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V. A. Malyshev

Publications and source records attributed to V. A. Malyshev.

At least 37 records · Page 2Linked to original sources
arXiv2014

One-dimensional excitonic systems with diagonal Lévy disorder: A detailed study of the absorption spectra and the disorder scaling of localization length

We present a detailed study of the effects of Lévy $α$-stable disorder distributions on the optical and localization properties of excitonic systems. These distributions are a generalization of commonly studied Gaussian randomness ($α= 2$). However, the more general case ($α< 2$) includes also heavy-tailed behavior with a divergent second moment. These types of distributions give rise to novel effects, such as exchange broadening of the absorption spectra and anomalous localization of the excitonic states, which has been found in various excitonic systems. We provide a thorough examination of the localization behavior and the absorption spectra of excitons in chains with Lévy $α$-stable diagonal disorder. Several regimes are considered in detail: (i) weak disorder and small systems, where finite size effects become significant; (ii) intermediate disorder and/or larger systems for which exciton states around the exciton band edge spread over a number of monomers, and (iii) strong disorder where the exciton wave functions resemble the individual molecular states. We propose analytical approaches to describe the disorder scaling of relevant quantities for these three regimes of localization, which match excellently with numerical results. We also show the appearance of short localization segments caused by outliers (monomers having transition energies larger than the exciton band width). Such states give rise to an additional structure in the absorption spectrum, density of states, and in the nontrivial disorder scaling of the absorption band width.

cond-mat.dis-nn↗
arXiv2013

Dynamical phase transition in the simplest molecular chain model

We consider the dynamics of the simplest chain of large number $N$ of particles. We find, in the double scaling limit, the partition of the parameter space onto two domains, where for one domain the supremum (over all time interval $(0,\infty)$ of relative extension tenda to $1$ as $N\to\infty$. and for the other this supremum tends to infinity as $N\to\infty$.

math-ph↗
arXiv2013

Bistable optical response of nanoparticle heterodimer: Mechanism, phase diagram, and switching time

We conduct a theoretical study of the bistable optical response of a nanoparticle heterodimer comprised of a closely spaced semiconductor quantum dot and metal nanoparticle. The bistable nature of the response results from the interplay between the quantum dot's optical nonlinearity and its self-action (feedback) originating from the presence of the metal nanoparticle. We show that the feedback is governed by a complex valued coupling parameter $G$. Both the real and imaginary parts of $G$ ($G_\mathrm{R}$ and $G_\mathrm{I}$) play an important role in the occurrence of bistability, which is manifested in an S-shaped dependence of the quantum dot excited state population on the intensity of the external field, and hysteresis of the population. From our calculations, we find that at $G_\mathrm{R} = 0$, the critical value for bistability to occur is $G_\mathrm{I} = 8Γ$, whereas at $G_\mathrm{I} = 0$, the critical value of $G_\mathrm{R} = 4Γ$, where $Γ$ is the polarization dephasing rate. Thus, there exist two different (limiting) mechanisms of bistability, depending on whether $G_\mathrm{R}$ is much larger or much smaller than $G_\mathrm{I}$. We also calculate the bistability phase diagram within the system's parameter space: spanned by $G_\mathrm{R}$, $G_\mathrm{I}$ and $Δ$, the latter being the detuning between the driving frequency and the transition frequency of the quantum dot. Additionally, switching times from the lower stable branch to the upper one (and {\it vise versa}) are calculated as a function of the intensity of the driving field. We show that the conditions for bistability to occur can be realized, for example, for a heterodimer comprised of a closely spaced CdSe (or CdSe/ZnSe) quantum dot and a gold nanosphere.

cond-mat.mtrl-sci↗
arXiv2013

Explicit asymptotic velocity of the boundary between particles and antiparticles

On the real line initially there are infinite number of particles on the positive half-line., each having one of $K$ negative velocities $v_{1}^{(+)},...,v_{K}^{(+)}$. Similarly, there are infinite number of antiparticles on the negative half-line, each having one of $L$ positive velocities $v_{1}^{(-)},...,v_{L}^{(-)}$. Each particle moves with constant speed, initially prescribed to it. When particle and antiparticle collide, they both disappear. It is the only interaction in the system. We find explicitly the large time asymptotics of $β(t)$ - the coordinate of the last collision before $t$ between particle and antiparticle.

math.PR↗
arXiv2013

Harmonic Chain with Weak Dissipation

We consider finite harmonic chain (consisting of N classical particles) plus dissipative force acting on one particle (called dissipating particle) only. We want to prove that "in the generic case" the energy (per particle) for the whole system tends to zero in the large time limit and then in the large N limit. "In the generic case" means: for almost all initial conditions and for almost any choice of the dissipating particle, in the thermodynamic limit.

