arXiv subjects

S. S. Seidov

Publications and source records attributed to S. S. Seidov.

15 recordsLinked to original sources

arXiv2026

Coherent states in quantum billiards constructed in the basis of the continued eigenfunctions

In the article a new approach to construction of generalized coherent states in quantum billiards is proposed. The coherent states are defined as the projections of a Gaussian wave function on the basis of the eigenstates of the quantum billiard, continued outside. The continuation is built as the solution of the equivalent Balian--Bloch equation, defined on the entire $\mathbb{R}^2$ and the projection operator is built using the resolvent of the Balian--Bloch equation. In the case of the one--dimensional potential well and billiards, belonging to the Coxeter group, the wave functions of the coherent states were expressed analytically via the Jacobi and Riemann theta functions.

nlin.CD↗

arXiv2026

Analytical solution of coupled self--consistency and linearised Usadel equations for the dirty superconductors at $T_c$ and with the proximity effect

In this manuscript we consider a superconducting film in the vicinity of the critical temperature and presence of the proximity effect. We analytically solve the corresponding linearised Usadel equation and the self-consistency equation, defining the critical temperature. This is a system of coupled differential and integral equations for the anomalous Green function and the order parameter of the superconductor. The proximity effect defines the boundary conditions. The formal solution of the system is found for the general case of the linearised boundary conditions defined by the proximity effect, reducing the set of equations to an eigenvalue problem. The latter defines the critical temperature of the superconducting phase transition and the spatial distributions of the anomalous Green function and the superconducting order parameter.

cond-mat.supr-con↗

arXiv2026

Quantum viscosity mechanism of the dissipative dynamics in the Dicke model expressed via Lindblad equation of motion

Quantum dissipation is studied in the superradiant phase of the Extended Dicke model. It is demonstrated analytically by quantum mechanical derivation of the Lindblad equation for the Dicke model in the superradiant state coupled to Caldeira-Leggett thermal bath, that the effective viscosity appearing in the semiclassical equations of motion of polaritonic condensate survives in the zero temperature limit T -> 0. The nonzero contribution to viscosity contains prefactor nB (ω, T ) + 1 with the Bose-Einstein function nB of harmonic oscillators in the thermal bath, indicating that virtual excitations of harmonic oscillators in the thermal bath coupled to the polaritons of Dicke model give rise to effective viscosity in the T -> 0 limit. Besides, it is demonstrated analytically, that correct expression for Lindbladian in the superradiant phase should be built using condensate-shifted creation and annihilation operators of the photons and pseudospin operators in Holstein-Primakoff representation of the coupled to photons two-level systems in order the system could relax to its minimum energy in T -> 0 limit due to thermal bath provided effective viscosity.

quant-ph↗

arXiv2025

Energy spectrum and quantum phase transition of the coupled single spin and an infinitely coordinated Ising chain

We consider a spin model, composed of a single spin, connected to an infinitely coordinated Ising chain. Theoretical models of this type arise in various fields of theoretical physics, such as theory of open systems, quantum control and quantum computations. In the thermodynamic limit of infinite chain, we map the chain Hamiltonian to the Hamiltonian of the Lipkin-Meshkov-Glik model and the system as a whole is described by a generalized Rabi Hamiltonian. Next the effective Hamiltonian is obtained using Foulton-Gouterman transformation. In thermodynamic limit we obtain the spectrum of the whole system and study the properties of the ground state quantum phase transition.

quant-ph↗

arXiv2024

Wigner current in multidimensional quantum billiards

In the present paper we derive the Wigner current of the particle in a multidimensional billiard -- the compact region of space in which the particle moves freely. The calculation is based on proposed by us previously method of imposing boundary conditions by convolution of the free particle Wigner function with some time independent function, defined by the shape of the billiard. This method allowed to greatly simplify the general expression for the Wigner current, representing its $\mathbf{p}$-component as a surface integral of the product of the shifted particles wave functions. The results are also connected to an alternative approach, which takes into account the boundary conditions by adding the $\propto δ'(x)$ term to the Hamiltonian. The latter is also generalized to the multidimensional case.

quant-ph↗

arXiv2024

Density of states in the heterostructure ferromagnetic insulator-superconductor-ferromagnetic insulator

We consider a spin valve composed of a superconducting film (S) between two ferromagnetic insulators (FI) on two sides. In the dirty limit the superconductor is described by Usadel equations. Appropriate boundary conditions were chosen for two S-FI interfaces, which are described via the interface parameter spin mixing angle. By numerically solving the Usadel equations, the density of states (DOS) at different spin mixing angles were obtained. It was shown previously that critical temperature of such FI-S-FI structure depends on the mutual alignment of the FI layers magnetization. We follow the evolution of DOS at change of misalignment of ferromagnets magnetization and probe the zero bias peak creation. The DOS characteristic features may give a fruitful information about triplet superconducting components creation and interplay inside the S layer.

