IQIM Postdoctoral and Graduate Student Seminar

Abstract: In the presence of chaos, wavepackets spread exponentially in time and, when isolated, can form large superpositions in just seconds or minutes even for ordinary macroscopic systems, despite the relative smallness of ħ. Heuristic arguments and examples suggest that decoherence from a weakly coupled environment restores the quantum-classical correspondence, but how weak and under what conditions? We bound the difference between quantum and classical trajectories for general Markovian open systems that holds when the strength of the environment-induced diffusion exceeds a threshold proportional to (ħ/S)^(4/3), where S is the characteristic action of the system. It applies to dynamics generated by arbitrary Hamiltonian and Lindblad operators associated with smooth classical functions H(x,p) and Lk(x,p), and holds for all observables and for times exponentially longer than the Ehrenfest timescale on which the correspondence breaks down in closed systems. Diffusive noise is unavoidable in open systems, but its strength is suppressed by ħ/S, hence vanishing in the classical limit and giving the appearance of reversible dynamics. The 4/3 exponent may be optimal as Toscano et al. have found evidence that the quantum-classical correspondence breaks down in some systems when the diffusion is any weaker.

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