arXiv subjects

A. R. Kolovsky

Publications and source records attributed to A. R. Kolovsky.

At least 19 recordsLinked to original sources

arXiv2026

Quantum transport along a tight-binding chain connected to Markovian reservoirs

We consider quantum transport of non-interacting particles in a tight-binding chain coupled to Markovian reservoirs at its boundaries and subject to uniform on-site dephasing. Using the masterequation approach, we derived the exact analytic solution for the mean current along the chain. This analytic solution is obtained in the framework of single-particle quantum mechanics and, thus, equally applies for transport of non-interacting bosons and fermions. In the absence of phase damping, the results are extended to the complete many-body solution for bosonic problem in the form of anti-normally ordered characteristic function. This function allows us to calculate the distribution function for the current at each bond in the chain as well as the inter-bond current correlation functions.

quant-ph↗

arXiv2024

Extraordinary resonant transmission in two-terminal fermionic transport

We analyze conductance of a two-leg ladder connected with fermionic reservoirs, focusing on the decoherence effect induced by the reservoirs. In the absence of decoherence the system exhibits both bound states in the continuum and Fano resonances. We found that the Fano resonances in transmittance are robust against decoherence, at the same time decoherence prevents collapse of resonances induced by bound states in the continuum.

cond-mat.other↗

arXiv2023

Signatures of Quantum Chaos and fermionization in the incoherent transport of bosonic carriers in the Bose-Hubbard chain

We analyse the stationary current of Bose particles across the Bose-Hubbard chain connected to a battery, focusing on the effect of inter-particle interactions. It is shown that the current magnitude drastically decreases as the strength of inter-particle interactions exceeds the critical value which marks the transition to quantum chaos in the Bose-Hubbard Hamiltonian. We found that this transition is well reflected in the non-equilibrium many-body density matrix of the system. Namely, the level-spacing distribution for eigenvalues of the density matrix changes from Poisson to Wigner-Dyson distributions. With the further increase of the interaction strength, the Wigner-Dyson spectrum statistics changes back to the Poisson statistics which now marks fermionization of the bosonic particles. With respect to the stationary current, this leads to the counter-intuitive dependence of the current magnitude on the particle number.

quant-ph↗

arXiv2023

Conductance transition with interacting bosons in an Aharonov-Bohm cage

We study transport of interacting bosons through an Aharonov-Bohm cage - a building block of flat band networks - with coherent pump and sink leads. In the absence of interactions the cage is insulating due to destructive interference. We find that the cage stays insulating up to a critical value of the pump strength in the presence of mean field interactions, while the quantum regime induces particle pair transport and weak conductance below the critical pump strength. A swift crossover from quantum into the classical regime upon further pump strength increase is observed. We solve the time dependent master equations for the density matrix of the many body problem both in the classical, pure quantum, and pseudoclassical regimes. We start with an empty cage and switch on driving. We characterize the transient dynamics, and the complexity of the resulting steady states and attractors. Our results can be readily realized using experimental platforms involving interacting ultracold atoms and photons on finetuned optical lattices.

cond-mat.mes-hall↗

arXiv2022

Quantum manifestation of the classical bifurcation in the driven dissipative Bose-Hubbard dimer

We analyze the classical and quantum dynamics of the driven dissipative Bose-Hubbard dimer. Under variation of the driving frequency, the classical system is shown to exhibit a bifurcation to the limit cycle, where its steady-state solution corresponds to periodic oscillation with the frequency unrelated to the driving frequency. This bifurcation is shown to lead to a peculiarity in the stationary single-particle density matrix of the quantum system. The case of the Bose-Hubbard trimer, where the discussed limit cycle bifurcates into a chaotic attractor, is briefly discussed.

cond-mat.other↗

arXiv2022

Ballistic transport of interacting Bose particles in the tight-binding chain

It is known that quantum transport of non-interacting Bose particles across the tight-binding chain is ballistic in the sense that the current does not depend on the chain length. We address the question whether the transport of strongly interacting bosons can be ballistic as well. We find such a regime and show that, classically, it corresponds to the synchronized motion of local non-linear oscillators. It is also argued that, unlike the case of non-interacting bosons, the transporting state responsible for the ballistic transport of interacting bosons is metastable, i.e., the current decays in course of time. An estimate for the decay time is obtained.

cond-mat.other↗

arXiv2021

Resonant transport of bosonic carriers through a quantum device

We analyze the current of Bose particles across the tight-binding chain connected at both ends to the particles reservoirs. Unlike the standard open Bose-Hubbard model, where the presence of reservoirs is taken into account by the Lindbladians acting on the first and the last sites of the chain, we use the semi-microscopic models for the reservoirs. This allows us to address the case of arbitrary reservoir temperature. In particular, we discuss the phenomenon of the resonant transmission for nearly condensed bosons, where the current across the chain is significantly enhanced for certain values of the gate voltage.

quant-ph↗

arXiv2021

Decay of symmetry-protected quantum states

We study the decay of bosonic many-body states in the three well Bose-Hubbard chain where bosons in the central well can escape into a reservoir. For vanishing inter-particle interaction this system supports a non-decaying many-body state which is the antisymmetric Bose-Einstein condensate with particles occupying only the edge wells. In the classical approach this quantum state corresponds to a symmetry protected non-decaying state which is stable even at finite interaction below a certain intensity threshold. Here we demonstrate that despite the classical counterpart is stable the antisymmetric Bose-Einstein condensate is always metastable at finite interatomic interactions due to quantum fluctuations.

