arXiv subjects

Vladimir Chernyak

Publications and source records attributed to Vladimir Chernyak.

17 recordsLinked to original sources

arXiv2026

Distribution of currents in a system of active particles with biased hops and Ising interactions

We consider an ensemble of particles performing a biased random walk on a two-dimensional lattice. Due to the adhesion between particles (nearest-neighbor Ising interactions), the probability of hopping depends on the number of neighbors and the strength of adhesive interaction. The asymmetry in the hopping directions leads to a macroscopic current of particles through the system. We theoretically compute the distribution of currents and verify the results in stochastic particle simulations. To make theoretical progress, one has to determine the probabilities of various particle configurations such as single particles, pairs, and different configurations of three-particle clusters. These probabilities are theoretically derived by formulating rate equations for the concentrations of various structures resembling Becker-Döring cluster equations. One intriguing finding is that the concentration of left-handed triplets is not equal to the concentration of right-handed triplets for non-zero asymmetry of hops and non-zero interaction between particles.

cond-mat.stat-mech↗

arXiv2020

Gauges, Loops, and Polynomials for Partition Functions of Graphical Models

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and optimization applications. The problem is of an exponential complexity with respect to the number of variables. In this manuscript, aimed at approximating the PF, we consider Multi-Graph Models where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge Function technique with the technique from the field of real stable polynomials. We show that the Gauge Function has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, it can be used to recover the Partition Function through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists in application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination of edges resulting in a sequence of models on decreasing in size graphs with the same Partition Function. Even though complexity of computing factors in the sequence models grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that Belief Propagation estimations in the sequence do not decrease, each low-bounding the Partition Function.

cs.LG↗

arXiv2019

Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism

In this work, we establish formally exact stochastic equations of motion (SEOM) theory to describe the dissipative dynamics of fermionic open systems. The construction of the SEOM is based on a stochastic decoupling of the dissipative interaction between the system and fermionic environment, and the influence of environmental fluctuations on the reduced system dynamics is characterized by stochastic Grassmann fields. Meanwhile, numerical realization of the time-dependent Grassmann fields has remained a long-standing challenge. To solve this problem, we propose a minimal auxiliary space (MAS) mapping scheme, with which the stochastic Grassmann fields are represented by conventional c-number fields along with a set of pseudo-levels. This eventually leads to a numerically feasible MAS-SEOM method. The important properties of the MAS-SEOM are analyzed by making connection to the well-established time-dependent perturbation theory and the hierarchical equations of motion (HEOM) theory. The MAS-SEOM method provides a potentially promising approach for accurate and efficient simulation of fermionic open systems at ultra-low temperatures.

cond-mat.stat-mech↗

arXiv2019

Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. II. Numerical Implementation

This paper provides a detailed account of the numerical implementation of the stochastic equation of motion (SEOM) method for the dissipative dynamics of fermionic open quantum systems. To enable direct stochastic calculations, a minimal auxiliary space (MAS) mapping scheme is adopted, with which the time-dependent Grassmann fields are represented by c-numbers noises and a set of pseudo-operators. We elaborate on the construction of the system operators and pseudo-operators involved in the MAS-SEOM, along with the analytic expression for the particle current. The MASSEOM is applied to study the relaxation and voltage-driven dynamics of quantum impurity systems described by the single-level Anderson impurity model, and the numerical results are benchmarked against those of the highly accurate hierarchical equations of motion (HEOM) method. The advantages and limitations of the present MAS-SEOM approach are discussed extensively.

cond-mat.stat-mech↗

arXiv2018

Stochastic Representation of Non-Markovian Fermionic Quantum Dissipation

Quantum Brownian motion plays a fundamental role in many areas of modern physics. In the path-integral formulation, the environmental quantum fluctuations driving the system dynamics can be characterized by auxiliary stochastic fields. For fermion bath environment the stochastic fields are Grassmann-valued, and cannot be represented by conventional classical numbers. In this Letter, we propose a strategy to map the nonclassical Grassmann fields onto Gaussian white noises along with a set of quantized pseudo-states. This results in a numerically feasible stochastic equation of motion (SEOM) method for fermionic open systems. The SEOM yields exact physical observables for noninteracting systems, and accurate approximate results for interacting systems. The practicality and accuracy of the proposed SEOM are exemplified by direct stochastic simulations conducted on a single-impurity Anderson model.

