Quasiclassical Approximation Research Articles

Neutrino evolution in dense matter and electromagnetic field

Neutrino evolution in dense matter and electromagnetic field is studied within quantum-field theoretical description on the base of a modification of the Standard Model, where the neutrinos are combined in S U(3)-multiplets. A quantum wave equation for neutrino in matter and electromagnetic field is obtained. In quasi-classical approximation a general method for calculating the probabilities of different spin-flavor transitions of neutrino in constant homogeneous field and moving matter with constant polarization is developed. In two-flavor model the explicit form of the solutions is obtained in constant electromagnetic field taking into account the transition magnetic moments. The obtained spin-flavor transition probabilities are compared to the results for unpolarized moving matter.

Spin Splitting Induced in a Superconductor by an Antiferromagnetic Insulator.

Inspired by recent feats in exchange coupling antiferromagnets to an adjacent material, we demonstrate the possibility of employing them for inducing spin splitting in a superconductor, thereby avoiding the detrimental, parasitic effects of ferromagnets employed to this end. We derive the Gor'kov equation for the matrix Green's function in the superconducting layer, considering a microscopic model for its disordered interface with a two-sublattice magnetic insulator. We find that an antiferromagnetic insulator with effectively uncompensated interface induces a large, disorder-resistant spin splitting in the adjacent superconductor. In addition, we find contributions to the self-energy stemming from the interfacial disorder. Within our model, these mimic impurity and spin-flip scattering, while another breaks the symmetries in particle-hole and spin spaces. The latter contribution, however, drops out in the quasiclassical approximation and thus, does not significantly affect the superconducting state.

Ionization of Impurities by Constant and Alternating Electric Fields in a Gap Graphene Modification

The probability of the ionization of impurities in graphene with a gap in its energy spectrum in co-directional constant and alternating electric fields is examined in the quasiclassical approximation. Analytical expressions for the probability of ionization in a constant electric field and a strong alternating electric field acting individually are obtained.

Topological Structures in Unconventional Scenario for 2D Cuprates

Numerous experimental data point to cuprates as d-d charge transfer unstable systems whose description implies the inclusion of the three many-electron valence states CuO $_{4}^{7-,6-,5-}$ (nominally Cu1+,2+,3+) on an equal footing as a well-defined charge triplet. We introduce a minimal model to describe the charge degree of freedom in cuprates with the on-site Hilbert space reduced to only the three states and make use of the S = 1 pseudospin formalism. The formalism constitutes a powerful method to study complex phenomena in interacting quantum systems characterized by the coexistence and competition of various ordered states. Overall, such a framework provides a simple and systematic methodology to predict and discover new kinds of orders. In particular, the pseudospin formalism provides the most effective way to describe different topological structures, in particular, due to a possibility of a geometrical two-vector description of the on-site states. We introduce and analyze effective pseudospin Hamiltonian with on-site and inter-site charge correlations, two types of a correlated one-particle transfer and two-particle, or the composite boson transfer. The latter is of a principal importance for the HTSC perspectives. The 2D S = 1 pseudospin system is prone to a creation of different topological structures, which form topologically protected inhomogeneous distributions of the eight local S = 1 pseudospin order parameters. We present a short overview of localized topological structures, typical for S = 1 (pseudo)spin systems, focusing on unexpected antiphase domain walls in parent cuprates and so-called quadrupole skyrmion, which are believed to be candidates for a topological charge excitation in parent or underdoped cuprates. Puzzlingly, these unconventional structures can be characterized by an uniform distribution of the mean on-site charge, that makes these invisible for X-rays. Quasi-classical approximation and computer simulation are applied to analyze localized topological defects and evolution of the domain structures in “negative-U” model under charge order-superfluid phase transition.

Confinement of an Electron in an Image Potential and an External Electrostatic Field

The quasi-classical approximation is used to determine the positions of the classical turning points upon motion of an electron that is bound by an image field and a constant homogeneous electric field of the same direction. Power expansions of the coordinates of the turning points in a wide range of electron energies and field strengths are obtained. The mechanism of one-dimensional confinement of an electron, which determines a completely discrete spectrum of states, is described. The dependence of the spatial width of the confinement region on the field strength and electron energy is determined. The dependences of the electron energy in different states on the external field strength are calculated numerically. Quasi-classical quantization is performed, and the dependence of the electron energy on the width of the confinement region is determined. The energy interval of a maximum density of electron states is found, which is determined by the dependence of the width of the confinement region on the electric field strength.

New fractional nonlinear integrable Hamiltonian systems

We have constructed a new fractional pseudo-differential metrized operator Lie algebra on the axis, enabling within the general Adler–Kostant–Symes approach the generation of infinite hierarchies of integrable nonlinear differential-fractional Hamiltonian systems of Korteweg–de Vries, Schrödinger and Kadomtsev–Petviashvili types. Using the natural quasi-classical approximation of the metrized fractional pseudo-differential operator Lie algebra, we construct a new metrized fractional symbolic Lie algebra and related infinite hierarchies of integrable mutually commuting fractional symbolic Hamiltonian flows, modeling Benney type hydrodynamical systems.

