Quantum corrections of work statistics in closed quantum systems

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Quantum thermodynamics

Background:

• The work characteristic function (CF) is crucial for understanding non-equilibrium quantum systems.
• Semiclassical approximations are valuable tools for bridging classical and quantum descriptions.
• The Feynman-Kac formula connects quantum evolution with classical stochastic processes.

Purpose of the Study:

• To investigate quantum corrections to the classical work characteristic function (CF).
• To establish the quantum-classical correspondence of the Feynman-Kac formula.
• To derive and analyze the leading quantum corrections to the work CF.

Main Methods:

• Semiclassical approximation techniques.
• Analysis of the Feynman-Kac formula in a quantum context.
• Perturbation theory to derive quantum corrections.
• Application to exactly solvable models like the forced harmonic and quartic oscillators.

Main Results:

• Quantum corrections to the work CF arise in even powers of Planck's constant (ℏ).
• Explicit formulas for the lowest-order quantum corrections (ℏ²) are derived.
• The physical origins of these quantum corrections are clarified.
• The derived formulas are validated using forced harmonic and quartic oscillators.

Conclusions:

• The study provides a rigorous framework for understanding quantum corrections to work CFs.
• The findings offer insights into the interplay between quantum mechanics and thermodynamics.
• The presented methods and results are applicable to various quantum systems.