Semiclassical transmission across transition states

Abstract

It is shown that the probability of quantum-mechanical transmission across a phase space bottleneck can be compactly approximated using an operator derived from a complex Poincaré return map. This result uniformly incorporates tunnelling effects with classically-allowed transmission and generalises a result previously derived for a classically small region of phase space.

To appear in Nonlinearity

References in corpus (5)

• Semiclassical Approximations in Phase Space with Coherent States
• Julia set describes quantum tunneling in the presence of chaos
• Tunneling Mechanism due to Chaos in a Complex Phase Space
• A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities
• Moyal star product approach to the Bohr-Sommerfeld approximation

Cited by in corpus (5)

• Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
• The efficient computation of transition state resonances and reaction rates from a quantum normal form
• Unstable Semiclassical Trajectories in Tunneling
• Quantum Theory of Reactive Scattering in Phase Space
• Uniform approximation of barrier penetration in phase space