Linking Quantum Physics and Classical Chaos

Ilya Prigogine

Violetta Sharoglazova, Marius Puplauskis, Lotte Hof +1 more

How classical chaos emerges from quantum mechanics remains a central open question, as the unitary evolution of isolated quantum systems forbids exponential sensitivity to initial conditions. A key insight is that this quantum-classical link is provided by measurement processes. In this work, we identify gain competition in a chaotic photon gas as an operational quantum measurement that selects single motional modes from an initial superposition through stochastic, nonlinear amplification. We show that this mechanism naturally gives rise to classical chaotic behavior, most notably sensitivity to initial conditions. Our results provide a concrete physical mechanism for the quantum-classical transition in a chaotic system and demonstrate that essential aspects of quantum measurement-state projection, Born-rule-like selection, and irreversibility-can naturally emerge from intrinsic gain dynamics.

George M. Zaslavsky

Robert C. Bishop

Sebastian Leontica, Andrew G. Green

Finding suitable characterizations of quantum chaos is a major challenge in many-body physics, with a central difficulty posed by the linearity of the Schrödinger equation. A possible solution for recovering non-linearity is to project the dynamics onto some variational manifold. The classical chaos induced via this procedure may be used as a signature of quantum chaos in the full Hilbert space. Here, we demonstrate analytically a previously heuristic connection between the Lyapunov spectrum from projection onto the matrix product state (MPS) manifold and the growth of entanglement. This growth occurs by squeezing a localized distribution on the variational manifold. The process qualitatively resembles the Cardy-Calabrese picture, where local perturbations to a moving MPS reference are interpreted as bosonic quasi-particles. Taking careful account of the number of distinct channels for these processes recovers the connection to the Lyapunov spectrum. Our results rigorously establish the physical significance of the projected Lyapunov spectrum, suggesting it as an alternative method of characterizing chaos in quantum many-body systems, one that is manifestly linked to classical chaos.

Todd A. Brun

In this work the decoherence formalism of quantum mechanics is explored and applied to a number of interesting problems in quantum physics. The boundary between quantum and classical physics is examined, and demonstration made that quantum histories corresponding to classical equations of motion become more probable for a broad class of models, including linear and nonlinear models of Brownian motion. The link between noise, dissipation, and decoherence is studied. This work is then applied to systems which classically exhibit dissipative chaotic dynamics. A theory is explicated for treating these systems, and the ideas are applied to a particular model of the forced, damped Duffing oscillator, which is chaotic for certain parameter values. Differences between classical and quantum chaos are examined, particularly differences arising in the structure of fractal strange attractors, and the conceptual difficulties in framing standard notions of chaos in a quantum system. A brief discussion of previous work on quantum chaos is included, and the differences between Hamiltonian and dissipative chaos pointed out; a somewhat different interpretation of quantum chaos from the standard one is suggested. A class of histories for quantum systems, in phase space rather than configuration space, is studied. Different ways of representing projections in phase space are discussed, and expressions for the probability of phase space histories are derived; conditions for such histories to decohere are also estimated in the semiclassical limit.