Origin of quantum chaos for two particles interacting by short-range potentials

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Condensed matter physics

Background:

• Investigating quantum chaos in interacting particle systems is crucial for understanding complex quantum phenomena.
• Confined one-dimensional systems offer a simplified yet fundamental model for studying quantum dynamics.

Purpose of the Study:

• To determine the conditions under which quantum chaos arises in a system of two interacting one-dimensional particles.
• To link the emergence of quantum chaos to specific characteristics of the system's classical dynamics.
• To explore the implications for analytical solutions and potential extensions to larger systems.

Main Methods:

• Analysis of spectrum statistics to identify signatures of quantum chaos.
• Comparison of quantum behavior with the underlying classical dynamics, focusing on momentum ergodicity.
• Theoretical investigation of the limitations imposed on exact solution methods like the Bethe ansatz.

Main Results:

• Quantum chaos emerges under conditions directly related to the ergodicity of particle momentum changes in the classical limit.
• The presence of quantum chaos obstructs the application of the Bethe ansatz for obtaining exact wave functions.
• The study identifies a clear link between classical ergodicity and quantum chaotic behavior.

Conclusions:

• The ergodicity of classical momentum dynamics is a key indicator for quantum chaos in two-particle systems.
• Exact analytical solutions via the Bethe ansatz are not feasible when quantum chaos is present.
• Findings provide insights into the behavior of complex quantum systems and suggest avenues for many-body research.