Excitonic density waves, biexcitons, and orbital-selective pairing in two-orbital correlated chains

We present a comprehensive study of a one-dimensional two-orbital model at and below quarter-filling that realizes a number of unconventional phases. In particular, we find an excitonic density wave in which excitons quasi-condense with finite center of mass momentum and an order parameter that changes phase with wave-vector $Q$. In this phase, excitons behave as hard-core bosons without charge order. In addition, excitons can pair to form bi-excitons in a state that is close to a charge density-wave instability. When pairing dominates over the inter-orbital repulsion, we encounter a regime in which one orbital is metallic, while the other forms a spin gapped superconductor, a genuine orbital selective paired state. All these results are supported by both, analytical and numerical calculations. By assuming a quasi-classical approximation, we solve the three-body hole-electron-spinon problem and show that excitons are held together by forming a bound state with spinons. In order to preserve the antiferromagnetic background, excitons acquire a dispersion that has a minimum away from $k=0$. The full characterization of the different phases is obtained by means of extensive density matrix renormalization group calculations.

Interplay between orbital-quantization effects and the Fulde-Ferrell-Larkin-Ovchinnikov instability in multiple-band layered superconductors

We explore superconducting instability for a clean two-band layered superconductor with deep and shallow bands in the magnetic field applied perpendicular to the layers. In the shallow band, the quasiclassical approximation is not applicable, and Landau quantization has to be accounted for exactly. The electronic spectrum of this band in the magnetic field is composed of the one-dimensional Landau-level minibands. With increasing magnetic field the system experiences series of Lifshitz transitions when the chemical potential enters and exits the minibands. These transitions profoundly influence the shape of the upper critical field at low temperatures. In addition, the Zeeman spin splitting may cause the nonuniform state with interlayer modulation of the superconducting order parameter (Fulde-Ferrell-Larkin-Ovchinnikov state). Typically, the quantization effects in the shallow band strongly promote the formation of this state. The uniform state remains favorable only in the exceptional resonance cases when the spin-splitting energy exactly matches the Landau-level spacing. Furthermore, for specific relations between electronic spectrum parameters, the alternating FFLO state may realize, in which the order parameter changes sign between the neighboring layers. For all above cases, the reentrant high-field superconducting states may emerge at low temperatures if the shallow band has significant contribution to the Cooper pairing.

Quasi-Classical Model of the Static Electrical Conductivity of Heavily Doped Degenerate Semiconductors at Low Temperatures

Germanium, silicon, gallium arsenide, and indium antimonide n-type crystals on the metal side of the insulator–metal transition (Mott transition) are considered. In the quasi-classical approximation, the static (direct current) electrical conductivity and the drift mobility of electrons of the c band, and electrostatic fluctuations of their potential energy and the mobility edge are calculated. It is considered that a single event of the elastic Coulomb scattering of a mobile electron occurs only in a spherical region of the crystal matrix with an impurity ion at the center. The results of calculations using the proposed formulas without using fitting parameters are numerically consistent with experimental data in a wide range of concentrations of hydrogenlike donors at their weak and moderate compensation by acceptors.

Mechanisms of 200 MeV electron radiation in diamond crystal in the axial orientation

Abstract The γ -radiation by electrons with the energy of ∼ 200 MeV in a 100 μ m-thick diamond crystal has been measured at the MAX-lab experimental facility, when the electrons are incident on the crystal along the 〈 100 〉 axis. In this case, the intensity of the -radiation with the energy ∼ 1–2 MeV is approximately 16 times higher than that in amorphous matter of the same thickness. Theoretical calculations based on the quasi-classical QED approximation are in good agreement with the experimental data. The analysis of the radiation mechanisms has shown that the main contribution to the radiation intensity resulted from electrons, moving in the above-barrier regime and at small angles to the crystal axis.

Charged and uncharged vortices in quasiclassical theory

The charging effect of a superconducting vortex core is very important for transport properties of superconducting vortices. The chiral p-wave superconductor, known as a topological superconductor (SC), has a Majorana fermion in a vortex core and the charging effect has been studied using microscopic Bogoliubov{de Gennes (BdG) theory. According to calculations based on the BdG theory, one type of the vortex is charged as well as the vortex of the s-wave SC, while the other is uncharged. We reproduce this interesting charging effect using an augmented quasiclassical theory in chiral p-wave SCs, by which we can deal with particle-hole asymmetry in the quasiclassical approximation.

Asymptotics of quasi-classical localized states in 2D system of charged hard-core bosons

The continuous quasi-classical two-sublattice approximation is constructed for the 2D system of charged hard-core bosons to explore metastable inhomogeneous states analogous to inhomogeneous localized excitations in magnetic systems. The types of localized excitations are determined by asymptotic analysis and compared with numerical results. Depending on the homogeneous ground state, the excitations are the ferro and antiferro type vortices, the skyrmion-like topological excitations or linear domain walls.

