arXiv subjects

James P. Lavine

Publications and source records attributed to James P. Lavine.

3 recordsLinked to original sources

arXiv2024

Is There Quantum Recurrence in the Presence of an Energy Continuum?

Suppose an initial state is coupled to a continuum of energy states. The population of the initial state is expected to decrease with time, but is the decrease monotonic? The occupation probability of the initial state is the survival probability and the question is equivalent to asking if there are intervals of time where the survival probability increases. Such regrowth is also referred to as regeneration or recurrence and it occurs in systems with a countable number of discrete states. Regrowth is investigated with a simple model that allows transitions between the initial state and continuum states, but transitions between continuum states are not permitted. The model uses the solution of Schroedinger's Equation for a full energy continuum. Such a continuum runs from -infinity to +infinity and is found to have only exponential decay in time. However, the survival probability for a truncated continuum turns out to have a wide variety of behaviors. Generally, the survival probability decreases by several orders of magnitudes, often as an exponential, and then has limited regrowth.

quant-ph↗

arXiv2023

Survival Probability of an Excited State in the Bixon-Jortner Model

When the initial state of a quantum mechanical system is an excited state, then it is expected that the occupation, or survival, probability of that state will decrease. This is studied numerically within the Bixon-Jortner model, which was introduced to model intramolecular radiationless transitions. Here a finite set of states is used and for a fixed number of states, the parameters of the model are the energy level separation and the strength of the transition matrix element. All three of these are varied to see their effects on the survival probability. After a short interval of time, the survival probability decay is often found to be an exponential. But the survival probability is then found to increase with further time and then decrease in a pattern that continues in time. This repopulation is a general feature when a countable set of states is present.

quant-ph↗

arXiv2022

Time development of a driven three-level lambda system: A case study

How does a driven system with many energy levels approach its steady state? Insights are gained by studying a system with three energy levels when the ground state is excited by a laser. The time-dependent occupation probabilities of the three energy levels show students how the system develops in time. The occupation probabilities come from the numerical solution of the Liouville-von Neumann equations for the density operator matrix elements when relaxation is included. A combination of the Interaction Picture, the Rotating Wave Approximation, and the assumption of resonance permit the eigenvalues of the Liouville-von Neumann equations to be found numerically and in closed-form in certain limits. The two methods are complementary and help students understand time-dependent systems. In addition, the eigenvalues allow the short-time and the long-time occupation probabilities to be connected to the relaxation parameters and the magnitude of the laser's electric field. Thus, this model three-level system illuminates how a driven system behaves over time and provides guidance for students studying time-dependent systems.

quant-ph↗