arXiv subjects

Vladimir Al. Osipov

Publications and source records attributed to Vladimir Al. Osipov.

18 recordsLinked to original sources

arXiv2026

Local correlations in long-range dual-unitary kicked Hamiltonian chains

Many-body Floquet models with exact space--time symmetry, such as the kicked Ising spin chain (KIC), provide natural examples of systems with dual-unitary dynamics. The requirement of exact space--time symmetry is, however, highly restrictive, as it permits only nearest-neighbor interactions. Based on a pair of Hadamard matrices, we construct a wide family of dual-unitary kicked spin chains with long-range interactions. We show that local two-point correlations in such models propagate along the light-cone edges $ |n| = r|t| $, where $r$ is the interaction range, and can be derived analytically for operators with local support. This approach is illustrated using the example of a kicked Ising spin chain with next-to-next-neighbor interactions.

quant-ph↗

arXiv2025

Exciton pairs coupled via the long-living phonons and their superfluorescent markers

A system of several Wannier-Mott excitons interacting with phonons in a bulk material is considered. We show that strong exciton-phonon coupling causes the formation of a coherent two-exciton state -- the exciton pair. Unlike the biexcitons, where the photons play the role of force carrier, the exciton pair is formed via entanglement with the long-living phonon mode: (i) The essentially multi-particle theory requires excitons (cobosons composed of an electron and a hole) to satisfy the mixed Bose-Fermi statistics; (ii) This allows us to formulate a system of non-linear dynamic equations, using the multiconfiguration Hartree method applied to the Frohlich Hamiltonian. The system of equations possesses a stationary solution, which, for the case of a single exciton, describes the excitonic polaron and corresponds to the exciton pair in the two-exciton case. We also compare the fluorescent spectra of exciton polarons and exciton pairs estimated from our theory with those observed in experiments on room-temperature superfluorescence (collective emission of fluorescent light) in hybrid perovskites to give an additional insight into the superfluorescence phenomenon.

cond-mat.mtrl-sci↗

arXiv2023

Local correlations in partially dual-unitary lattice models

We consider the problem of local correlations in the kicked, dual-unitary coupled maps on D-dimensional lattices. We demonstrate that for D>=2, fully dual-unitary systems exhibit ultra-local correlations: the correlations between any pair of operators with local support vanish in a finite number of time steps. In addition, for $D=2$, we consider the partially dual-unitary regime of the model, where the dual-unitarity applies to only one of the two spatial directions. For this case, we show that correlations generically decay exponentially and provide an explicit formula for the correlation function between the operators supported on two and four neighbouring sites.

cond-mat.stat-mech↗

arXiv2023

Hartree method for molecular polaritons

The formation of the composite photonic-excitonic particle, known as a polariton, is a phenomenon emerging in materials possessing strong coupling to light. The organic-based materials besides the strong light-matter coupling also demonstrate strong interaction of electronic and vibrational degrees of freedom. We study the vibration-assisted polariton wavefunction evolution treating both types of interactions as equally strong. Using the multiconfiguration Hartree approach we derive the equations of motion for the polariton wavefunction, where the vibration degrees of freedom interact with the polariton quantum field through the mean-field Hartree term.

physics.chem-ph↗

arXiv2020

Nonperturbative theory of power spectrum in complex systems

The power spectrum analysis of spectral fluctuations in complex wave and quantum systems has emerged as a useful tool for studying their internal dynamics. In this paper, we formulate a nonperturbative theory of the power spectrum for complex systems whose eigenspectra -- not necessarily of the random-matrix-theory (RMT) type -- posses stationary level spacings. Motivated by potential applications in quantum chaology, we apply our formalism to calculate the power spectrum in a tuned circular ensemble of random $N \times N$ unitary matrices. In the limit of infinite-dimensional matrices, the exact solution produces a universal, parameter-free formula for the power spectrum, expressed in terms of a fifth Painlevé transcendent. The prediction is expected to hold universally, at not too low frequencies, for a variety of quantum systems with completely chaotic classical dynamics and broken time-reversal symmetry. On the mathematical side, our study brings forward a conjecture for a double integral identity involving a fifth Painlevé transcendent.

math-ph↗

arXiv2017

Accumulation effects in modulation spectroscopy with high repetition rate pulses: recursive solution of optical Bloch equations

