another for small N, and of the same order of magnitude for large N. A method is proposed for predicting the character of melting in shell clusters by comparing the potential barriers for shell rotation and intershell particle jumping.

The melting of two-dimensional and three-dimensional Coulomb micro- and macroclusters is studied. Temperature dependences of radial and angular square deviations of particles are investigated. The melting of microclusters has two stages : at lower temperature there is a transition from a frozen phase to a state with a rotatory reorientation of “crystalline” shells relative to each other, different pairs of shells melting at different temperatures. In the case of large N and high triangular symmetry inside the cluster, orientational melting takes place only for external pairs of shells. In this case external shells lose their order. At higher temperature a transition with a loss of radial shell order occurs. The origin of two-stage melting is in the smallness of the barrier energy relative to the rotation of shells in comparison with the barrier corresponding to the radial disordering of shells. It is shown also that the temperatures of orientational and total melting are at 5–15 times lower than the temperatures of disappearance of corresponding potential barriers. The influence of confinement anisotropy on the character of cluster melting is considered. It is found that at some degree of anisotropy the melting becomes one stage. The last is connected with an increase of the ratios of barriers of intershell rotation to barriers of jumps of a particle between the shells.

The boson lattice Hubbard model is used to study the role of quantum fluctuations of the phase and local density of the superfluid component in establishing a global superconducting state for a system of mesoscopic Josephson junctions or grains. The quantum Monte Carlo method is used to calculate the density of the superfluid component and fluctuations in the number of particles at sites of the two-dimensional lattice for various average site occupation numbers n 0 (i.e., number of Cooper pairs per grain). For a system of strongly interacting bosons, the phase boundary of the ordered superconducting state lies above the corresponding boundary for its quasiclassical limit—the quantum XY-model—and approaches the latter as n 0 increases. When the boson interaction is weak in the boson Hubbard model (i.e., the quantum fluctuations of the phase are small), the relative fluctuations of the order parameter modulus are significant when n 0

A Mott exciton in coupled quantum wells in a transverse magnetic field H is considered. An expression for the exciton spectrum in an arbitrary magnetic field for large separations D between quantum wells containing an electron (e) and a hole (h) is given. The exciton spectrum in a strong magnetic field for different Landau levels at arbitrary D has been calculated. Changes in the parameter D/l, where $$l = \sqrt {{{\hbar c} \mathord{\left/ {\vphantom {{\hbar c} {eH}}} \right. \kern-\nulldelimiterspace} {eH}}} $$ is the magnetic length, cause rearrangement of the magnetoexciton dispersion curves ℰ(P), where P is the conserved “magnetic” momentum, which is a function of the separation between the electron and hole in the plane of the quantum wells. Off-center (“roton”) extrema occur only for D/l

The formation of a superfluid exciton liquid in a system of spatially separated electrons and holes in a system of two coupled quantum wells is predicted and its properties are investigated. The ground-state energy and the equilibrium density of the exciton liquid are calculated as functions of distance D between the quantum wells. The properties of a rarefied exciton gas with dipole-dipole repulsions are considered, where this gas is the metastable phase for D

We discuss drag effects in a two-layer system of spatially separated electrons and excitons: the entrainment of excitons by moving electrons, and the entrainment of electrons by moving excitons. For the case of excitons entrained by electrons we find the drag velocity υ drag, and for electrons entrained by excitons we compute the induced electric field E 2. These drag effects can be sensitive indicators of the phase state of the excitons and of phase transitions in the exciton system (to a liquid phase, superfluid state, etc.)

Excitons in coupled quantum wells with spatially separated electrons (e) and holes (h) in a high transverse magnetic field (H) are considered. The exciton energies are calculated for various Landau levels and arbitrary interwell separations (D). The change of parameter D l (where l = hc eH ) leads to a reconstruction of the exciton dispersion laws e(P) ( P is the conserved “magnetic” momentum of the magnetoexciton, being proportional to the mean distance between e and h along the wells). Noncentral (“roton”) extrema exist only for interlayer separations D l smaller than the critical one (the latter depends on exciton quantum numbers). Impurity states in CQWs are also calculated.