Searcharxiv⌕ Search

arXiv subjects

Paul Brumer

Publications and source records attributed to Paul Brumer.

120 records · Page 7Linked to original sources
arXiv2002

Entanglement-Assisted Coherent Control in Nonreactive Diatom-Diatom Scattering

Intriguing quantum effects that result from entangled molecular rovibrational states are shown to provide a novel means for controlling both differential and total collision cross sections in identical particle diatom-diatom scattering. Computational results on elastic and inelastic scattering of para--H$_2$ and para--H$_2$ are presented, with the collision energy ranging from 400 cm$^{-1}$ to the ultracold regime. The experimental realization and possible extension to other systems are discussed.

quant-ph↗
arXiv2002

When is Quantum Decoherence Dynamics Classical?

A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong decoherence theory, showing a strong dependence on the nature of the system-environment coupling. For example, for the traditionally assumed linear coupling, the classical and quantum results are shown to be in exact agreement.

quant-ph↗
arXiv2002

Phase Control of Nonadiabaticity-induced Quantum Chaos in An Optical Lattice

The qualitative nature (i.e. integrable vs. chaotic) of the translational dynamics of a three-level atom in an optical lattice is shown to be controllable by varying the relative laser phase of two standing wave lasers. Control is explained in terms of the nonadiabatic transition between optical potentials and the corresponding regular to chaotic transition in mixed classical-quantum dynamics. The results are of interest to both areas of coherent control and quantum chaos.

quant-ph↗
arXiv2000

Coherent Control of Quantum Chaotic Diffusion

Extensive coherent control over quantum chaotic diffusion using the kicked rotor model is demonstrated and its origin in deviations from random matrix theory is identified. Further, the extent of control in the presence of external decoherence is established. The results are relevant to both areas of quantum chaos and coherent control.

quant-ph↗
arXiv2000

Coherently Controlled Nanoscale Molecular Deposition

Quantum interference effects are shown to provide a means of controlling and enhancing the focusing a collimated neutral molecular beam onto a surface. The nature of the aperiodic pattern formed can be altered by varying laser field characteristics and the system geometry.

quant-ph↗
arXiv1997

Exponentially rapid decoherence of quantum chaotic systems

We use a recent result to show that the rate of loss of coherence of a quantum system increases with increasing system phase space structure and that a chaotic quantal system in the semiclassical limit decoheres exponentially with rate $2 λ_2$, where $λ_2$ is a generalized Lyapunov exponent. As a result, for example, the dephasing time for classically chaotic systems goes to infinity logarithmically with the temperature, in accord with recent experimental results.

chao-dyn↗
arXiv1997

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 $ρ(p,q)$. Of particular interest is $λ_2$, 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 $λ$ 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 $\hbar\to 0$ limit yields the classical, fully chaotic, result for the quantum cat map.

chao-dyn↗
arXiv1996

Quantum-Classical Correspondence via Liouville Dynamics: I. Integrable Systems and the Chaotic Spectral Decomposition

A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the cancellation of essential singularities, is demonstrated. The application to chaotic systems requires an understanding of classical Liouville eigenfunctions and a Liouville spectral decomposition, developed herein. General approaches to the construction of these Liouville eigenfunctions and classical spectral projectors in quantum and classical mechanics are discussed and are employed to construct Liouville eigenfunctions for classically chaotic systems. Correspondence for systems whose classical analogs are chaotic is discussed, based on this decomposition, in the following paper.

chao-dyn↗
arXiv1996

Quantum-Classical Correspondence via Liouville Dynamics: II. Correspondence for Chaotic Hamiltonian Systems

We prove quantum-classical correspondence for bound conservative classically chaotic Hamiltonian systems. In particular, quantum Liouville spectral projection operators and spectral densities, and hence classical dynamics, are shown to approach their classical analogs in the $h\rightarrow 0$ limit. Correspondence is shown to occur via the elimination of essential singularities. In addition, applications to matrix elements of observables in chaotic systems are discussed.

chao-dyn↗
arXiv1996

Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics

Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly. The quantum dynamics near the classical limit displays both exponential separation of adjacent distributions and long time relaxation, two characteristic features of classical chaotic motion.

chao-dyn↗
arXiv1993

Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation

A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach yields well behaved mixed quantum states for tori for which the corresponding Schrodinger equation has no solutions, as well as an extended spectrum for tori where the Schrodinger equation can be solved. Quantum-classical correspondence is demonstrated for the class of mappings considered, with the Wigner-Weyl density $ρ(p,q,t)$ going to the correct classical limit. An application to the cat map yields, in a direct manner, nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the correspondence limit.

chao-dyn↗