Application of the phase modulated pulsed light for advance spectroscopic measurements is the area of growing interest. The phase modulation of the light causes modulation of the signal. Separation of the spectral components of the modulations allows to distinguish the contributions of various interaction pathways. The lasers with high repetition rate used in such experiments can lead to appearance of the accumulation effects, which become especially pronounced in systems with long-living excited states. Recently it was shown, that such accumulation effects can be used to evaluate parameters of the dynamical processes in the material. In this work we demonstrate that the accumulation effects are also important in the quantum characteristics measurements provided by modulation spectroscopy. In particular, we consider a model of quantum two-level system driven by a train of phase-modulated light pulses, organised in analogy with the 2D spectroscopy experiments. We evaluate the harmonics' amplitudes in the fluorescent signal and calculate corrections appearing from the accumulation effects. We show that the corrections can be significant and have to be taken into account at analysis of experimental data.

physics.optics↗

arXiv2017

Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems

We present a non-perturbative analysis of the power-spectrum of energy level fluctuations in fully chaotic quantum structures. Focussing on systems with broken time-reversal symmetry, we employ a finite-$N$ random matrix theory to derive an exact multidimensional integral representation of the power-spectrum. The $N\rightarrow \infty$ limit of the exact solution furnishes the main result of this study -- a universal, parameter-free prediction for the power-spectrum expressed in terms of a fifth Painlevé transcendent. Extensive numerics lends further support to our theory which, as discussed at length, invalidates a traditional assumption that the power-spectrum is merely determined by the spectral form factor of a quantum system.

nlin.CD↗

arXiv2016

The nature of relaxation processes revealed by the action signals of phase modulated light fields

We introduce a generalized theoretical approach to study action signals induced by the absorption of two-photons from two phase modulated laser beams and subject it to experimental testing for two types of photoactive samples, solution of rhodamine 6G and GaP photodiode. In our experiment, the phases of the laser beams are modulated at the frequencies f1 and f2, respectively. The action signals, such as photoluminescence and photocurrent, which result from the absorption of two photons, are isolated at frequencies m f (f=|f1-f2|, m=0,1,2...). We demonstrate that the ratio of the amplitudes of the secondary (m=2) and the primary (m=1) signals is sensitive to the type of relaxation process taken place in the system and thus can be used for its identification. Such sensitivity originates from cumulative effects of non-equilibrated state of the system between the light pulses. When the cumulative effects are small, i.e. the relaxation time is much shorter then the laser repetition rate or the laser intensity is high enough to dominate the system behavior, the ratio achieves its reference value 1:4 (the signature of two-photon absorption). In the intermediate regimes the ratio changes rapidly with the growth of intensity from zero value in case of second order relaxation process, while it demonstrates slow monotonic decrease for linear relaxation. In the article we also determine the value of the recombination rate in a GaP photodiode by using the above approach.

physics.optics↗

arXiv2016

Fluorescence correlation spectroscopy in thin films at reflecting substrates as a means to study nanoscale structure and dynamics at soft-matter interfaces

Structure and dynamics at soft-matter interfaces play an important role in nature and technical applications. Optical single-molecule investigations are non-invasive and capable to reveal heterogeneities at the nanoscale. In this work we develop an autocorrelation function (ACF) approach to retrieve tracer diffusion parameters obtained from fluorescence correlation spectroscopy (FCS) experiments in thin liquid films at reflecting substrates. This approach then is used to investigate structure and dynamics in 100 nm thick 8CB liquid crystal films on silicon wafers with five different oxide thicknesses. We find a different extension of the structural reorientation of 8CB at the solid-liquid interface for thin and for thick oxide. For the thin oxides, the perylenediimide tracer diffusion dynamics in general agrees with the hydrodynamic modeling using no-slip boundary conditions with only a small deviation close to the substrate, while a considerably stronger decrease of the interfacial tracer diffusion is found for the thick oxides.

cond-mat.soft↗

arXiv2016

Wavelet analysis on symbolic sequences and two-fold de Bruijn sequences

The concept of symbolic sequences play important role in study of complex systems. In the work we are interested in ultrametric structure of the set of cyclic sequences naturally arising in theory of dynamical systems. Aimed at construction of analytic and numerical methods for investigation of clusters we introduce operator language on the space of symbolic sequences and propose an approach based on wavelet analysis for study of the cluster hierarchy. The analytic power of the approach is demonstrated by derivation of a formula for counting of {\it two-fold de Bruijn sequences}, the extension of the notion of de Bruijn sequences. Possible advantages of the developed description is also discussed in context of applied p

math-ph↗

arXiv2013

Universality in spectral statistics of "open" quantum graphs

The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their spectral statistics exhibit universality at the "soft" edges of the spectrum. The same spectral behavior is observed in many classical non-unitary ensembles of random matrices with rotationally invariant measures.

