arXiv subjects

Vladimir Gasparian

Publications and source records attributed to Vladimir Gasparian.

At least 19 recordsLinked to original sources

arXiv2026

Scattering matrix elements and energy spectrum of one-dimensional hybrid PT-symmetric finite systems

In this work, we provide a complete description of the scattering matrix elements and electron energy spectrum in one dimensional PT-symmetric hybrid finite systems, using the characteristic determinant approach. We present an analytical formulation of the problem and obtain a closed-form expression for the energy spectrum of the system, consisting of a region of real potential (passive region) surrounded by regions of gain and loss on the left and right, respectively. It has been shown that under certain conditions and a specific ratio between the real and imaginary parts of the complex potentials, it is possible to find analytical expressions for the spectral singularities at which the scattering matrix elements of the hybrid structure tend to infinity at a specific real energy. Within the framework of the same approach, we present a compact analytical expression for the quantization condition that determines the energy spectrum of a model corresponding to the placement of a rigid lattice within a finite-sized box.

cond-mat.mes-hall↗

arXiv2025

Characteristic determinant approach to the spectrum of one-dimensional $\mathcal{P}\mathcal{T}$-symmetric systems

We obtain a closed form expression for the energy spectrum of $\mathcal{P}\mathcal{T}$-symmetric superlattice systems with complex potentials of periodic sets of two $δ$-potentials in the elementary cell. In the presence of periodic gain and loss we analyzed in detail a diatomic crystal model, varying either the scatterer distances or the potential heights. It is shown that at a certain critical value of the imaginary part of the complex amplitude, topological states depending on the lattice size and the configuration of the unit cell can disappear. This may happened at the $\mathcal{PT}$-symmetry breaking (exceptional) points.

cond-mat.mes-hall↗

arXiv2024

Tunneling time in coupled-channel systems

In present work, we present a couple-channel formalism for the description of tunneling time of a quantum particle through a composite compound with multiple energy levels or a complex structure that can be reduced to a quasi-one-dimensional multiple-channel system.

cond-mat.other↗

arXiv2023

Toward extracting scattering phase shift from integrated correlation function

In present work, a relation that connects the integrated correlation function of a trapped two-particle system to infinite volume particles scattering phase shift is derived. It has the potential to provide an alternative approach for extracting two-particle scattering phase shift from integrated correlation function in lattice simulation at small Euclidean time region. Both (i) perturbation calculation of 1+1 dimensional lattice Euclidean field theory model of fermions interacting with a contact interaction and (ii) Monte Carlo simulation of a 1D exactly solvable quantum mechanics model are carried out to test the proposed relation. In contrast to conventional two-step approach of extracting energy levels from temporal correlation function in lattice simulation at large Euclidean time first and then applying Lüscher formula to convert energy levels into scattering phase shifts, we show that the difference of integrated correlation functions between interacting and noninteracting trapped systems converges rapidly to infinite volume limit that is given in terms of scattering phase shifts at small Euclidean time region.

hep-lat↗

arXiv2023

Tunneling time and Faraday/Kerr effects in $\mathcal{PT}$-symmetric systems

We review the generalization of tunneling time and anomalous behaviour of Faraday and Kerr rotation angles in parity and time ($\mathcal{P}\mathcal{T}$)-symmetric systems. Similarities of two phenomena are discussed, both exhibit a phase transition-like anomalous behaviour in certain range of model parameters. Anomalous behaviour of tunneling time and Faraday/Kerr angles in $\mathcal{P}\mathcal{T}$-symmetric systems is caused by the motion of poles of scattering amplitudes in energy/frequency complex plane.

cond-mat.other↗

arXiv2023

Tunneling time in $\mathcal{P}\mathcal{T}$-symmetric systems

In the present work we propose a generalization of tunneling time in parity and time ($\mathcal{P}\mathcal{T}$)-symmetric systems. The properties of tunneling time in $\mathcal{P}\mathcal{T}$-symmetric systems are studied with a simple contact interactions periodic finite size diatomic $\mathcal{P}\mathcal{T}$-symmetric model. The physical meaning of negative tunneling time in $\mathcal{P}\mathcal{T}$-symmetric systems and its relation to spectral singularities is discussed.

