Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems

Area of Science:

• Statistical Physics
• Quantum Thermodynamics
• Quantum Information Theory

Background:

• Thermal states are fundamental in statistical physics.
• The emergence and properties of thermal states in closed quantum systems remain incompletely understood.
• Understanding thermalization is crucial for quantum thermodynamics and quantum information applications.

Purpose of the Study:

• To investigate the conditions under which thermal states arise in closed quantum systems with local Hamiltonians.
• To determine the stability of thermal states against local perturbations (noise).
• To provide finite-size bounds for these phenomena.

Main Methods:

• Analysis of quantum quenches in finite quantum lattices with local Hamiltonians.
• Demonstration of equilibration for states with exponentially decaying correlations.
• Establishing local equivalence between equilibrium states and thermal states.
• Rigorous analysis of thermal state stability under local disturbances.

Main Results:

• States with exponentially decaying correlations equilibrate after a quantum quench.
• The equilibrium state is locally equivalent to a thermal state under specific conditions (sufficiently small free energy, exponentially decaying correlations).
• Thermal states are stable against local noise if their correlations decay exponentially.
• All results are accompanied by finite-size bounds.

Conclusions:

• This study clarifies the conditions for thermal state emergence and stability in closed quantum systems.
• The findings are crucial for advancing quantum thermodynamics and understanding noise resilience in quantum systems.
• The established finite-size bounds are vital for practical applications and future research.