Operator Size at Finite Temperature and Planckian Bounds on Quantum Dynamics

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Condensed matter physics

Background:

• A long-standing belief posits a "Planckian" bound for dissipative timescales (τ) in strongly coupled quantum systems: τ≳(ℏ/k_{B}T).
• Despite supporting evidence, a universally applicable timescale (τ) satisfying this bound has remained elusive.
• Previous conjectured Planckian bounds have limitations, particularly in weakly coupled theories.

Purpose of the Study:

• To define a new timescale (τ) related to operator size at finite temperatures.
• To propose a universal Planckian bound for dissipative timescales.
• To explain the applicability and limitations of previously conjectured Planckian bounds.

Main Methods:

• Definition of operator size at finite temperature.
• Formulation of a conjecture for a universal dissipative timescale (τ).
• Consistency checks against known many-body theories.

Main Results:

• A novel definition of operator size at finite temperature is introduced.
• A conjectured timescale (τ) is proposed, representing the time for small operators to become large.
• This conjectured timescale is consistent with all known many-body theories.

Conclusions:

• The proposed timescale (τ) provides a universal Planckian bound for dissipative processes.
• This framework explains why some previous Planckian bounds fail in weakly coupled systems.
• The findings elucidate the relevance of Planckian timescales in both quantum transport and chaos.