Andrey R. Kolovsky

• Doktor Nauk (доктор физ.-мат. наук)
• Researcher at Russian Academy of Sciences

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 de...

We analyze quantum transport of charged fermionic particles in the tight-binding lattice connecting two particle reservoirs (the leads). If the lead chemical potentials are different they create an electric field which tilts the lattice. We study the effect of this tilt on quantum transport in the presence of weak relaxation/decoherence processes i...

We study the effects of relaxation/decoherence processes on quantum transport of noninteracting Fermi particles across the disordered tight-binding chain, where we distinguish between relaxation processes in the contacts (external decoherence) and those in the chain (internal decoherence). It is shown that external decoherence reduces conductance f...

We revisit the problem of two-terminal transport of non-interacting Fermi particles in a mesoscopic device. First, we generalize the transport problem by taking into consideration relaxation processes in contacts (which are characterized by the contact self-thermalization rate γ) and then solve it by using the master equation approach. In the limit...

We analyze the stationary current of Bose particles across the Bose-Hubbard chain connected to a battery, focusing on the effect of interparticle interactions. It is shown that the current magnitude drastically decreases as the strength of interparticle interactions exceeds the critical value which marks the transition to quantum chaos in the Bose-...

We propose a simple, yet feasible, model for quantum transport of fermionic carriers across tight-binding chain connecting two reservoirs maintained at arbitrary temperatures and chemical potentials. The model allows for elementary derivation of the master equation for the reduced single particle density matrix in a closed form in both Markov and B...

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 Bos...

We study the 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 i...

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. In the presence of mean field interactions the cage stays insulating up to a critical value of the pump strength....

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 i...

It is known that the quantum transport of noninteracting Bose particles across a 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 t...

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 i...

We analyze Josephson's oscillation of Bose particles in the open two-site Bose-Hubbard system. First, we excite the system from the vacuum state into a state suitable for observing the oscillation by using a special protocol for external driving. Next, we switch off the driving and observe the oscillation. It is shown that the main mechanism for th...

We revisit the problem of quantum bi- and multistability by considering the dissipative double resonance model. For a large driving frequency, this system has a simpler phase structure than the driven dissipative nonlinear oscillator, the paradigm model for classical and quantum bistability. This allows us to obtain an analytical estimate for the l...

We propose a simple, yet feasible, model for quantum transport of fermionic carriers across tight-binding chain connecting two reservoirs maintained at arbitrary temperatures and chemical potentials. The model allows for elementary derivation of the master equation for the reduced single particle density matrix in a closed form in both Markov and B...

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...

We revisit the problem of quantum bi- and multi-stability by considering the dissipative Double Resonance Model. For a large driving frequency, this system has a simpler phase structure than the driven dissipative nonlinear oscillator -- the paradigm model for classical and quantum bistability. This allows us to obtain an analytical estimate for th...

We analyze Josephson's oscillation of Bose particles in the open (dissipative) Bose-Hubbard dimer. First, we excite the dimer from the vacuum state into a state suitable for observing the oscillation by using a special protocol for external driving. Next, we switch off the driving and observe the oscillation. It is shown that the main mechanism for...

We analyze the current of Bose particles across a 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 last sites of the chain, we use semimicroscopic models for the reservoirs. This all...

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...

We revisit the phenomenon of the resonant transmission of fermionic carriers through a quantum device connected to two contacts with different chemical potentials. We show that, besides the traditional Landauer-Büttiker approach in solid-state physics, this phenomenon can also be described by the non-Markovian master equation for the reduced densit...

We revisit the phenomenon of the resonant transmission of fermionic carriers through a quantum device connected to two contacts with different chemical potentials. We show that, besides the traditional in solid-state physics Landauer-B\"uttiker approach, this phenomenon can be also described by the non-Markovian master equation for the reduced dens...

We analyse stationary current of the bosonic particles in a flux rhombic lattice connecting two particle reservoirs. For vanishing interparticle interactions the current is shown to monotonically decrease as the flux is increased and become strictly zero for the Peierls phase equal to π. Nonzero interactions modify this dependence and for moderate...