cond-mat.quant-gas↗

arXiv2020

Open Fermi-Hubbard model: Landauer's vs. master equation approaches

We introduce a simple model for the quantum transport of Fermi particles between two contacts connected by a lead. It generalizes the Landauer formalizm by explicitly taken into account the relaxation processes in the contacts. We calculate the contact resistance and non-equilibrium quasi-momentum distribution of the carriers in the lead and show that they strongly depend on the rate of relaxation processes.

cond-mat.quant-gas↗

arXiv2020

Quantum transport in the flux rhombic lattice

We analyse stationary current of the bosonic particles in the flux rhombic lattice connecting two particle reservoirs. For vanishing inter-particle interactions the current is shown to monotonically decrease as the flux is increased and become strictly zero for the Peierls phase equal to $π$. Non-zero interactions modify this dependence and for moderate interaction strength the current is found to be independent of the flux value.

quant-ph↗

arXiv2019

Chaotic and regular dynamics in the three-site Bose-Hubbard model

We analyze the energy spectrum of the three-site Bose-Hubbard model. It is shown that this spectrum is a mixture of the regular and irregular spectra associated with the regular and chaotic components of the classical Bose-Hubbard model. We find relative volumes of these components by using the pseudoclassical approach. Substituting these values in the Berry-Robnik distribution for the level spacing statistics we obtain good agreement with the numerical data.

cond-mat.quant-gas↗

arXiv2019

The open Bose-Hubbard chain: Pseudoclassical approach

We analyze stationary current of bosonic carriers in the Bose-Hubbard chain of length $L$ where the first and the last sites of the chain are attached to reservoirs of Bose particles acting as the particle source and sink, respectively. The analysis is curried out by using the pseudoclassical approach which reduces the original quantum problem to the classical problem for $L$ coupled nonlinear oscillators. It is shown that an increase of oscillator nonlinearity (which is determined by the strength of inter-particle interactions) results in a transition from the ballistic transport regime, where the stationary current is independent of the chain length, to the diffusive regime, where the current is inverse proportional to $L$.

quant-ph↗

arXiv2018

NOON state of Bose atoms in the double-well potential via an excited state quantum phase transition

We suggest a simple scheme for creating a NOON state of repulsively interacting Bose atoms in the double-well potential. The protocol consists of two steps. First, by setting atom-atom interactions to zero, the system is driven to the upper excited state. Second, the interactions is slowly increased and, simultaneously, the inter-well tunneling is decreased to zero. We analyze fidelity of the final state to the NOON state depending on the number of atoms, ramp rate, and fluctuations of the system parameters. It is shown that for a given fidelity the ramp rate scales algebraically with the number of atoms.

cond-mat.quant-gas↗

arXiv2014

Wannier-Stark states in double-periodic lattices I: one-dimensional lattices

We analyze the Wannier-Stark spectrum of a quantum particle in generic one-dimensional double-periodic lattices. In the limit of weak static field the spectrum is shown to be a superposition of two Wannier-Stark ladders originated from two Bloch subbands. As the strength of the field is increased, the spectrum rearranges itself into a single Wannier-Stark ladder. We derive analytical expressions which describe the rearrangement employing the analogy between the Wannier-Stark problem and the driven two-level system in the strong-coupling regime.

quant-ph↗

arXiv2014

Wannier-Stark states in double-periodic lattices II: two-dimensional lattices

We analyze the Wannier-Stark spectrum of a quantum particle in tilted two-dimensional lattices with the Bloch spectrum consisting of two subbands, which could be either separated by a finite gap or connected at the Dirac points. For rational orientations of the static field given by an arbitrary superposition of the translation vectors the spectrum is a ladder of energy bands. We obtain asymptotic expressions for the energy bands in the limit of large and weak static fields and study them numerically for intermediate field strength. We show that the structure of energy bands determines the rate of spreading of a localized wave packets which is the quantity measured in laboratory experiments. It is shown that wave-packet dispersion becomes a fractal function of the field orientation in the long-time regime of ballistic spreading.

quant-ph↗

arXiv2013

Landau-Zener tunneling in 2D periodic structures in the presence of a gauge field II: Electric breakdown

We analyze dynamics of a quantum particle in a square lattice in the Hall configuration beyond the single-band approximation. For vanishing gauge (magnetic) field this dynamics is defined by the inter-band Landau-Zener tunneling, which is responsible for the phenomenon known as the electric breakdown. We show that in the presence of a gauge field this phenomenon is absent, at least, in its common sense. Instead, the Landau-Zener tunneling leads to appearance of a finite current which flows in the direction orthogonal to the vector of a potential (electric) field.

cond-mat.mes-hall↗

arXiv2012

Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional lattice II

We study the quantum dynamics of a charged particle in a two-dimensional lattice, subject to constant and homogeneous electric and magnetic fields. We find that different regimes characterize these motions, depending on a combination of conditions, corresponding to weak and strong electric field intensities, rational or irrational directions of the electric field with respect to the lattice, and small or large values of the magnetic (Peierls) phase.

quant-ph↗

arXiv2010

Cyclotron-Bloch dynamics of a quantum particle in a 2D lattice

This paper studies the quantum dynamics of a charged particle in a 2D square lattice, under the influence of electric and magnetic fields, the former being aligned with one of the lattice axes and the latter perpendicular to the lattice plane. While in free space these dynamics consist of uniform motions in the direction orthogonal to the electric field vector, we find that, in a lattice, this directed drift takes place only for specific initial conditions and for electric field magnitudes smaller than a critical value. Otherwise, the quantum wave--packet spreads ballistically in both directions orthogonal to the electric field. We quantify this ballistic spreading and identify the subspace of initial conditions insuring directed transport with the drift velocity. We also describe the effect of disorder in the system.

quant-ph↗