Classical Particle in a Complex Elliptic Potential

Abstract

This paper reports a numerical study of complex classical trajectories of a particle in an elliptic potential. This study of doubly-periodic potentials is a natural sequel to earlier work on complex classical trajectories in trigonometric potentials. For elliptic potentials there is a two-dimensional array of identical cells in the complex plane, and each cell contains a pair of turning points. The particle can travel both horizontally and vertically as it visits these cells, and sometimes the particle is captured temporarily by a pair of turning points. If the particle's energy lies in a conduction band, the particle drifts through the lattice of cells and is never captured by the same pair of turning points more than once. However, if the energy of the particle is not in a conduction band, the particle can return to previously visited cells.

12 pages, 7 figures

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• The ODE/IM Correspondence
• Interference in Bohmian Mechanics with Complex Action
• Complex Correspondence Principle
• Classical Trajectories for Complex Hamiltonians
• Spontaneous Breaking of Classical PT Symmetry
• Complex trajectory method in time-dependent WKB
• Conduction bands in classical periodic potentials

Cited by in corpus (10)

• Integrable nonlocal asymptotic reductions of physically significant nonlinear equations
• Bohmian quantum trajectories from coherent states
• PT-symmetry breaking in complex nonlinear wave equations and their deformations
• Quantum tunneling as a classical anomaly
• Probability Density in the Complex Plane
• Various Scattering Properties of a New PT-symmetric non-Hermitian potential
• Infinitely many inequivalent field theories from one Lagrangian
• Understanding complex dynamics by means of an associated Riemann surface
• Complex Trajectories in a Classical Periodic Potential
• PT-symmetrically deformed shock waves