We introduce a simple model for the quantum transport of Fermi particles between two contacts connected by a lead. It generalizes the Landauer formalism by explicitly taking into account the relaxation processes in the contacts. We calculate the contact resistance and nonequilibrium quasimomentum distribution of the carriers in the lead and show th...

We study the decay of bosonic many-body states in the triple-well Bose-Hubbard model where bosons in the central well can escape into a reservoir. For vanishing interparticle interaction this system supports a nondecaying many-body state which is the antisymmetric Bose-Einstein condensate with particles occupying only the edge wells. In the classic...

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 t...

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...

We revisit the Born-Markov approximation for an open quantum system by considering a microscopic model of the bath, namely, the Bose-Hubbard chain in the parameter region where it is chaotic in the sense of quantum chaos. It is shown that strong ergodic properties of the bath justify all approximations required for deriving the Markovian master equ...

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 $\pi$. Non-zero interactions modify this dependence and for m...

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 classi...

We revisit quantum dynamics of the damped and driven nonlinear oscillator. In the classical case this system has two stationary solutions (the limit cycles) in the certain parameter region, which is the origin of the celebrated bistability phenomenon. The quantum-classical correspondence for the oscillator dynamics is discussed in details.

We revisit the Born-Markov approximation for an open quantum system by considering a microscopic model of the bath, namely, the Bose-Hubbard chain in the parameter region where it is chaotic in the sense of Quantum Chaos. It is shown that strong ergodic properties of the bath justify all approximations required for deriving the Markovian master equ...

We analyze the 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 a particle source and sink, respectively. The analysis is carried out by using the pseudoclassical approach which reduces the original quantum problem to t...

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...

We analyze the quantum state of fermionic carriers in a transport channel attached to a particle reservoir. The analysis is done from first principles by considering microscopic models of the reservoir and transport channel. In the case of infinite effective temperature of the reservoir we demonstrate a full agreement between the results of straigh...

Depletion dynamics of an open system of weakly interacting fermions with two‐body random interactions is studied. In this model, fermions are escaping from the high‐energy one‐particle orbitals, that mimics the evaporation process used in laboratory experiments with neutral atoms to cool them to ultra‐low temperatures. It is shown that due to self‐...

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 t...

We theoretically analyze the depletion dynamics of an ensemble of cold atoms in a quasi-one-dimensional optical lattice where atoms in one of the lattice sites are subject to decay. Unlike the previous studies of this problem in Labouvie et al., Phys. Rev. Lett. 116, 235302 (2016), we focus on the case where the system is brought to the chaotic reg...

We theoretically analyze the depletion dynamics of an ensemble of cold atoms in a quasi one-dimensional optical lattice where atoms in one of the lattice sites are subject to decay. Unlike the previous studies of this problem in R. Labouvie, {\em et. al}, Phys. Rev. Lett. {\bf 116}, 235302 (2016) we focus on the case where the system is brought to...

We analyze quantum state of fermionic carriers in a transport channel attached to a particle reservoir. The analysis is done from the first principles by considering microscopic models of the reservoir and transport channel. In the case of infinite effective temperature of the reservoir we demonstrate a full agreement between the results of straigh...

We study depletion dynamics of an open system of weakly interacting fermions with two-body random interactions. In this model fermions are escaping from the high-energy one-particle orbitals, that mimics the evaporation process used in laboratory experiments with neutral atoms to cool them to ultra-low temperatures. It is shown that due to dynamica...

We study the current of Bose particles between two reservoirs connected by a one-dimensional channel. We analyze the problem from first principles by considering a microscopic model of conductivity in the noninteracting limit. Equations for the transient and the stationary current are derived analytically. The asymptotic current has a form similar...

We study the current of Bose particles between two reservoirs connected by a one-dimensional channel. We analyze the problem from first principles by considering a microscopic model of conductivity in the noninteracting limit. Equations for the transient and the stationary current are derived analytically. The asymptotic current has a form similar...

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 are slowly increased and, simultaneously, the interwell tunneling is...

We analyze the energy spectrum and eigenstates of cold atoms in a tilted brick-wall optical lattice. When the tilt is applied, the system exhibits a sequence of topological phase transitions reflected in an abrupt change of the eigenstates. It is demonstrated that these topological phase transitions can be easily detected in a laboratory experiment...

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...

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...

