Dynamical Crossing of an Infinitely Degenerate Critical Point

Bachmann, Sven; Fraas, Martin and Graf, Gian Michele (2017): Dynamical Crossing of an Infinitely Degenerate Critical Point. In: Annales Henri Poincare, Vol. 18, No. 5: pp. 1755-1776

Abstract

We study the evolution of a driven harmonic oscillator with a time-dependent frequency . At time , the Hamiltonian undergoes a point of infinite spectral degeneracy. If the system is initialized in the instantaneous vacuum in the distant past, then the asymptotic future state is a squeezed state, whose parameters are explicitly determined. We show that the squeezing is independent on the sweeping rate. This manifests the failure of the adiabatic approximation at points, where infinitely many eigenvalues collide. We extend our analysis to the situation, where the gap at remains finite. We also discuss the natural geometry of the manifold of squeezed states. We show that it is realized by the Poincar, disk model viewed as a Kahler manifold.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1424-0637
• Language: English