Quantum tunneling as a classical anomaly

Abstract

Classical mechanics is a singular theory in that real-energy classical particles can never enter classically forbidden regions. However, if one regulates classical mechanics by allowing the energy E of a particle to be complex, the particle exhibits quantum-like behavior: Complex-energy classical particles can travel between classically allowed regions separated by potential barriers. When Im(E) -> 0, the classical tunneling probabilities persist. Hence, one can interpret quantum tunneling as an anomaly. A numerical comparison of complex classical tunneling probabilities with quantum tunneling probabilities leads to the conjecture that as ReE increases, complex classical tunneling probabilities approach the corresponding quantum probabilities. Thus, this work attempts to generalize the Bohr correspondence principle from classically allowed to classically forbidden regions.

12 pages, 7 figures

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Cited by in corpus (13)

• Generating Finite Dimensional Integrable Nonlinear Dynamical Systems
• On Quantum Tunneling in Real Time
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• Quantum tunneling from paths in complex time
• Lorentzian path integral for quantum tunneling and WKB approximation for wave-function
• Effective protection of quantum coherence by non-Hermitian driving
• Chaotic diffusion of complex trajectory and its quantum signature
• Complexified Synchrony
• False vacuum decay of excited states in finite-time instanton calculus
• Path of a tunneling particle
• Energy effective mass dependence of electron tunneling through CdS/CdSe, AlxGa1-xAs/GaAs and AlSb/InAs Multiple Quantum Barriers
• Dynamical system analysis of quantum tunneling in an asymmetric double-well potential