We analyze the spectrum and eigenstates of a quantum particle in a bipartite two-dimensional tight-binding dice network with short range hopping under the action of a dc bias. We find that the energy spectrum consists of a periodic repetition of one-dimensional energy band multiplets, with one member in the multiplet being strictly flat. The corres...

We analyze the spectrum and eigenstates of a quantum particle in a bipartite two-dimensional tight-binding dice network with short range hopping under the action of a dc bias. We find that the energy spectrum consists of a periodic repetition of one-dimensional energy band multiplets, with one member in the multiplet being strictly flat. The corres...

We analyze microscopic models of the particle source or sink which consist of a one- or two-site Bose-Hubbard model (the system) weakly coupled to a many-site Bose-Hubbard model (the reservoir). Assuming unequal filling factors for the system and reservoir, we numerically study equilibration dynamics and compare it with the solution of the master e...

Many-body physics of identical particles is commonly believed to be a sovereign territory of Quantum Mechanics. The aim of this contribution is to show that it is actually not the case and one gets useful insights into a quantum many-body system by using the theory of classical dynamical systems. In the contribution we focus on one paradigmatic mod...

We study numerically a model of quantum dot with interacting fermions. At strong interactions with small conductance the model is reduced to the Sachdev-Ye-Kitaev black hole model while at weak interactions and large conductance it describes a Landau Fermi liquid in a regime of quantum chaos. We show that above the Aberg threshold for interactions...

We study numerically a model of quantum dot with interacting fermions. At strong interactions with small conductance the model is reduced to the Sachdev-Ye-Kitaev black hole model while at weak interactions and large conductance it describes a Landau Fermi liquid in a regime of quantum chaos. We show that above the Aberg threshold for interactions...

We theoretically analyze the ground state of weakly interacting bosons in the flux ladder—the system that has been recently realized by means of ultracold atoms in the specially designed optical lattice [M. Atala, M. Aidelsburger, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Nat. Phys. 10, 588 (2014)]. It is argued that, for the system param...

We discuss the dynamical response of strongly interacting Bose atoms in an adiabatically tilted optical lattice. The analysis is performed in terms of the multilevel Landau-Zener tunneling. Different regimes of tunneling are identified and analytical expressions for the doublon number, which is the quantity measured in laboratory experiments, are d...

We discuss the dynamical response of strongly interacting Bose atoms in an adiabatically tilted optical lattice. The analysis is performed in terms of the multi-level Landau-Zenner tunneling. Different regimes of tunneling are identified and analytical expressions for the doublon number, which is the quantity measured in laboratory experiments, are...

We discuss applications of the theory of quantum chaos to one of the paradigm models of many-body quantum physics — the Bose–Hubbard (BH) model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the BH model and the...

We discuss the quantum phase transition between the Mott-insulator state and the density-wave state of cold Bose atoms in a two-dimensional (2D) square lattice as the lattice is adiabatically tilted along one of its primary axes. It is shown that a small misalignment of the tilt drastically changes the result of the adiabatic passage and, instead o...

We discuss the quantum phase transition from the Mott-insulator state to the density-wave state for cold Bose atoms in a 2D square lattice as the lattice is adiabatically tilted along one of its primary axes. It is shown that a small misalignment of the tilt drastically changes the result of the adiabatic passage and, instead of the density-wave st...

We analyze the Wannier-Stark spectrum of a quantum particle in a 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 Wann...

Recent experimental progress in the creation of synthetic electric and magnetic fields, acting on cold atoms in a two-dimensional lattice, has attracted renewed interest to the problem of a quantum particle in the Hall configuration. The present work contains a detailed analysis of the eigenstates of this system, called Landau-Stark states, and of...

We consider the dynamics of a charged particle in a finite along the x-direction square lattice in the presence of a normal to the lattice plane magnetic field and an in-plane electric field aligned with the y-axis. For a vanishing magnetic field this dynamics would be common Bloch oscillations where the particle oscillates in the y-direction with...

We consider dynamics of a charged particle in a finite along the $x$ direction square lattice in the presence of normal to the lattice plane magnetic field and in-plane electric field aligned with the $y$ axis. For vanishing magnetic field this dynamics would be common Bloch oscillations where the particle oscillates in the $y$ direction with ampli...

