Exponential energy growth due to slow parameter oscillations in quantum mechanical systems

TL;DR

This paper demonstrates that slow, periodic parameter oscillations in quantum systems can cause exponential energy growth, with potential for cooling phases and quantum state desertion, especially in systems like quantum billiards and graphs.

Contribution

It reveals how slow parameter oscillations induce exponential energy growth and quantum state changes, a novel insight into quantum system dynamics under periodic variations.

Findings

Exponential energy growth observed in quantum systems with slow parameter oscillations.

Cooling phases can occur before energy acceleration.

Quantum states with specific quantum numbers can be abandoned during evolution.

Abstract

It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., quantum billiards and quantum graphs) with periodically divided configuration space. In special cases, the process can also lead to a long period of cooling that precedes the acceleration, and to the desertion of the states with a particular value of the quantum number.