cond-mat.stat-mech↗

arXiv2018

Dynamical Consequences of Time-Reversal Symmetry for Systems with Odd Number of Electrons: Conical Intersections, Semiclassical Dynamics, and Topology

In this manuscript we identify the main differences between the effects of Kramers symmetry on the systems with even and odd number of electrons, the ways how the aforementioned symmetry affects the structure of the Conical Seams (CSs), and how it shows up in semiclassical propagation of nuclear wavepackets, crossing the CSs. We identify the topological invariants, associated with CSs, in three cases: even and odd number of electrons with time-reversal symmetry, as well as absence of the latter. We obtain asymptotically exact semiclassical analytical solutions for wavepackets scattered on a CS for all three cases, identify topological features in a non-trivial shape of the scattered wavepacket, and connect them to the topological invariants, associated with CSs. We argue that, due to robustness of topology, the non-trivial wavepacket structure is a topologically protected evidence of a wavepacket having passed through a CS, rather than a feature of a semiclassical approximation.

physics.chem-ph↗

arXiv2017

Utilizing Microcavities to Suppress Third-order Cascades in Fifth-order Raman Spectra

Nonlinear optical signals in the condensed phase are often accompanied by sequences of lower-order processes, known as cascades, which share the same phase matching and power dependence on the incoming fields and are thus hard to distinguish. The suppression of cascading in order to reveal the desired nonlinear signal has been a major challenge in multidimensional Raman spectroscopy, i.e., the $χ^{(5)}$ signal being masked by cascading signals given by a product of two $χ^{(3)}$ processes. Since cascading originates from the exchange of a virtual photon between molecules, it can be manipulated by performing the experiment in an optical microcavity. Using a quantum electrodynamical (QED) treatment we demonstrate that the $χ^{(3)}$ cascading contributions can be greatly suppressed. By optimizing the cavity size and the incoming pulse directions, we show that up to $\sim$99.5\% suppression of the cascading signal is possible.

quant-ph↗

arXiv2017

Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach

Thermostatically Controlled Loads (TCL), e.g. air-conditioners and heaters, are by far the most wide-spread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control of temperature -- changing from on to off, and vice versa, depending on temperature. Aggregation of a large group of similar devices into a statistical ensemble is considered, where the devices operate following the same dynamics subject to stochastic perturbations and randomized, Poisson on/off switching policy. We analyze, using theoretical and computational tools of statistical physics, how the ensemble relaxes to a stationary distribution and establish relation between the relaxation and statistics of the probability flux, associated with devices' cycling in the mixed (discrete, switch on/off, and continuous, temperature) phase space. This allowed us to derive and analyze spectrum of the non-equilibrium (detailed balance broken) statistical system and uncover how switching policy affects oscillatory trend and speed of the relaxation. Relaxation of the ensemble is of a practical interest because it describes how the ensemble recovers from significant perturbations, e.g. forceful temporary switching off aimed at utilizing flexibility of the ensemble in providing "demand response" services relieving consumption temporarily to balance larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.

eess.SY↗

arXiv2015

Polaron dynamics with a multitude of Davydov D$_2$ trial states

We propose an extension to the Davydov D$_2$ Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the "multi-D$_2$ Ansatz" is a linear combination of Davydov D$_2$ trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schrödinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D$_1$ and D$_2$ Ansätze. With an increase in the number of the Davydov D$_2$ trial states in the multi-D$_2$ Ansatz, deviation from the exact Schrödinger dynamics is gradually diminished, leading to a numerically exact solution to the Schrödinger equation.

physics.chem-ph↗

arXiv2015

Symmetry and the critical phase of the two-bath spin-boson model: Ground-state properties

A generalized trial wave function termed as the "multi-D1 Ansatz" has been developed to study the ground state of the spin-boson model with simultaneous diagonal and off-diagonal coupling in the sub-Ohmic regime. Ground-state properties including the energy and the spin polarization are investigated, and the results are consistent with those from the exact diagonalization and density matrix renormalization group approaches for the cases involving two oscillators and two baths described by a continuous spectral density function. Breakdown of the rotational and parity symmetries along the continuous quantum phase transition separating the localized phase from the critical phase has been uncovered. Moreover, the phase boundary is determined accurately with the corresponding symmetry parameters of the rotational and parity symmetries. A critical value of the spectral exponent s* = 0.49(1) is predicted in the weak coupling limit, which is in agreement with the mean-field prediction of 1/2, but much smaller than the earlier literature estimate of 0.75(1).

