Alexey V. Ponomarev

Atomic current across an optical lattice.

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.

Thermal equilibration between two quantum systems.

Two identical finite quantum systems prepared initially at different temperatures, isolated from the environment, and subsequently brought into contact are demonstrated to relax towards Gibbs-like quasiequilibrium states with a common temperature and small fluctuations around the time-averaged expectation values of generic observables. The temporal thermalization process proceeds via a chain of intermediate Gibbs-like states. We specify the conditions under which this scenario occurs and corroborate the quantum equilibration with two different models.

ac-Driven Atomic Quantum Motor

We propose an ac-driven quantum motor consisting of two different, interacting ultracold atoms placed into a ring-shaped optical lattice and submerged in a pulsating magnetic field. While the first atom carries a current, the second one serves as a quantum starter. For fixed zero-momentum initial conditions the asymptotic carrier velocity converges to a unique nonzero value. We also demonstrate that this quantum motor performs work against a constant load.

Quantum ratchet transport with minimal dispersion rate

We analyze the performance of quantum ratchets by considering the dynamics of an initially localized wave packet loaded into a flashing periodic potential. The directed center-of-mass motion can be initiated by the uniform modulation of the potential height, provided that the modulation protocol breaks all relevant time- and spatial-reflection symmetries. A poor performance of quantum ratchet transport is characterized by a slow net motion and a fast diffusive spreading of the wave packet, while the desirable optimal performance is the contrary. By invoking a quantum analog of the classical Peclet number, namely the quotient of the group velocity and the dispersion of the propagating wave packet, we calibrate the transport properties of flashing quantum ratchets and discuss the mechanisms that yield low-dispersive directed transport.

Mapping the Arnold web with a graphic processing unit

The Arnold diffusion constitutes a dynamical phenomenon which may occur in the phase space of a non-integrable Hamiltonian system whenever the number of the system degrees of freedom is M ≥ 3. The diffusion is mediated by a web-like structure of resonance channels, which penetrates the phase space and allows the system to explore the whole energy shell. The Arnold diffusion is a slow process; consequently, the mapping of the web presents a very time-consuming task. We demonstrate that the exploration of the Arnold web by use of a graphic processing unit-supercomputer can result in distinct speedups of two orders of magnitude as compared with standard CPU-based simulations.The Arnold diffusion constitutes a dynamical phenomenon wh ich may occur in the phase space of a nonintegrable Hamiltonian system whenever the number of the sy stem degrees of freedom is M ≥ 3. The diffusion is mediated by a web-like structure of resonance channels, w hich penetrates the phase space and allows the system to explore the whole energy shell. The Arnold diffusi on is a slow process; consequently the mapping of the web presents a very time-consuming task. We demonstrate that the exploration of the Arnold web by use of a graphic processing unit (GPU)-supercomputer can result i n distinct speedups of two orders of magnitude as compared to standard CPU-based simulations.

Quantum Chaos, Transport, and Control—in Quantum Optics

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 in philosophy and outset. However, as we shall discuss in the present review, chaos, and, more specifically, quantum chaos opens up novel perspectives for our understanding of the dynamics of increasingly complex quantum systems, and of ultimate quantum control by tailoring complexity.

Quantum thermal equilibration from equipartition

The problem of mutual equilibration between two finite, identical quantum systems, A and B, prepared initially at different temperatures is elucidated. We show that the process of energy exchange between the two systems leads to accurate equipartition within energy shells in the Hilbert space of the total non-interacting, composite system, A \otimes B. This scenario occurs under the general condition of a weak interaction between the systems. We predict that the sole hypothesis of such equipartition is sufficient to obtain a relaxation of the peers, A and B, towards a common thermal-like state. This conjecture is fully corroborated by an exact diagonalization of several quantum models.

Oscillons: An encounter with dynamical chaos in 1953?

We discuss the works of one of electronic art pioneers, Ben F. Laposky (1914-2000), and argue that he might have been the first to create a family of essentially nonlinear analog circuits that allowed him to observe chaotic attractors.

Microscopic and mean-field dynamics of cold atoms in optical lattices

The Bloch dynamics of degenerate cold atoms in optical lattices is a paradigmatic problem of quantum transport theory, arid under virtually perfect experimental control. If a Bose-Einstein condensate (BEC) is loaded into truly 1D lattices, and for sufficiently small filling factors, the problem can be treated within the Bose-Hubbard model. The nonlinearity can stabilise the BEC against dispersion whilst moving across the lattice, giving rise to soliton-like solutions