We discuss the master equation approach to diffusive current of bosonic or fermionic carriers in one- and two-dimensional lattices. This approach is shown to reproduce all known results of the linear response theory, including the integer quantum Hall effect for fermionic carriers. The main advantage of the approach is that it allows to calculate t...

We analyze the eigenstates of a two-dimensional lattice with additional harmonic confinement in the presence of an artificial magnetic field. While the softness of the confinement makes a distinction between bulk and edge states difficult, the interplay of harmonic potential and lattice leads to a different classification of states in three energy...

We consider a Bose-Hubbard dimer scattered from a potential barrier. A numerical approach has been developed to treat the stationary scattering problem. It allows to compute the tunneling and dissociation probabilities for arbitrary shape of the potential barrier and arbitrary kinetic energy of the dimer. The obtained results are shown to be in agr...

We consider a quantum particle in tilted two-dimensional lattices in the tight-binding approximations. We found that for some lattice geometries and certain orientations of the static force with respect to the lattice primary axes the particle can freely move across the lattice in the direction perpendicular to the vector of the static force. This...

We study the interband Landau-Zener tunneling of a quantum particle in the Hall configuration, i.e., in the presence of normal to the lattice plane gauge field (for example, magnetic field for a charged particle) and in-plane potential field (electric field for a charged particle). The interband tunneling is induced by the potential field and for v...

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 t...

We study a quantum particle in a tilted honeycomb lattice in the tight-binding approximation. First we discuss the particle eigenstates, i.e., the stationary Wannier-Stark states. These states are proved to be extended states for the rational directions of the static field and localized states for the irrational directions. We find energy bands of...

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...

We analyze the driven Harper model, which appears in the problem of tight-binding electrons in the Hall configuration (normal to the lattice plane magnetic field plus in-plane electric field). The presence of an electric field extends the celebrated Harper model, which is parametrized by the Peierls phase, into the driven Harper model, which is add...

We study under-barrier tunneling for a pair of energetically bound bosonic atoms in an optical lattice with a barrier. We identify conditions under which this exotic molecule tunnels as a point particle with the coordinate given by the bound pair center of mass and discuss the atomic co-tunneling beyond this regime. In particular, we quantitatively...

Finite topological quantum systems can undergo continuous metastable quantum phase transitions to change their topological nature. Here we show how to nucleate the transition between ring currents and dark soliton states in a toroidally trapped Bose-Einstein condensate. An adiabatic passage to wind and unwind its phase is achieved by explicit globa...

Quantum dynamics of a charged particle in a 2D lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations (the case of vanishing electric field) and Bloch oscillations (zero magnetic field), details of which has not yet been completely understood. In the present work we suggest to study this pro...

This paper studies the quantum dynamics of a charged particle in a two-dimensional 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...

This paper proposes a simple setup for introducing an artificial magnetic field for neutral atoms in 2D optical lattices. This setup is based on the phenomenon of photon-assisted tunneling and involves a low-frequency periodic driving of the optical lattice. This low-frequency driving does not affect the electronic structure of the atom and can be...

The paper introduces a semi-analytical method for calculating the Hall conductivity in the single-band approximations. The method goes beyond the linear response theory and, thus, imposes no limitation on the electric fields magnitude. It is shown that the Hall current decreases with increase of the electric field, if the Bloch frequency (which is...

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...

We discuss a method for creating bright matter solitons by loading a Bose-Einstein condensate of atoms in a driven tilted optical lattice. It is shown that one can realize the self-focusing regime for the wave-packet dynamics by properly adjusting the phase of the driving field with respect to the phase of Bloch oscillations. If atom-atom interacti...

We suggest a method for creating bright matter solitons by loading a BEC of atoms in a driven tilted optical lattice. It is shown that one can realize the self-focussing regime for the wave-packet dynamics by properly adjusting the phase of the driving field with respect to the phase of Bloch oscillations. If atom-atom interactions are larger than...

The dynamics of cold Bose atoms in driven tilted optical lattices is analyzed focusing on destruction of Wannier-Stark localization and the phenomenon of band collapse. It is argued that an understanding of the experimental results requires thorough account for interaction effects. These are suppression of the ballistic spreading of atoms for reson...