nlin.CD↗

arXiv2013

Clustering of periodic orbits and ensembles of truncated unitary matrices

Periodic orbits in chaotic systems form clusters, whose elements traverse approximately the same points of the phase space. The distribution of cluster sizes depends on the length n of orbits and the parameter p which controls closeness of orbits actions. We show that counting of cluster sizes in the baker's map can be turned into a spectral problem for an ensemble of truncated unitary matrices. Based on the conjecture of the universality for the eigenvalues distribution at the spectral edge of these ensembles, we obtain asymptotics of the second moment of cluster distribution in a regime where both n and p tend to infinity. This result allows us to estimate the average cluster size as a function of the number of encounters in periodic orbits.

nlin.CD↗

arXiv2011

Counting of Sieber-Richter pairs of periodic orbits

In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to the switch in the momentum direction) pass through approximately the same points of the phase space. By considering symbolic dynamics of the system one can introduce a natural ultrametric distance between periodic orbits and organize them into clusters. Each cluster consists of orbits approaching closely each other in the phase space. We study the distribution of cluster sizes for the backer's map in the asymptotic limit of long trajectories. This problem is equivalent to the one of counting degeneracies in the length spectrum of the {\it de Bruijn} graphs. Based on this fact, we derive the probability $¶_k$ that $k$ randomly chosen periodic orbits belong to the same cluster. Furthermore, we find asymptotic behaviour of the largest cluster size $|\Cll_{\max}|$ and derive the probability $P(t)$ that a random periodic orbit belongs to a cluster of the size smaller than $t|\Cll_{\max}|$, $t\in[0,1]$.

math-ph↗

arXiv2010

Correlations of RMT Characteristic Polynomials and Integrability: Hermitean Matrices

Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general theory of tau-functions, we (i) identify a zoo of hierarchical relations satisfied by tau-functions in an abstract infinite-dimensional space, and (ii) present a technology to translate these relations into hierarchically structured nonlinear differential equations describing the correlation functions of characteristic polynomials in the physical, spectral space. Implications of this formalism for fermionic, bosonic, and supersymmetric variations of zero-dimensional replica field theories are discussed at length. A particular emphasis is placed on the phenomenon of fermionic-bosonic factorisation of random-matrix-theory correlation functions.

math-ph↗

arXiv2009

Statistics of thermal to shot noise crossover in chaotic cavities

Recently formulated integrable theory of quantum transport [Osipov and Kanzieper, Phys. Rev. Lett. 101, 176804 (2008); arXiv:0806.2784] is extended to describe sample-to-sample fluctuations of the noise power in chaotic cavities with broken time-reversal symmetry. Concentrating on the universal transport regime, we determine dependence of the noise power cumulants on the temperature, applied bias voltage, and the number of propagating modes in the leads. Intrinsic connection between statistics of thermal to shot noise crossover and statistics of Landauer conductance is revealed and briefly discussed.

cond-mat.mes-hall↗

arXiv2009

Random Bures mixed states and the distribution of their purity

Ensembles of random density matrices determined by various probability measures are analysed. A simple and efficient algorithm to generate at random density matrices distributed according to the Bures measure is proposed. This procedure may serve as an initial step in performing Bayesian approach to quantum state estimation based on the Bures prior. We study the distribution of purity of random mixed states. The moments of the distribution of purity are determined for quantum states generated with respect to the Bures measure. This calculation serves as an exemplary application of the "deform-and-study" approach based on ideas of integrability theory. It is shown that Painlevé equation appeared as a part of the presented theory.

cond-mat.stat-mech↗

arXiv2008

Integrable theory of quantum transport in chaotic cavities

The problem of quantum transport in chaotic cavities with broken time-reversal symmetry is shown to be completely integrable in the universal limit. This observation is utilised to determine the cumulants and the distribution function of conductance for a cavity with ideal leads supporting an arbitrary number $n$ of propagating modes. Expressed in terms of solutions to the fifth Painlevé transcendent and/or the Toda lattice equation, the conductance distribution is further analysed in the large-$n$ limit that reveals long exponential tails in the otherwise Gaussian curve.

cond-mat.mes-hall↗

arXiv2007

Are Bosonic Replicas Faulty?

Motivated by the ongoing discussion about a seeming asymmetry in the performance of fermionic and bosonic replicas, we present an exact, nonperturbative approach to zero-dimensional replica field theories belonging to the broadly interpreted "beta=2" Dyson symmetry class. We then utilise the formalism developed to demonstrate that the bosonic replicas do correctly reproduce the microscopic spectral density in the QCD inspired chiral Gaussian unitary ensemble. This disproves the myth that the bosonic replica field theories are intrinsically faulty.

cond-mat.dis-nn↗