arXiv subjects

N. Sh. Izmailian

Publications and source records attributed to N. Sh. Izmailian.

At least 19 recordsLinked to original sources

arXiv2020

How Magnetic Field Inhomogeneity of Plane Wiggler Affects Spontaneous Radiation of Electrons

The spectral distribution of spontaneous emission of electrons moving in a plane wiggler with inhomogeneous magnetic field is calculated. We show that electrons do complicated motion consisting of slow(strophotron) and fast(undulator) parts. The equations of motion are averaged over fast undulator part and we obtain equations for connected motion. It is shown, that the account of inhomogenity of the magnetic field leads to appearance of additional peaks in the spectral distribution of spontaneous radiation.

physics.acc-ph↗

arXiv2018

The Influence of Absorption and Gain on Photonic Density of States

The photonic density of states (PDS) of the eigen polarizations (EPs) in cholesteric liquid crystal (CLC) cells are calculated. The exact analytic expressions for the reflection and transmission matrices for the finite thickness CLC layer are used. We obtained the dependences for the PDS on the parameters characterizing absorption and gain, as well as the CLC cell thickness, CLC local dielectric anisotropy and refractive index of CLC layer surrounding. The possibility of connections between the PDS and the density of the light energy accumulated in the medium are investigated and it was shown that these characteristics have analogous spectra and, besides, the influences of the problem parameters on these characteristics also were analogous. We have shown, that the decrement of the refractive index of CLC layer surroundings leads to a sharp increase of the maximum PDS and, consequently, leads to a sharp decrement of the laser excitation threshold. The PDS dependence on the refraction coefficients of the substrates of the Fabry-Perot resonator filled with a CLC planar layer was investigated, too. It is shown that the subject system can work as a low threshold laser or a multi-position trigger.

physics.optics↗

arXiv2017

The Effect of Defect Layer on Lasing in Cholesteric Liquid Crystal

The photonic density of states (PDS) of eigen polarizations (EPs) in cholesteric liquid crystal (CLC) cells with a defect layer inside are calculated. The dependences for the PDS and light intensity in the defect layer on the parameters characterizing absorption and gain are obtained. We investigated the possibility of connections between the PDS and the density of the light energy accumulated in the system. The influence of the defect layer and CLC layer on the PDS are investigated. It is shown that the PDS is maximum when the defect is in the centre of the system. We showed also that the subject system can work as a low threshold laser, a multiposition trigger, filter, etc.

physics.optics↗

arXiv2017

Physics of Cold Atomic Fermi Gases

We consider a cold two-species atomic Fermi gas confined in a trap. We combine the Hermitian coupling between the states (we assume them to be the states with different spins) with the Cooper pairing of atoms with these different spins. This opens up a new prospect for investigation of interplay between various phenomena involving Raman coupling (e.g., atom lasers, dark-state polaritons) and effects caused by Cooper pairing of particles (e.g., superfluidity). We have obtained a threshold of transition from oscillatory to amplifying behavior of matter waves.

cond-mat.quant-gas↗

arXiv2017

X-Ray Radiation Generation in Heat Engines Using Electron Cooling

We consider a relativistic quantum heat engine that goes through a thermodynamical cycle consisting of stages involving laser-assisted cooling of electrons and the generation of Xray radiation. Quantum treatment of the processes makes it possible to obtain the necessary condition and the amount of work extracted from the interaction ingredients, as well as the efficiency of the heat engine. We have also found that the efficiency of the relativistic engine is less than the one for the nonrelativistic case for the same momenta. The obtained results set the limits to the cooling, as well as the intensity of X-ray radiation, in the quantum regime of the interaction of electrons with laser fields.

physics.acc-ph↗

arXiv2014

Mathematical Modeling of Graphite-to-Diamond Transition

The energetic evaluations of graphite-to-diamond transition by electron irradiation are performed. The heat conduction problem is solved for the diamond synthesis when a pulse-periodic source of energy is located within a graphite cylinder; time dependences of temperature and pressure are found. It is shown, that the temperatures and pressures implemented in graphite are sufficient for graphite-to-diamond transition under electron bombardment.

