arXiv subjects

Arkady Kurnosov

Publications and source records attributed to Arkady Kurnosov.

8 recordsLinked to original sources

arXiv2026

Characterization of Chaotic Evolution in Quantum Systems Induced by Random Hermitian Matrices

In a recent paper, a semiclassical Lyapunov exponent associated with a quantum Hamiltonian represented by a finite-dimensional Hermitian matrix was defined and placed on a mathematical foundation. The Lyapunov exponent characterizes the early stages of the evolution toward the ergodic state, while the late stages are characterized by the spectral gap of the corresponding Markov matrix. Here, we apply this formalism to five random-matrix ensembles. For each ensemble, we derive the mean Lyapunov exponent, its variance, and the spectral gap as functions of energy. We also present the corresponding thermal averages. Extensive numerical data are compared with the theoretical predictions.

nlin.CD↗

arXiv2025

Observed enhanced emission at higher-order exceptional points in RF circuits

The Purcell effect -- stemming directly from the celebrated Fermi's Golden Rule -- links the enhanced emissivity of an emitter to the local density of states (LDoS) of a surrounding cavity. Under typical circumstances the LDoS is assumed to have a Lorentzian lineshape. Here, we go beyond the traditional Purcell framework by designing RF cavities with non-Lorentzian LDoS caused by higher-order non-Hermitian exceptional point degeneracies (EPDs) where $N\geq 2$ eigenfrequencies and their associated eigenmodes coalesce. We experimentally demonstrate a non-conventional emissivity enhancement (as compared to the isolated resonance regime) that increases with the EPD order $N$. The theoretical analysis traces its origin to an $N$-th power Lorentzian LDoS line shape that dominates under judicious spatially designed cavity losses. Our results reveal a new route to design cavities that do not rely on ultrahigh $Q$-factor resonators or small modal volumes.

physics.optics↗

arXiv2025

The mechanism of electrical conduction in glassy semiconductors

We argue that the dominant charge carrier in glassy semiconducting alloys is a compound particle in the form of an electron or hole bound to an intimate pair of topological lattice defects; the particle is similar to the polaron solution of the Su-Schrieffer-Heeger Hamiltonian. The spatial component of the density of states for these special polarons is determined by the length scale of spatial modulation of electronegativity caused by a separate set of standalone topological defects. The latter length scale is fixed by the cooperativity size for structural relaxation; the size is largely independent of temperature in the glass but above melting, it decreases with temperature. Thus we predict that the temperature dependence of the electrical conductivity should exhibit a jump in the slope near the glass transition; the size of the jump is predicted to increase with the fragility of the melt. The predicted values of the jump and of the conductivity itself are consistent with experiment.

cond-mat.mes-hall↗

arXiv2024

Nonlinear Wavepacket Dynamics in Proximity to a Stationary Inflection Point

A stationary inflection point (SIP) in the Bloch dispersion relation of a periodic waveguide is an exceptional point degeneracy where three Bloch eigenmodes coalesce forming the so-called frozen mode with a divergent amplitude and vanishing group velocity of its propagating component. We have developed a theoretical framework to study the time evolution of wavepackets centered at an SIP. Analysis of the evolution of statistical moments distribution of linear pulses shows a strong deviation from the conventional ballistic wavepacket dynamics in dispersive media. The presence of nonlinear interactions dramatically changes the situation, resulting in a mostly ballistic propagation of nonlinear wavepackets with the speed and even the direction of propagation essentially dependent on the wavepacket amplitude. Such a behavior is unique to nonlinear wavepackets centered at an SIP and can be used for the realization of a novel family of beam power routers for classical waves.

physics.optics↗

arXiv2023

Optical Kinetic Theory of Nonlinear Multi-mode Photonic Networks

Recent experimental developments in multimode nonlinear photonic circuits (MMNPC), have motivated the development of an optical thermodynamic theory that describes the equilibrium properties of an initial beam excitation. However, a non-equilibrium transport theory for these systems, when they are in contact with thermal reservoirs, is still {\it terra incognita}. Here, by combining Landauer and kinematics formalisms we develop a one-parameter scaling theory that describes the transport in one-dimensional MMNPCs from a ballistic to a diffusive regime. We also derive a photonic version of the Wiedemann -Franz law that connects the thermal and power conductivities. Our work paves the way toward a fundamental understanding of the transport properties of MMNPC and may be useful for the design of all-optical cooling protocols.

physics.optics↗

arXiv2023

Reconfigurable Enhancement of Actuation Forces by Engineered Losses in non-Hermitian Metamaterials

While boosting signals with amplification mechanisms is a well established approach, attenuation mechanisms are typically considered an anathema because they degrade the efficiency of the structures employed to perform useful operations on these signals. An emerging alternate viewpoint promotes losses as a novel design element by utilizing the notion of exceptional point degeneracies (EPDs) points in parameter space where the eigenvalues of the underlying system and the associated eigenvectors simultaneously coalesce. Here, we demonstrate a direct consequence of such eigenbasis collapse in elastodynamics, an unusual enhancement of actuation force by a judiciously designed non-Hermitian metamaterial supporting an EPD that is coupled to an actuation source. Intriguingly, the EPD enables this enhancement while maintaining a constant signal quality. Our work constitutes a proof-of-principle design which can promote a new class of reconfigurable nano-indenters and robotic-actuators. Importantly, it reveals the ramifications of non-Hermiticity in boosting the Purcell emissivity enhancement factor beyond its expected value, which can guide the design of metamaterials with enhanced emission that does not deteriorate signal quality for mechanical, acoustic, optical, and photonic applications.

physics.app-ph↗

arXiv2022

Adiabatic monoparametric autonomous motors enabled by self-induced nonconservative forces

Archetypal motors produce work when two slowly varying degrees of freedom (DOF) move around a closed loop of finite area in the parameter space. Here, instead, we propose a simple autonomous {\it monoparametric} optomechanical engine that utilizes nonlinearities to turn a constant energy current into a nonconservative mechanical force. The latter self-sustains the periodic motion of a mechanical DOF whose frequency is orders of magnitude smaller than the photonic DOF. We have identified conditions under which the maximum extracted mechanical power is invariant and show a new type of self-induced robustness of the power production against imperfections and driving noise.

physics.app-ph↗

arXiv2018

Temperature-driven narrowing of the insulating gap as a precursor of the insulator-to-metal transition: Implications for the electronic structure of solids

We present a microscopic picture rationalizing the surprisingly steep decrease of the band gap with temperature in insulators, crystalline or otherwise. The gap narrowing largely results from fluctuations of long-wavelength optical phonons---when the latter are present---or their disordered analogs, if the material is amorphous. We elaborate on this notion to show that possibly with the exception of weakly bound solids made of closed-shell atoms, the existence of an insulating gap or pseudo-gap in a periodic solid implies that optical phonons must be present, too. This means that in an insulating solid, the primitive cell must have at least two atoms and/or that a charge density wave is present. As a corollary, a (periodic) elemental solid whose primitive unit contains only one atom will ordinarily be a metal, possibly unless the element belongs to group 18 of the periodic table, consistent with observation. Some implications of the present results for quantum solids are briefly discussed, such as that the ground state of the Wigner crystal must be anti-ferromagnetic. A simple field theory of the metal-insulator transition is constructed that ties long-wavelength optical vibrations with fluctuations of an order parameter for the metal-insulator transition; symmetry-breaking aspects of the latter transition are thereby highlighted.

cond-mat.mtrl-sci↗