Quantum anomalies and linear response theory

Abstract

The analysis of diffusive energy spreading in quantized chaotic driven systems, leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation a driven chaotic system exhibits stochastic-like diffusion in energy space with a coefficient $D$ that is proportional to the intensity ${\epsilon }^2$ of the driving. In the corresponding quantized problem the coherent transitions are characterized by a generalized Wigner time $t_{\epsilon }$, and a self-generated (intrinsic) dephasing process leads to non-linear dependence of $D$ on ${\epsilon }^2$.

arXiv comment8 pages, 2 figures, textual improvements (as in published version)

References in corpus (14)

• Dynamic localization in quantum dots: analytical theory
• Chaos and energy spreading for time-Dependent Hamiltonians, and the various Regimes in the theory of Quantum Dissipation
• Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle
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• Rate of energy absorption for a driven chaotic cavity
• Semilinear Response
• Rate of energy absorption by a closed ballistic ring
• Semilinear response for the heating rate of cold atoms in vibrating traps
• Parametric invariant Random Matrix Model and the emergence of multifractality
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• Anomalous decay of a prepared state due to non-Ohmic coupling to the continuum
• Quantum decay into a non-flat continuum

Cited by in corpus (1)

• "Weak Quantum Chaos" and its resistor network modeling