cond-mat.mtrl-sci↗

arXiv2014

A generalised formulation of the Laplacian approach to resistor networks

An analytic approach is presented to developing exact expressions for the two-point resistance between arbitrary nodes on certain non-regular resistor networks. This generalises previous approaches, which only deliver results for networks of more regular geometry. The new approach exploits the second minor of the Laplacian matrix associated with the given network to obtain the resistance in terms its eigenvalues and eigenvectors. The method is illustrated by application to the resistor network on the globe lattice, for which the resistance between two arbitrary nodes is obtained in the form of single summation.

math-ph↗

arXiv2014

Universal Amplitude Ratios for Constrained Critical Systems

The critical properties of systems under constraint differ from their ideal counterparts through Fisher renormalization. The mathematical properties of Fisher renormalization applied to critical exponents are well known: the renormalized indices obey the same scaling relations as the ideal ones and the transformations are involutions in the sense that re-renormalizing the critical exponents of the constrained system delivers their original, ideal counterparts. Here we examine Fisher renormalization of critical amplitudes and show that, unlike for critical exponents, the associated transformations are not involutions. However, for ratios and combinations of amplitudes which are universal, Fisher renormalization is involutory.

cond-mat.stat-mech↗

arXiv2014

The two-point resistance of fan networks

The problem of the two-point resistance in various networks has recently received considerable attention. Here we consider the problem on a fan-resistor network, which is a segment of the cobweb network. Using a recently developed approach, we obtain the exact resistance between two arbitrary nodes on such a network. As a byproduct, the analysis also delivers the solution of the spanning tree problem on the fan network.

cond-mat.stat-mech↗

arXiv2013

The two-point resistance of a resistor network: A new formulation and application to the cobweb network

We consider the problem of two-point resistance in a resistor network previously studied by one of us [F. Y. Wu, J. Phys. A {\bf 37}, 6653 (2004)]. By formulating the problem differently, we obtain a new expression for the two-point resistance between two arbitrary nodes which is simpler and can be easier to use in practice. We apply the new formulation to the cobweb resistor network to obtain the resistance between two nodes in the network. Particularly, our results prove a recently proposed conjecture on the resistance between the center node and a node on the network boundary. Our analysis also solves the spanning tree problem on the cobweb network.

cond-mat.stat-mech↗

arXiv2011

Universal amplitude ratios for scaling corrections on Ising strips with fixed boundary conditions

We study the (analytic) finite-size corrections in the Ising model on the strip with fixed ($+ -$) boundary conditions. We find that subdominant finite-size corrections to scaling should be to the form $a_k/N^{2k-1}$ for the free energy $f_N$ and $b_k^{(n)}/N^{2k-1}$ for inverse correlation length $ξ_n^{-1}$, with integer value of $k$. We investigate the set $\{a_k, b_k^{(n)}\}$ by exact evaluation and their changes upon varying anisotropy of coupling. We find that the amplitude ratios $b_k^{(n)}/a_k$ remain constant upon varying coupling anisotropy. Such universal behavior are correctly reproduced by the conformal perturbative approach.

cond-mat.stat-mech↗

arXiv2011

The dimer model on the triangular lattice

We analyze the partition function of the dimer model on an $\mathcal{M} \times \mathcal{N}$ triangular lattice wrapped on torus obtained by Fendley, Moessner and Sondhi [Phys. Rev. B \textbf{66}, 214513 (2002)]. From a finite-size analysis we have found that the dimer model on such a lattice can be described by conformal field theory having central charge $c=1$. The shift exponent for the specific heat is found to depend on the parity of the number of lattice sites $\mathcal{N}$ along a given lattice axis: e.g., for odd $\mathcal{N}$ we obtain the shift exponent $λ=1$, while for even $\mathcal{N}$ it is infinite ($λ=\infty$). In the former case, therefore, the finite-size specific-heat pseudocritical point is size dependent, while in the latter case, it coincides with the critical point of the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2011