cond-mat.supr-con↗

arXiv2024

Quantum Dicke battery supercharging in the "bound luminocity" state

Quantum batteries, which are quantum systems to be used for storage and transformation of energy, are attracting research interest recently. A promising candidate for their investigation is the Dicke model, which describes an ensemble of two--level systems interacting with a single--mode electromagnetic wave in a resonator cavity. In order to charge the battery, a coupling between the ensemble of two--level systems and resonator cavity should be turned off at a certain moment of time. This moment of time is chosen in such a way, that the energy gets fully stored in the ensemble of two--level systems. In our previous works we have investigated a ``bound luminosity'' superradiant state of the extended Dicke model and found analytical expressions for dynamics of coherent energy transfer between superradiant condensate and the ensemble of the two--level systems. Here, using our previous results, we have derived analytically the superlinear law for the quantum battery charging power $P\sim N^{3/2}$ as function of the number $N$ of the two--level systems in the battery, and also $N$-dependence for the charging time $t_c\sim N^{-1/2}$. The $N$--exponent $3/2$ of the charging power is in quantitative correspondence with the recent result ${1.541}$ obtained numerically by other authors. The physics of the Dicke quantum battery charging is considered in detail.

quant-ph↗

arXiv2023

Correspondence between Dicke-model semiclasscial dynamics in the superradiant dipolar phase and the Euler heavy top

Analytic expression is found for the frequency dependence of transmission coefficient of a transmission line inductively coupled to the microwave cavity with superradiant condensate. Sharp transmission drops reflect condensate's frequencies spectrum. These results pave way to direct detection of emergence of the superradiant condensates in quantum metamaterials. Results are based on the analytic solutions of the nonlinear semiclassical dynamics of superradiant photonic condensate in the Dicke model of an ensemble of two-level atoms dipolar coupled to the electromagnetic field in the microwave cavity. In adiabatic limit with respect to photon degree of freedom the system is approximately integrable, with evolution being expressed via Jacobi elliptic functions of real time. Depending on the coupling strength, the semiclassical coordinate of superradiant condensate in the ground state either oscillates in one of the two degenerate minima of condensate's potential energy or traverses between them over the saddle point. An experimental setup for measuring of the breakdown of the normal phase of the Dicke model via coupling to the transmission line is proposed. A one-to-one mapping of semiclassical motion of superradiant condensate on the nodding of unstable Lagrange "sleeping top" also turns Dicke model into analogue device for modelling dynamics of mechanical systems.

physics.optics↗

arXiv2023

Dicke model semiclassical dynamics in superradiant dipolar phase in the 'bound luminosity' state

Analytic solution of semiclassical dynamics equations of the Dicke model in a superradiant state is presented. The time dependences of the amplitudes of superradiant bosonic condensate and coherent two-level atomic array in the microwave cavity prove to be expressed via Jacobi elliptic functions of real time and manifest existence of an adiabatic invariant of motion in the strongly coupled system. The periodic beatings of the photonic and atomic coherent state amplitudes are shifted in time revealing an effect of 'bound luminosity', when energy stored in the two-level system during 'darkness' in the cavity is suddenly converted into photonic condensate that 'illuminates' the cavity for half a period, before it plunges into 'darkness' again.

quant-ph↗

arXiv2023

Wigner function dynamics with boundaries expressed as convolution

In the present paper a method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. Starting with the problem of a reflection from an impenetrable wall, the obtained solution is then generalized to the case of a particle confined in an infinite well in arbitrary dimensions. It is known, that boundary value problems in the phase space formulation of the quantum mechanics are surprisingly tricky. The complications arise from nonlocality of the expression involved in calculation of the Wigner function. Several ways of treating such problems were proposed. They are rather complicated and even exotic, involving, for example, corrections to the kinetic energy proportional to the derivatives of the Dirac delta--function. The presented in the manuscript approach is simpler both from analytical point of view and regarding numerical calculation. The solution is brought to a form of convolution of the free particle solution with some function, defined by the shape of the well. This procedure requires calculation of an integral, which can be done by developed analytical and numerical methods.

quant-ph↗

arXiv2022

Quantum dynamics of a $4π$-kink in Josephson junctions parallel arrays with large kinetic inductances

