Arjendu K. Pattanayak

Controlling the Ratchet Effect for Cold Atoms

Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.

Characterizing the metastable balance between chaos and diffusion

Abstract We examine some new diagnostics for the behavior of a field ρ evolving in an advective–diffusive system. One of these diagnostics is approximately the Fourier second moment (denoted as χ2) and the other is the linear entropy or field intensity S, the latter being significantly easier to compute or measure. We establish that as a result of chaos the increasing structure in ρ is accompanied by χ increasing exponentially rapidly in time at a rate given by ρ-dependent Lyapunov exponents Λi and dominated by the largest one Λmax. Noise or diffusive coarse-graining of ρ causes χ to decrease as χ 2 ≈ 1 4 Dt , where D is a measure of the diffusion. When both effects are present the competition between the processes leads to metastability for χ followed by a final diffusive tail. The initial stages may be chaotic or diffusive depending upon the value of Λ−1max2Dχ2(0) but the metastable value of χ2 is given by χ 2∗ = ∑ i Λ i /2D irrespective. Since S =−2Dχ 2 , similar analysis applies to S, and in particular there exists a metastable decay rate for S given by S ∗ = ∑ i Λ i . These arguments are verified for a simple case, the Arnol’d Cat Map with added diffusive noise.

Parameter scaling in the decoherent quantum-classical transition for chaotic systems.

The quantum to classical transition for a system depends on many parameters, including a scale length for its action, variant Plancks over 2 pi, a measure of its coupling to the environment, D, and, for chaotic systems, the classical Lyapunov exponent, lambda. We propose measuring the proximity of quantum and classical evolutions as a multivariate function of (Plancks over 2 pi,lambda,D) and searching for transformations that collapse this hypersurface into a function of a composite parameter zeta= Plancks over 2 pi alpha)lambda beta D gamma. We report results for the quantum Cat Map and Duffing oscillator, showing accurate scaling behavior over a wide parameter range, indicating that this may be used to construct universality classes for this transition.

Chaos and Lyapunov exponents in classical and quantal distribution dynamics

We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions

Nonmonotonicity in the quantum-classical transition: chaos induced by quantum effects.

\rho(p,q)

Stabilizing an attractive Bose-Einstein condensate by driving a surface collective mode

. Of particular interest is

Calculation of eigenvalues of a strongly chaotic system using Gaussian wave-packet dynamics

\lambda_2

Chaos and dynamical complexity in the quantum to classical transition

, an exponent which quantifies the rate at which chaotically evolving distributions acquire structure at increasingly smaller scales and which is generally larger than the maximal Lyapunov exponent

Entanglement and its relationship to classical dynamics

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Experimental signatures of the quantum-classical transition in a nanomechanical oscillator modeled as a damped-driven double-well problem

for trajectories. The approach is trajectory-independent and is therefore applicable to both classical and quantum mechanics. In the latter case we show that the