Driven Topological Systems in the Classical Limit

Periodically-driven quantum systems can exhibit topologically non-trivial behaviour, even when their quasi-energy bands have zero Chern numbers. Much work has been conducted on non-interacting quantum-mechanical models where this kind of behaviour is present. However, the inclusion of interactions in out-of-equilibrium quantum systems can prove to be quite challenging. On the other hand, the classical counterpart of hard-core interactions can be simulated efficiently via constrained random walks. The non-interacting model proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013)], has a special point for which the system is equivalent to a classical random walk. We consider the classical counterpart of this model, which is exact at a special point even when hard-core interactions are present, and show how these quantitatively affect the edge currents in a strip geometry. We find that the interacting classical system is well described by a mean-field theory. Using this we simulate the dynamics of the classical system, which show that the interactions play the role of Markovian, or time dependent disorder. By comparing the evolution of classical and quantum edge currents in small lattices, we find regimes where the classical limit considered gives good insight into the quantum problem.Comment: 15 pages, 15 figures, new content on the quantum mode

Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective 1D Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matterwave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the purely classical simulation, suggesting that observing such exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the non-interacting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms.Comment: Close to the published versio

Do crossover functions depend on the shape of the interaction profile?

We examine the crossover from classical to non-classical critical behaviour in two-dimensional systems with a one-component order parameter. Since the degree of universality of the corresponding crossover functions is still subject to debate, we try to induce non-universal effects by adding interactions with a second length scale. Although the crossover functions clearly depend on the range of the interactions, they turn out to be remarkably robust against further variation of the interaction profile. In particular, we find that the earlier observed non-monotonic crossover of the effective susceptibility exponent occurs for several qualitatively different shapes of this profile.Comment: 7 pages + 4 PostScript figures. Accepted for publication in Europhysics Letters. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

Quantum non-linear evolution of inflationary tensor perturbations

We study the quantum mechanical evolution of the tensor perturbations during inflation with non-linear tensor interactions. We first obtain the Lindblad terms generated by non-linear interactions by tracing out unobservable sub-horizon modes. Then we calculate explicitly the reduced density matrix for the super-horizon modes, and show that the probability of maintaining the unitarity of the squeezed state decreases in time. The decreased probability is transferred to other elements of the reduced density matrix including off-diagonal ones, so the evolution of the reduced density matrix describes the quantum-to-classical transition of the tensor perturbations. This is different from the classicality accomplished by the squeezed state, the suppression of the non-commutative effect, which is originated from the quadratic, linear interaction, and also maintains the unitarity. The quantum-to-classical transition occurs within 5 - 10 e-folds, faster than the curvature perturbation.Comment: (v1) 39 pages, (v2) typos corrected, to be published in Journal of High Energy Physic

A Laminar Cortical Model for 3D Perception of Slanted and Curved Surfaces and of 2D Images: Developement, attention, and Bistability

A model of laminar visual cortical dynamics proposes how 3D boundary and surface representations of slated and curved 3D objects and 2D images arise. The 3D boundary representations emerge from interactions between non-classical horizontal receptive field interactions with intracorticcal and intercortical feedback circuits. Such non-classical interactions contextually disambiguate classical receptive field responses to ambiguous visual cues using cells that are sensitive to angles and disparity gradients with cortical areas V1 and V2. These cells are all variants of bipole grouping cells. Model simulations show how horizontal connections can develop selectively to angles, how slanted surfaces can activate 3D boundary representations that are sensitive to angles and disparity gradients, how 3D filling-in occurs across slanted surfaces, how a 2D Necker cube image can be represented in 3D, and how bistable Necker cuber percepts occur. The model also explains data about slant aftereffects and 3D neon color spreading. It shows how habituative transmitters that help to control developement also help to trigger bistable 3D percepts and slant aftereffects, and how attention can influence which of these percepts is perceived by propogating along some object boundaries.Air Force Office of Scientific Research (F49620-01-1-0397, F49620-98-1-0108); Defense Advanced Research Projects Agency and the Office of Naval Research (N0014-95-1-0409, N00014-01-1-0624, N00014-95-1-0657); National Science Foundation (IIS-97-20333

Properties of the Boltzmann equation in the classical approximation

We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.Comment: 37 pages, 21 figure

Simulation of interaction Hamiltonians by quantum feedback: a comment on the dynamics of information exchange between coupled systems

Since quantum feedback is based on classically accessible measurement results, it can provide fundamental insights into the dynamics of quantum systems by making available classical information on the evolution of system properties and on the conditional forces acting on the system. In this paper, the feedback-induced interaction dynamics between a pair of quantum systems is analyzed. It is pointed out that any interaction Hamiltonian can be simulated by local feedback if the levels of decoherence are sufficiently high. The boundary between genuine entanglement generating quantum interactions and non-entangling classical interactions is identified and the nature of the information exchange between two quantum systems during an interaction is discussed.Comment: 14 pages, 4 figures; invited paper for the special issue of J. Opt. B on quantum contro