Bijection between spin $S=\frac{p^{M}-1}{2}$ and a cluster of $M$ spins $σ=\frac{p-1}{2}$

We propose a general method by which a spin-$S$ is decomposed into spins less than $S$. We have obtain the exact mapping between spin $S=\frac{p^{M}-1}{2}$ and a cluster of $M$ spins $σ=\frac{p-1}{2}$. We have discuss the possible applications of such transformations. In particular we have show how a general $d+1$ dimensional spin-$\frac{p-1}{2}$ model with general interactions can be reduced to $d$-dimensional spin-$S$ model with $S=\frac{p^{M}-1}{2}$.

math-ph↗

arXiv2010

Exact Solution of a Monomer-Dimer Problem: A Single Boundary Monomer on a Non-Bipartite Lattice

We solve the monomer-dimer problem on a non-bipartite lattice, the simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the non-bipartite nature of the lattice, the well-known method of a Temperley bijection of solving single-monomer problems cannot be used. In this paper we derive the solution by mapping the problem onto one on close-packed dimers on a related lattice. Finite-size analysis of the solution is carried out. We find from asymptotic expansions of the free energy that the central charge in the logarithmic conformal field theory assumes the value $c=-2$.

cond-mat.stat-mech↗

arXiv2010

Boundary conditions and amplitude ratios for finite-size corrections of a one-dimensional quantum spin model

We study the influence of boundary conditions on the finite-size corrections of a one-dimensional (1D) quantum spin model by exact and perturbative theoretic calculations. We obtain two new infinite sets of universal amplitude ratios for the finite-size correction terms of the 1D quantum spin model of $N$ sites with free and antiperiodic boundary conditions. The results for the lowest two orders are in perfect agreement with a perturbative conformal field theory scenario proposed by Cardy [Nucl. Phys. B {\bf 270}, 186 (1986)].

cond-mat.stat-mech↗

arXiv2010

Ising model with mixed boundary conditions: universal amplitude ratios

In the vicinity of boundaries the bulk universality class of critical phenomena splits into several boundary universality classes, depending upon whether the tendency to order in the boundary is smaller or larger than in the bulk. For Ising universality class there are five different boundary universality classes: periodic, antiperiodic, free, fixed and mixed (mixture of the last two). In this paper we present the new set of the universal amplitude ratios for the mixed boundary universality class. The results are in perfect agreement with a perturbated conformal field theory scenario proposed by Cardy \cite{cardy86}.

cond-mat.stat-mech↗

arXiv2010

Asymptotic expansion for the resistance between two maximum separated nodes on a $M \times N$ resistor network

We analyze the exact formulae for the resistance between two arbitrary notes in a rectangular network of resistors under free, periodic and cylindrical boundary conditions obtained by Wu [J. Phys. A 37, 6653 (2004)]. Based on such expression, we then apply the algorithm of Ivashkevich, Izmailian and Hu [J. Phys. A 35, 5543 (2002)] to derive the exact asymptotic expansions of the resistance between two maximum separated nodes on an $M \times N$ rectangular network of resistors with resistors $r$ and $s$ in the two spatial directions. Our results is $ \frac{1}{s}R_{M\times N}(r,s)= c(ρ)\, \ln{S}+c_0(ρ,ξ)+\sum_{p=1}^{\infty} \frac{c_{2p}(ρ,ξ)}{S^{p}} $ with $S=M N$, $ρ=r/s$ and $ξ=M/N$. The all coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio $ξ_{eff} = \sqrtρ\;ξ$ for free and periodic boundary conditions and $ξ_{eff} = \sqrtρ\;ξ/2$ for cylindrical boundary condition and show that all finite size correction terms are invariant under transformation $ξ_{eff} \to {1}/ξ_{eff}$.

cond-mat.stat-mech↗

arXiv2006

Logarithmic Conformal Field Theory and Boundary Effects in the Dimer Model

We study the finite-size corrections of the dimer model on $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections in a crucial way depend on the parity of $N$; we also show that such unusual finite-size behavior can be fully explained in the framework of the $c=-2$ logarithmic conformal field theory.

cond-mat.stat-mech↗