We present a theoretical study of the quantum dynamics of \textit{two} magnetic fluxons (MFs) trapped in Josephson junction parallel arrays (JJPAs) with large kinetic inductances. The Josephson phase distribution of two trapped MFs satisfies a topological constraint, i.e., a total variation of Josephson phases along a JJPA is $4π$. In such JJPAs the characteristic length of Josephson phase distribution ("the size" of MF) is drastically reduced to be less than a single cell size. Two extreme dynamic patterns will be distinguished: two weakly interacting MFs and two merged MFs, i.e., a $4π$-kink. Taking into account the repulsive interaction between two MFs located in the same or adjacent cells we obtain the energy band spectrum $E_{4π}(p)$ for a quantum $4π$-kink. The coherent quantum dynamics of a $4π$-kink demonstrates the quantum beats with the frequency and amplitude strongly deviating from ones observed for two independent MFs. In the presence of applied dc and ac bias current of frequency $f$ a weakly incoherent quantum dynamics of a $4π$-kink results in the Bloch oscillations and the seminal current steps with values $I^{(n)}_{4π}=enf$ which are two times less than ones for two independent MFs.

cond-mat.supr-con↗

arXiv2021

Quantum beats of a magnetic fluxon in a two-cell SQUID

We report a detailed theoretical study of a coherent macroscopic quantum-mechanical phenomenon - quantum beats of a single magnetic fluxon trapped in a two-cell SQUID of high kinetic inductance. We calculate numerically and analytically the low-lying energy levels of the fluxon, and explore their dependence on externally applied magnetic fields. The quantum dynamics of the fluxon shows quantum beats originating from its coherent quantum tunneling between the SQUID cells. We analyze the experimental setup based on a three-cell SQUID, allowing for time-resolved measurements of quantum beats of the fluxon.

quant-ph↗

arXiv2021

Quantum dynamics of a single fluxon in Josephson junctions parallel arrays with large kinetic inductances

We present a theoretical study of coherent quantum dynamics of a single magnetic fluxon (MF) trapped in Josephson junction parallel arrays (JJPAs) with large kinetic inductances. The MF is the topological excitation carrying one quantum of magnetic flux, $Φ_0$. The MF is quantitatively described as the $2π$-kink in the distribution of Josephson phases, and for JJPAs with high kinetic inductances the characteristic length of such distribution ("the size" of MF) is drastically reduced. Characterizing such MFs by the Josephson phases of three consecutive Josephson junctions we analyse the various coherent macroscopic quantum effects in the MF quantum dynamics. In particular, we obtain the MF energy band originating from the coherent quantum tunnelling of a single MF between adjacent cells of JJPAs. The dependencies of the band width $Δ$ on the Josephson coupling energy $E_J$, charging energy $E_C$ and the inductive energy of a cell $E_L$, are studied in detail. In long linear JJPAs the coherent quantum dynamics of MF demonstrates decaying quantum oscillations with characteristic frequency $f_{qb}=Δ/h$. In short annular JJPAs the coherent quantum dynamics of MF displays complex oscillations controlled by the Aharonov-Casher phase $χ\propto V_g$, where $V_g$ is an externally applied gate voltage. In the presence of externally applied dc bias, $I$, a weakly incoherent dynamics of quantum MF is realized in the form of macroscopic Bloch oscillations leading to a typical "nose" current-voltage characteristics of JJPAs. As ac current with frequency $f$ is applied the current-voltage characteristics displays a set of equidistant current steps at $I_n=2en f$.

cond-mat.supr-con↗

arXiv2020

Spontaneous symmetry breaking and Husimi Q-functions in extended Dicke model

We study the emergence of a parity breaking coherent photonic state of a photon mode coupled to finite array of two-level systems, represented by pseudospins 1/2. The pseudospin-photon interaction is realised via a shift of the photonic oscillator equilibrium position by an amount linear in Cartesian component of the total pseudospin. We demonstrate analytically, that the instability is manifested in an upturn from concave to convex of the ground state energy dependence on the total pseudospin component coupled to the photons. The perturbation, sufficient for parity breaking, tends to zero in the ultrastrong limit of light-matter coupling. We present phase diagram of finite pseudospin-photon system, that demonstrates this feature. Evolution of Husimi Q-functions of the pseudospin and photon subsystems, and of the pseudospin entropy, along different trajectories across the phase diagram is presented.

cond-mat.stat-mech↗

arXiv2018

Conductivity of anisotropic inhomogeneous superconductors above critical temperature

We propose a model and derive analytical expressions for conductivity in heterogeneous fully anisotropic conductors with ellipsoid superconducting inclusions. This model and calculations are useful to analyze the observed temperature dependence of conductivity anisotropy in various anisotropic superconductors, where superconductivity onset happens inhomogeneously in the form of isolated superconducting islands. The results are applied to explain the experimental data on resistivity above the transition temperature $T_c$ in the high-temperature superconductor $\mathrm{YBa_2Cu_4O_8}$ and in the organic superconductor $β$-(BEDT-TTF)$_{2}$I$_{3}$. The comparison of resistivity data and diamagnetic response in $β$-(BEDT-TTF)$_{2}$I$_{3}$ allows us to estimate the size of superconducting inclusions as $d\sim 1μm$.

cond-mat.supr-con↗