Dynamical system analysis of quantum tunneling in an asymmetric double-well potential

Abstract

We study quantum tunneling in an asymmetric double-well potential using a dynamical systems--based approach rooted in the Ehrenfest formalism. In this framework, the time evolution of a Gaussian wave packet is governed by a hierarchy of coupled equations linking lower- and higher-order position moments. An approximate closure scheme, required to render the system tractable, yields a reduced dynamical system for the mean and variance, with skewness explicitly entering due to the potential's asymmetry. Stability analysis of this system identifies energy thresholds for detectable tunneling across the barrier and reveals regimes where tunneling, though theoretically allowed, remains practically undetectable. Comparison with full numerical solutions of the time-dependent Schrödinger equation shows that, beyond reproducing key tunneling features, the dynamical systems approach provides an interpretable description of quantum transport through tunneling in an effective asymmetric two-level system.

Accepted in Physics Letters A

References in corpus (21)

• Quantum state engineering with Josephson-junction devices
• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• Coupled quantum dots as quantum gates
• Matter-wave interferometry in a double well on an atom chip
• Observation of directly interacting coherent two-level systems in a solid
• Tunnel splittings for one dimensional potential wells revisited
• Condensate splitting in an asymmetric double well for atom chip based sensors
• Optical Weak Link between Two Spatially Separate Bose-Einstein Condensates
• Semiquantal dynamics of fluctuations: Ostensible quantum chaos
• Statistical moments for classical and quantum dynamics: formalism and generalized uncertainty relations
• Tunneling and energy splitting in an asymmetric double-well potential
• Complex trajectory method in time-dependent WKB
• Semi-classical formula for quantum tunneling in asymmetric double-well potentials
• Classical and quantum behavior of the harmonic and the quartic oscillators
• Quantum tunneling as a classical anomaly
• Instanton theory of tunnelling in molecules with asymmetric isotopic substitutions
• Quantum tunneling and level crossings in the squeeze-driven Kerr oscillator
• Localization or tunneling in asymmetric double-well potentials
• Chaos in the Quantum Double Well Oscillator: The Ehrenfest View Revisited
• Ehrenfest approach to open double-well dynamics
• Quantum dynamics from fixed points and their stability