Quantum work for sudden quenches in Gaussian random Hamiltonians.

Area of Science:

• Quantum thermodynamics
• Statistical mechanics
• Nonequilibrium systems

Background:

• Stochastic variables like work are crucial in nonequilibrium quantum thermodynamics.
• Jarzynski and Crooks fluctuation theorems are key for understanding systems driven from equilibrium.
• The work probability density function (pdf) depends on initial/final Hamiltonians and temperature.

Purpose of the Study:

• To derive a general analytic expression for the work characteristic function G(u).
• To describe the behavior of the work pdf for sudden quenches in quantum systems.
• To validate the expression across different Gaussian ensembles and temperature ranges.

Main Methods:

• Utilizing random matrix theory.
• Developing an analytic expression for the work characteristic function G(u).
• Analyzing sudden quenches in quantum systems.

Main Results:

• A simple analytic expression for G(u) valid for all traditional Gaussian ensembles.
• The formula accurately describes G(u) for sudden quenches.
• The derived expression holds for all temperature ranges.

Conclusions:

• The study provides a significant advancement in understanding stochastic work in quantum systems.
• The analytic expression offers a powerful tool for theoretical and experimental investigations.
• This work bridges the gap between theoretical predictions and experimental observations in quantum thermodynamics.