math-ph↗
arXiv2013

Linear Hamiltonian Systems under Microscopic Random Influence

It is known that a linear hamiltonian system has too many invariant measures, thus the problem of convergence to Gibbs measure has no sense. We consider linear hamiltonian systems of arbitrary finite dimension and prove that, under the condition that one distinguished coordinate is subjected to dissipation and white noise, then, for almost any hamiltonians and almost any initial conditions, there exists the unique limiting distribution. Moreover, this distribution is Gibbsian with the temperature depending on the dissipation and of the variance of the white noise.

math-ph↗
arXiv2013

Mathematics for some classes of networks

Network (as a general notion) is not a mathematical object - there is no even any definition. However, there is a lot of good rigorous mathematics for well-defined classes of networks. In sections 1-3 we give a short overview of classes of networks which interested the authors for some time. In section 4 we consider in detail a new class of networks, related to markets with many agents.

math-ph↗
arXiv2012

Response to the Comment on "Excitons in Molecular Aggregates with Lévy Disorder: Anomalous Localization and Exchange Broadening of Optical Spectra"

In previous work, we have predicted novel effects, such as exchange broadening, anomalous scaling of the localization length and a blue shift of the absorption spectrum with increasing disorder strength, for static disorder models described by stable distributions with stability index α<1. The main points of the Comment are that the outliers introduced by heavy tails in the disorder distribution (i) do not lead to deviations from the conventional scaling law for the half width at half maximum (HWHM) of the absorption spectrum and (ii) do not lead to non-universality of the distribution of localization lengths. We show below that the findings reported by us in the Letter are correct and that the wrong conclusions of the Comment arise from focusing on small σ values.

cond-mat.dis-nn↗
arXiv2012

Self-organized circular flow of classical point particles

We consider newtonian dynamics of $N$ charged particles on the circle with nearest neigbour interaction with Coulomb repulsive potential $r^{-1}$ . Also there is an external accelerating force which is nonzero only on a small part of the circle. We construct homogeneous solutions where the velocities of all particles are approximately equal and their density is approximately uniform. This gives a qualitative mathematical model for some features of the direct electric current (DC), in agreement with a suggestion by R. Feynman.

math-ph↗
arXiv2012

Fine structure of one-dimensional discrete point system

We consider the system of $N$ points on the segment of the real line with the nearest-neighbor Coulomb repulsive interaction and external force $F$. For the fixed points of such systems (fixed configurations) we study the asymptotics (in $N$ and $l$) of finite differences of order $l$. Classical theory of finite differences is extensively used.

math-ph↗
arXiv2012

Dynamics of Phase Boundary with Particle Annihilation

Infinitely many particles of two types ("plus" and "minus") jump randomly along the one-dimensional lattice $\mathbf{Z}_{\varepsilon}=\varepsilon\mathbf{Z}$. Annihillations occur when two particles of different time occupy the same site. Assuming that at time $t=0$ all "minus" particles are placed on the left of the origin and all "plus" particles are on the right of it, we study evolution of $β_\varepsilon(t)$, the boundary between two types. We prove that in large density limit $ε\to 0$ the boundary $β_\varepsilon(t)$ converges to a deterministic limit. This particle system can be interpreted as a microscopic model of price formation on economic markets with large number of players.

math-ph↗
arXiv2012

Analytic dynamics of one-dimensional particle system with strong interaction

We study here the small time dynamics of $N$ electrons on the circle with Coul;omb repulsive interaction and study the series for the velocities (initially zero). The main result is the estimates of the convergence radius from below. We explain how this result is related to the problem of very fast establishing of direct electric current.

math-ph↗
arXiv2012

Critical states of strongly interacting many-particle systems on a circle

In multicomponent systems with strong local interaction one can encounter some phenomena absent in the standard systems of statistical physics and other multicomponent systems. Namely, a system with $N$ components in the bounded volume of order 1 (macroscale) has the natural microscale of the order $\frac{1}{N}$. Applying the macroscopic force (of order 1) on the system, and thus on any of its components, one normally gets changes on the macroscale itself and simultaneously small, of the order $\frac{1}{N}$, changes of the microcomponents. In the systems, considered below, with the strong Coulomb repulsion between the particles, however, one can observe the influence of such force on the equilibrium state only on a scale, much smaller that the standard microscale. Otherwise speaking, the information about the macroforce is not available neither on the macrocale nor on the standard microscale, but only on a finer scale. If this phenomenon does not depend on the continuity properties of the applied force, then the mere existence of the equilibrium depends essentially on the continuity properties of the external force.

math-ph↗
arXiv2012

Macrodimension - an invariant of local dynamics

We define a Markov process on the set of countable graphs with spins. Transitions are local substitutions in the graph. It is proved that the scaling macrodimension is an invariant of such dynamics.

math-ph↗
arXiv2011

Accumulation on the boundary for one-dimensional stochastic particle system

We consider infinite particle system on the positive half-line moving independently of each other. When a particle hits the boundary it immediately disappears, and the boundary moves to the right on some fixed quantity (particle size). We study the speed of the boundary movement (growth). Possible applications - dynamics of the traffic jam growth, growth of thrombus, epitaxy. Nontrivial mathematics is related to the correlation between particle dynamics and boundary growth.

math.PR↗