Universal time fluctuations in near-critical out-of-equilibrium quantum dynamics

Area of Science:

• Quantum physics
• Statistical mechanics
• Condensed matter theory

Background:

• Out-of-equilibrium quantum systems exhibit complex temporal dynamics.
• Time fluctuations are typically negligible in large systems but can be amplified in small quench experiments.
• Understanding these fluctuations is crucial for characterizing non-equilibrium quantum phenomena.

Purpose of the Study:

• To investigate the behavior and significance of time fluctuations in quantum systems undergoing small quenches.
• To determine conditions under which time fluctuations can become dominant over equilibrium fluctuations.
• To explore the universality of these fluctuations near critical points.

Main Methods:

• Theoretical analysis of out-of-equilibrium quantum dynamics.
• Investigation of quench protocols near critical points.
• Calculation of distribution functions for dynamically evolving observable expectation values.
• Explicit verification using the quantum Ising model.

Main Results:

• Time fluctuations can be significantly enhanced in small quench experiments, especially near critical points.
• These enhanced fluctuations can exceed equilibrium quantum fluctuations.
• The distribution function of observable expectation values exhibits universal behavior, determined by critical exponents and boundary conditions, for relevant operators.
• For non-relevant operators or at regular points, the distribution becomes Gaussian.

Conclusions:

• The study reveals that time fluctuations play a critical role in small quench experiments in quantum systems.
• Universality in the distribution functions of observable expectation values near critical points is demonstrated.
• The findings provide a new perspective on quantum fluctuations in non-equilibrium settings and are validated by the quantum Ising model calculation.