The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation. If the static field is varied the system shows a plethora of dynamical phenomena. In the strong field limit we demonstrat...

This paper studies a simple model of conductivity—a quantum particle (an atom) in a lattice, subject to a static field and interacting with the bath of Bose atoms. Results from direct numerical simulations of the system dynamics and statistical analysis of the eigenstates are compared with predictions from linear response theory, analytical solutio...

We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type: The corresponding mean-field system described by a discrete nonlinear Schr\"odinger equation can show a dynamical (or modulation) instability due to chaotic dynamics and equipartiti...

This Letter studies the dynamics of a quantum particle in 2D lattices with on-site disorder in the presence of a static field. It is shown that the particle is localized along the field direction, while in the orthogonal direction to the field it shows diffusive dynamics for algebraically large times. For weak disorder an analytical expression for...

This paper discusses the master equation approach to the derivation of the Esaki-Tsu equation for drift current. It is shown that the relaxation term in the master equation can be identified by measuring the velocity distribution of the carriers. We also show that the standard form of the relaxation term, used earlier to derive the Esaki-Tsu equati...

The work discusses transport of cold atoms in optical lattices. Two related but different problems are considered: interacting Bose atoms subject to a static field (i.e., the atoms in a tilted lattice); and non-interacting atoms in a tilted lattice in the presence of a buffer gas. For these two systems we found, respectively: periodic, quasiperiodi...

We consider a Bose-Einstein condensate of ultracold atoms loaded into a square optical lattice and subject to a static force. For vanishing atom-atom interactions the atoms perform periodic Bloch oscillations for arbitrary direction of the force. We study the stability of these oscillations for non-vanishing interactions, which is shown to depend o...

We analyze the Bogoliubov spectrum of the Bose-Hubbard model with a finite number of sites and Bose particles by using a semiclassical approach. This approach allows us to take into account the finite-size effects responsible for evolution of the Bogoliubov spectrum into an irregular (chaotic) spectrum at higher energies. A manifestation of this tr...

We analyze the Bogoliubov spectrum of the three-site Bose-Hubbard model with a finite number of Bose particles by using a semiclassical approach. The Bogoliubov spectrum is shown to be associated with the low-energy regular component of the classical Hubbard model. We identify the full set of the integrals of motion of this regular component and, q...

The paper discusses the problem of correspondence between the classical and quantum approaches to the description of chaotic dynamics of a mesoscopic particle. The condition for the equivalence of both approaches is given.

We study the dynamics of an electron in a standing wave of a microwave field. For large field amplitude the system undergoes a transition to a chaotic regime which is shown to be entirely related with the transition to relativistic dynamics. A possible laboratory experiment is shortly discussed.

Chaos implies unpredictability, fluctuations, and the need for statistical modelling. Quantum optics has developed into one of the most advanced subdisciplines of modern physics in terms of the control of matter on a microscopic scale, and, in particular, of isolated, single quantum objects. Prima facie, both fields therefore appear rather distant...

We consider a small ensemble of Bose atoms in a ring optical lattice with weak disorder. The atoms are assumed to be initially prepared in a superfluid state with non-zero quasimomentum and, hence, may carry matter current. It is found that the atomic current persists in time for a low value of the quasimomentum but decays exponentially for a high...

We analyse Bloch oscillations (i.e., oscillations induced by a static force) of strongly interacting Bose atoms {\em beyond} the hard-core bosons model. It is shown that residual interactions between the atoms modulate Bloch oscillations, where the type of modulations depends on the magnitude of the static force.

We devise a microscopic model for the emergence of a collision-induced, fermionic atomic current across a tilted optical lattice. Tuning the--experimentally controllable--parameters of the microscopic dynamics allows us to switch from Ohmic to negative differential conductance.

The paper studies the dynamics of a Bose-Einstein condensate loaded in a 1D parabolic optical lattice and excited by a sudden shifting of the lattice center. Depending on the initial shift, this dynamics is either the dipole or Bloch oscillations of the atoms. The effects of the dephasing and atom-atom interactions on the above atomic oscillations...

We devise a microscopic model for the emergence of a collision-induced, fermionic atomic current across a tilted optical lattice. Tuning the - experimentally controllable - parameters of the microscopic dynamics allows to switch from Ohmic to negative differential conductance.