Quantum Mpemba Effect in Random Circuits

Area of Science:

• Quantum physics
• Statistical mechanics
• Complex systems

Background:

• The Mpemba effect describes how nonequilibrium systems can relax faster when initially further from equilibrium.
• In quantum mechanics, this effect is observed in closed systems, relating to symmetry and entanglement dynamics.
• Understanding quantum relaxation dynamics is crucial for developing quantum technologies.

Purpose of the Study:

• To investigate the quantum Mpemba effect in charge-preserving random quantum circuits.
• To identify the conditions and mechanisms governing faster relaxation in asymmetric quantum states.
• To provide a general framework for understanding the Mpemba effect in chaotic quantum systems.

Main Methods:

• Employed extensive numerical simulations of charge-preserving random circuits.
• Utilized analytical arguments to understand the underlying physical mechanisms.
• Studied the dynamics of symmetry restoration and approach to the grand-canonical ensemble for different initial states.

Main Results:

• Demonstrated that more asymmetric initial states (tilted ferromagnets) relax faster, restoring symmetry more quickly.
• Observed that certain other states (tilted antiferromagnets) do not exhibit the quantum Mpemba effect.
• Identified a general mechanism based on the spreading of nonconserved operators relative to conserved densities.

Conclusions:

• The quantum Mpemba effect is linked to the initial asymmetry of quantum states in random circuits.
• The spreading of nonconserved operators provides a unifying explanation for the observed phenomenon.
• This work clarifies the emergence of Mpemba physics in chaotic quantum systems, relying on fundamental principles like locality, unitarity, and symmetry.