Quantum Interstate Phase Differences and Multiphoton Processes: Quantum Jumps or Dynamic Beats?

Whether quantum state transitions occur by instantaneous jumps (a la Bohr) or deterministic dynamics (Schrödinger's preference) has been intensely debated. Recent experimental measurements of shelved electrons have reignited the debate. We examine aspects of the time-dependent numerical solutions of the Schrödinger equation in quantum systems with two and three levels perturbed by a sinusoidal field. A geometrical construction involving quantum state phase differences illuminates the role of interstate phase differences in a deterministic, rather than random, process of multiphoton absorption. Alternate halves of the Rabi cycle exhibit phase reversals much like the classical beats of coupled oscillators. For non-zero detuning, population inversion does not occur because the exciting field drifts out of the proper phase before inversion is complete. A close correspondence with classical, coupled oscillator beats offers insights for interpretation of deterministic quantum dynamics and suggests an experimental test for the correctness of this picture depending on the long-time phase stability of exciting fields.

Connecting the Dunham Expansion to the Dissociation Limit for Interatomic Potentials: Application to Lennard-Jones m- n Potentials.

Dunham generated the expansion for energy levels of a rotating, vibrating diatomic molecule from an expansion of the potential about the equilibrium position. For partition functions, however, the energy levels are needed all the way to dissociation. Analytic Morse oscillator energies are not very useful because the exponential decay of the Morse potential is much too short-ranged for any physical system. The longer-range Lennard-Jones 12-6 potential could be used, but quantum energies have not previously been conveniently fit. I show how Dunham coefficients begin a set of asymptotic functions for any interaction potential, one function arising from each successive term in the WKB expansion. I apply this to the family of Lennard-Jones m- n (LJ m- n) potentials with an R-m repulsive term and R-n attractive term ( m > n) and demonstrate how m can be used as a parameter to adjust either the equilibrium distance or harmonic frequency. I present an empirical parametrization of LJ m- n vibrotor energies starting with Dunham coefficients generated from four terms in the WKB expansion. This information is combined with data from numerically solved energies and asymptotic limits to fit the functions all the way to dissociation. One can also treat exp-6 and similar model potentials with different repulsive parts using the same method because the expansion form is controlled by the long-range part of the potential.

Periodic boundary condition induced breakdown of the equipartition principle and other kinetic effects of finite sample size in classical hard-sphere molecular dynamics simulation.

We examine consequences of the non-Boltzmann nature of probability distributions for one-particle kinetic energy, momentum, and velocity for finite systems of classical hard spheres with constant total energy and nonidentical masses. By comparing two cases, reflecting walls (NVE or microcanonical ensemble) and periodic boundaries (NVEPG or molecular dynamics ensemble), we describe three consequences of the center-of-mass constraint in periodic boundary conditions: the equipartition theorem no longer holds for unequal masses, the ratio of the average relative velocity to the average velocity is increased by a factor of [N/(N-1)]1/2, and the ratio of average collision energy to average kinetic energy is increased by a factor of N/(N-1). Simulations in one, two, and three dimensions confirm the analytic results for arbitrary dimension.