Quasiclassical Theory of Spin Dynamics in Superfluid $$^3$$ 3 He: Kinetic Equations in the Bulk and Spin Response of Surface Majorana States

We develop a theory based on the formalism of quasiclassical Green's functions to study the spin dynamics in superfluid $^3$He. First, we derive kinetic equations for the spin-dependent distribution function in the bulk superfluid reproducing the results obtained earlier without quasiclassical approximation. Then we consider a spin dynamics near the surface of fully gapped $^3$He-B phase taking into account spin relaxation due to the transitions in the spectrum of localized fermionic states. The lifetime of longitudinal and transverse spin waves is calculate taking into account the Fermi-liquid corrections which lead to the crucial modification of fermionic spectrum and spin responses.

Microscopic Theory of Pinning of Multiquantum Vortex in Cylindrical Cavity

We have proposed and developed a microscopic model of depinning (escape) of a multiquantum vortex in a superconductor with a cylindrical nonconducting cavity with the transverse size smaller than or on the order of the superconducting coherence length ξ0 at zero temperature. The spectrum of subgap quasiparticle excitations in two- and three-quantum vortices trapped by a cylindrical cavity has been calculated in the quasiclassical approximation. It is shown that the transformation of the spectrum is accompanied by break of anomalous spectral branches due to normal reflection of quasiparticles from the surface of a defect. A microscopic (spectral) criterion for multiquantum vortex pinning has been proposed; according to this criterion, the multiquantum vortex can be trapped in the cavity during the formation of a minigap in the elementary excitation spectrum near the Fermi level. Self-consistent calculations of density of states N(r, e) for two- and three-quantum vortices trapped by a cylindrical cavity of radius on the order of ξ0 have been performed using quasiclassical Eilenberger equations. In the pure limit and for low temperatures T ≪ T c , peculiarities observed in the N(r, e) distribution reflect the presence of M anomalous spectral branches in the M-quantum vortex and confirm the correctness of the spectral criterion of pinning (depinning) of a multiquantum vortex.

Quantum theory of multiscale coarse-graining.

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.

Квазиклассическая модель статической электропроводности сильно легированных вырожденных полупроводников при низких температурах

AbstractGermanium, silicon, gallium arsenide, and indium antimonide n -type crystals on the metal side of the insulator–metal transition (Mott transition) are considered. In the quasi-classical approximation, the static (direct current) electrical conductivity and the drift mobility of electrons of the c band, and electrostatic fluctuations of their potential energy and the mobility edge are calculated. It is considered that a single event of the elastic Coulomb scattering of a mobile electron occurs only in a spherical region of the crystal matrix with an impurity ion at the center. The results of calculations using the proposed formulas without using fitting parameters are numerically consistent with experimental data in a wide range of concentrations of hydrogenlike donors at their weak and moderate compensation by acceptors.

Transition radiation on a superlattice in finite thickness plate generated by two acoustic waves

Forward transition radiation from relativistic electrons is investigated in an ultrasonic superlattice excited in a finite thickness plate by two acoustic waves. In the quasi-classical approximation formulae are derived for the vector potential of the electromagnetic field and for the spectral-angular distribution of the radiation intensity. Zone structures appear in the plate, which makes it possible (by an appropriate choice of the frequencies of the two acoustic waves) to control the spectral-angular distribution of the radiation through changes in the parameters of the medium. The acoustic waves generate new resonance peaks in the spectral and angular distribution of the radiation intensity. The heights of the peaks can be tuned by choosing the parameters of the acoustic waves. Numerical examples are presented for a plate of fused quartz.

Stationary and non-stationary solutions of the evolution equation for neutrino in matter

We study solutions of the equation which describes the evolution of a neutrino propagating in dense homogeneous medium in the framework of the quantum field theory. In the two-flavor model the explicit form of Green function is obtained, and as a consequence the dispersion law for a neutrino in matter is derived. Both the solutions describing the stationary states and the spin-flavor coherent states of the neutrino are found. It is shown that the stationary states of the neutrino are different from the mass states, and the wave function of a state with a definite flavor should be constructed as a linear combination of the wave functions of the stationary states with coefficients, which depend on the mixing angle in matter. In the ultra-relativistic limit the wave functions of the spin-flavor coherent states coincide with the solutions of the quasi-classical evolution equation. Quasi-classical approximation of the wave functions of spin-flavor coherent states is used to calculate the probabilities of transitions between neutrino states with definite flavor and helicity.

Quasi-classical localized states in the 2D ferrimagnet

We consider highly anisotropic 2D quantum s = 1/2 (pseudo)magnetic system which is equivalent to the frequently used system of charged hard-core bosons on a square lattice. In the continuous quasi-classical approximation, the types of localized excitations are determined by asymptotic analysis and compared with numerical results. Depending on the homogeneous ground state, the excitations are the ferro and antiferro type vortices, the skyrmion-like topological excitations or linear domain walls.

Application of Quasi-Classical Approximation to Describe Black Holes

Application of Quasi-Classical Approximation to Describe Black Holes