![]() ![]() Our results clarify how the correspondence principle applies in the context of quantum and classical work distributions and contribute to the understanding of work and nonequilibrium work relations in the quantum regime. We also derive the form of the quantum work distribution at the boundary between classically allowed and forbidden regions, where this distribution tunnels into the forbidden region. Hence, in the semiclassical limit, the quantum work distribution converges to the classical distribution, decorated by a quantum interference pattern. Neglecting the interferences between trajectories reduces the distribution to that of the corresponding classical process. We find that a semiclassical work distribution, built from classical trajectories that connect the initial and final energies, provides an excellent approximation to the quantum work distribution when the trajectories are assigned suitable phases and are allowed to interfere. In this paper, we employ semiclassical methods, combined with numerical simulations of a driven quartic oscillator, to study the correspondence between classical and quantal definitions of work in systems with 1 degree of freedom. While this two-point measurement definition of quantum work can be justified heuristically by appeal to the first law of thermodynamics, its relationship to the classical definition of work has not been carefully examined. This definition leads to statistical distributions of work that satisfy nonequilibrium work and fluctuation relations. Batterman argues that the interpretation of the correspondence principle which he advocates has historical support which can be found in Niels Bohr's early writing on the quantum theory.For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. The correspondence principle, when properly interpreted already supplies a unified account of chaos-for both classical and quantum mechanics. Batterman argues that a proper understanding of the correspondence principle resolves the problem of defining quantum chaos. Batterman argues that this definition is to be resisted, since to a certain degree it divorces the issue of chaos from the dynamics. ![]() The virtue of this view is that it seems to be "theory neutral." On this definition, quantum mechanics is completely inhospitable to chaos. One approach to a quantum definition for chaos is to adopt an algorithmic complexity definition. While there is at least some consensus on how to define chaos in classical physics,the question of a definition for chaos in quantum mechanics is completely open. One question he is asking is that of a definition of chaos for quantum systems. ![]() Batterman is investigating the connections between classical and quantum mechanics,in light of the fact that classical systems appear to allow generic chaotic behavior while quantum systems do not. Primary Place of Performance Congressional District:ĭr. University of Illinois at Urbana-Champaign E-stability is defined in virtual or notional time using an ordinary differential equation that is as- sociated with the stochastic dynamics of learning. Robert Batterman (Principal Investigator) Sponsored Research Office:.Overmann DBI Div Of Biological Infrastructure BIO Direct For Biological Sciences Chaos, Quantization and the Correspondence Principle NSF Org: ![]()
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