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Area of Science:

  • Quantum Chaos
  • Statistical Mechanics
  • High Energy Physics

Background:

  • A conjectured bound (λ_L ≤ 2πT/ℏ) relates Lyapunov exponents (λ_L) to temperature (T) and Planck's constant (ℏ) in thermal quantum systems.
  • This bound implies a potential lower limit on temperature for systems with a fixed Lyapunov exponent, suggesting chaotic systems may not reach zero temperature.
  • Classical dynamical systems, though deterministic, might exhibit thermal behaviors due to quantum corrections.

Purpose of the Study:

  • To investigate if quantum corrections can induce thermal behavior in systems that are classically deterministic.
  • To explore the implications of the conjectured Lyapunov exponent bound in quantum systems.
  • To analyze the conditions under which the bound is saturated.

Main Methods:

  • Investigated semiclassical particle motions near hyperbolic fixed points.
  • Analyzed quantum corrections to classical dynamics.
  • Examined particle motion in an inverse harmonic potential and a c=1 matrix model.

Main Results:

  • Quantum corrections can induce energy emission obeying a Boltzmann distribution, suggesting thermal behavior.
  • This quantum-induced emission is analogous to acoustic Hawking radiation in quantum fluids.
  • Integrable systems, such as inverse harmonic potentials and c=1 matrix models, can saturate the conjectured bound.

Conclusions:

  • Quantum mechanics may impose a fundamental lower bound on temperature for chaotic systems.
  • Quantum corrections can lead to emergent thermal properties in deterministic systems.
  • The conjectured bound on Lyapunov exponents can be saturated even in integrable systems.