cond-mat.other↗

arXiv2023

Polar magneto-optic Kerr and Faraday effects in finite periodic \texorpdfstring{$\mathcal{P}\mathcal{T}$}{PT}-symmetric systems

We discuss the anomalous behavior of the Faraday (transmission) and polar Kerr (reflection) rotation angles of the propagating light, in finite periodic parity-time ($\mathcal{P}\mathcal{T}$) symmetric structures, consisting of $N$ cells. The unit cell potential is two complex $δ$-potentials placed on both boundaries of the ordinary dielectric slab. It is shown that, for a given set of parameters describing the system, a phase transition-like anomalous behavior of Faraday and Kerr rotation angles in a parity-time symmetric systems can take place. In the anomalous phase the value of one of the Faraday and Kerr rotation angles can become negative, and both angles suffer from spectral singularities and give a strong enhancement near the singularities. We also shown that the real part of the complex angle of KR, $θ^{R}_1$, is always equal to the $θ^{T}_1$ of FR, no matter what phase the system is in due to the symmetry constraints. The imaginary part of KR angles $θ^{R^{r/l}}_2$ are related to the $θ^{T}_2$ of FR by parity-time symmetry. Calculations based on the approach of the generalized nonperturbative characteristic determinant, which is valid for a layered system with randomly distributed delta potentials, show that the Faraday and Kerr rotation spectrum in such structures has several resonant peaks. Some of them coincide with transmission peaks, providing simultaneous large Faraday and Kerr rotations enhanced by an order one or two of magnitude. We provide a recipe for funding a one-to-one relation in between KR and FR.

physics.optics↗

arXiv2022

Anomalous Faraday effect in a $\mathcal{P}\mathcal{T}$-symmetric dielectric slab

In this letter we discuss a phase transition-like anomalous behavior of Faraday rotation angles in a simple parity-time ($\mathcal{P}\mathcal{T}$) symmetric model with two complex $δ$-potential placed at both boundaries of a regular dielectric slab. In anomalous phase, the value of one of Faraday rotation angles may turn negative, and both angles suffer spectral singularities and yield strong enhancement near singularities.

cond-mat.mes-hall↗

arXiv2022

Friedel formula and Krein's theorem in complex potential scattering theory

In this work, the generalization of Friedel formula and Krein's theorem in complex potential scattering theory is presented. The consequence of various symmetry constraints on dynamical system are discussed. In addition, Muskhelishvili-Omnès representation of Krein's theorem is also given and discussed.

cond-mat.other↗

arXiv2021

Charged particles interaction in both a finite volume and a uniform magnetic field II: topological and analytic properties of a magnetic system

In present work, we discuss some topological features of charged particles interacting a uniform magnetic field in a finite volume. The edge state solutions are presented, as a signature of non-trivial topological systems, the energy spectrum of edge states show up in the gap between allowed energy bands. By treating total momentum of two-body system as a continuous distributed parameter in complex plane, the analytic properties of solutions of finite volume system in a magnetic field is also discussed.

hep-lat↗

arXiv2021

Charged particles interaction in both a finite volume and a uniform magnetic field

A formalism for describing charged particles interaction in both a finite volume and a uniform magnetic field is presented. In the case of short-range interaction between charged particles, we show that the factorization between short-range physics and finite volume long-range correlation effect is possible, a Lüscher formula-like quantization condition is thus obtained.

hep-lat↗

arXiv2019

Straightening of light in a one dimensional dilute photonic crystal

Light transport in a dilute photonic crystal is considered. The analytical expression for the transmission coefficient is derived.Straightening of light under certain conditions in a one-dimensional photonic crystal is predicted. Such behavior is caused by the formation of a localized state in transversal motion. The main contribution to the central diffracted wave transmission coefficient is due to states, that either close to the conductance bands bottom or deeply localized in the forbidden gap. Both these states suppress mobility in the transverse direction and force light to be straightened. Straightening of light in the optical region along with small reflection make these systems very promising for use in solar cells.