cond-mat.quant-gas↗

arXiv2014

Ground state properties of sub-Ohmic spin-boson model with simultaneous diagonal and off-diagonal coupling

By employing the variational approach, density matrix renormalization group (DMRG), exact diagonalization as well as symmetry and mean-field analyses, the ground state properties of the two-bath spin boson model with simultaneous diagonal and off-diagonal coupling are systematically studied in the sub-Ohmic regime. A novel quantum phase transition from a doubly degenerate "localized phase" to the other doubly degenerate "delocalized phase" is uncovered. Via the multi-D1 ansatz as the variational wave function, transition points are determined accurately, consistent with the results from DMRG and exact diagonalization. An effective spatial dimension $d_{eff} = 2.37(6)$ is then estimated, which is found to be compatible with the mean-field prediction. Furthermore, the quantum phase transition is inferred to be of first order for the baths described by a continuous spectral density function. In the case of single mode, however, the transition is softened.

cond-mat.stat-mech↗

arXiv2014

Spin-Boson Model with Diagonal and Off-Diagonal Coupling to Two Independent Baths: Ground-State Phase Transition in the Deep Sub-Ohmic Regime

We investigate a spin-boson model with two boson baths that are coupled to two perpendicular components of the spin by employing the density matrix renormalization group method with an optimized boson basis. It is revealed that in the deep sub-Ohmic regime there exists a novel second-order phase transition between two types of doubly degenerate states, which is reduced to one of the usual type for nonzero tunneling. In addition, it is found that expectation values of the spin components display jumps at the phase boundary in the absence of bias and tunneling.

quant-ph↗

arXiv2003

Periodic and Quasi-Periodic Compensation Strategies of Extreme Outages caused by Polarization Mode Dispersion and Amplifier Noise

Effect of birefringent disorder on the Bit Error Rate (BER) in an optical fiber telecommunication system subject to amplifier noise may lead to extreme outages, related to anomalously large values of BER. We analyze the Probability Distribution Function (PDF) of BER for various strategies of Polarization Mode Dispersion (PMD) compensation. A compensation method is proposed that is capable of more efficient extreme outages suppression, which leads to substantial improvement of the fiber system performance.

physics.optics↗

arXiv2003

Compensation for Extreme Outages caused by Polarization Mode Dispersion and Amplifier noise

Joint effect of weak birefringent disorder and amplifier noise on transmission in optical fiber communication systems appears to be strong. The probability of an extreme outage that corresponds to anomalously large values of Bit Error Rate (BER) is perceptible. We analyze the dependence of the Probability Distribution Function (PDF) of BER on the first-order and also higher-order PMD compensation schemes.

physics.optics↗

arXiv2003

Extreme Outages due to Polarization Mode Dispersion

We investigate the dependence of the bit-error-rate (BER) caused by amplifier noise in a linear optical fiber telecommunication system on the fiber birefringence. We show that the probability distribution function (PDF) of BER obtained by averaging over many realizations of birefringent disorder has an extended tail corresponding to anomalously large values of BER. We specifically discuss the dependence of the tail on such details of the pulse detection at the fiber output as "setting the clock" and filtering procedures.

physics.optics↗

arXiv2003

Probability of anomalously large Bit-Error-Rate in long haul optical transmission

We consider a linear model of optical pulse transmission through fiber with birefringent disorder in the presence of amplifier noise. Both disorder and noise are assumed to be weak, i.e. the average bit-error rate (BER) is small. The probability of rare violent events leading to the values of BER much larger than its typical value is estimated. We show that the probability distribution has a long algebraic tail.

cond-mat.stat-mech↗

arXiv2000

Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials

The mean first passage time (MFPT) for photoexcitations diffusion in a funneling potential of artificial tree-like light-harvesting antennae (phenylacetylene dendrimers with generation-dependent segment lengths) is computed. Effects of the non-linearity of the realistic funneling potential and slow random solvent fluctuations considerably slow down the center-bound diffusion beyond a temperature-dependent optimal size. Diffusion on a disordered Cayley tree with a linear potential is investigated analytically. At low temperatures we predict a phase in which the MFPT is dominated by a few paths.

cond-mat.dis-nn↗