physics.optics↗

arXiv2019

Transmission coefficient of interacting few-body system in one dimensional space

We present a novel way of defining transmission coefficient of one spatial dimensional few interacting electrons system. The formalism is based on the probability interpretation of unitarity of physical scattering $S$-matrix. The relation of our formalism to the well-established method for describing the conducting properties of non-interacting systems, Landauer-Büttiker formula, is discussed. The transport properties of interacting two-electron system is also discussed as a specific example of our formalism.

cond-mat.mes-hall↗

arXiv2017

Time dependent Faraday rotation

Faraday rotation in a magnetoactive medium with time dependent dielectric permittivity tensor is analyzed through both its diagonal and non-diagonal elements. Continuous and pulse incident laser field cases are considered. In a continuous case linear increasing of Faraday rotation angle with time is obtained.In the continuous laser field case Faraday angle of rotation in both time dependent diagonal and non-diagonal element cases shows an increase with periodic oscillations as either positive (time-dependent dielectric permittivity case) or negative (time dependent gyration vector case) and follows a general pattern. Ultrashort pulse can scan the time dependent dielectric permittivity through the Faraday rotation angle.

physics.optics↗

arXiv2017

Capsize of polarization in dilute photonic crystals

We investigate, experimentally and theoretically, polarization rotation effects in dilute photonic crystals with transverse permittivity inhomogeneity perpendicular to the traveling direction of waves. A capsize, namely a drastic change of polarization to the perpendicular direction is observed in a one-dimensional photonic crystal in the frequency range $10÷140$ GHz. To gain more insights into the rotational mechanism, we have developed a theoretical model of dilute photonic crystal, based on Maxwell's equations with a spatially dependent two dimensional inhomogeneous dielectric permittivity. We show that the polarization's rotation can be explained by an optical splitting parameter appearing naturally in Maxwell's equations for magnetic or electric fields components. This parameter is an optical analogous of Rashba like spin-orbit interaction parameter present in quantum waves, introduces a correction to the band structure of the two-dimensional Bloch states, creates the dynamical phase shift between the waves propagating in the orthogonal directions and finally leads to capsizing of the initial polarization. Excellent agreement between theory and experiment is found.

physics.app-ph↗

arXiv2017

An solvable three-body model in finite volume

In this work, based on consideration of periodicity and asymptotic forms of wave function, we propose a novel approach to the solution of finite volume three-body problem by mapping a three-body problem into a higher dimensional two-body problem. The idea is demonstrated by an example of two light spinless particles and one heavy particle scattering in one spatial dimension. This 1D three-body problem resembles a two-body problem in two spatial dimensions mathematically, and quantization condition of 1D three-body problem is thus derived accordingly.

hep-lat↗

arXiv2017

An numerical approach for finite volume three-body interaction

In present work, we study an numerical approach to one dimensional finite volume three-body interaction, the method is demonstrated by considering a toy model of three spinless particles interacting with pair-wise $δ$-function potentials. The numerical results are compared with the exact solutions of three spinless bosons interaction when strength of short-range interactions are set equal for all pairs.

hep-lat↗

arXiv2016

Complex Faraday and Kerr Rotations in Right and Left Handed Films

By studying the rotations of the polarization of light propagating in right and left handed films, with emphasis on the transmission (Faraday effect) and reflec- tions (Kerr effect) of light and through the use of complex values representing the rotations, it can be shown that the real portions of the complex angle of Faraday and Kerr rotations are odd functions with respect to the refractive index n and that the respective imaginary portions of the angles are an even function of n. Multiple reflections within the medium lead to the maximums of the real portions of Faraday and Kerr effects to not coincide with zero ellipticity. It will also be shown that in the thin film case with left handed materials there are large resonant enhancements of the reflected Kerr angle that could be obtained experimentally.

physics.optics↗