Equilibration via Gaussification in Fermionic Lattice Systems

Area of Science:

• Quantum physics
• Many-body systems
• Statistical mechanics

Background:

• Understanding the dynamics of quantum systems far from equilibrium is crucial.
• Noninteracting fermionic Hamiltonians are fundamental models in condensed matter physics.
• The process of equilibration and the emergence of Gaussian states are key phenomena.

Purpose of the Study:

• To investigate the conditions under which non-Gaussian states equilibrate to Gaussian states.
• To analyze the dynamics of quadratic noninteracting fermionic Hamiltonians.
• To provide a rigorous proof for the convergence to a generalized Gibbs ensemble.

Main Methods:

• Utilizing two core assumptions: clustering of correlations in the initial state and delocalizing transport in the Hamiltonian.
• Developing a general argument applicable to pure and mixed initial states.
• Applying the framework to various lattice systems and spin systems.

Main Results:

• Proving that non-Gaussian initial states become locally indistinguishable from fermionic Gaussian states in a controlled time.
• Demonstrating that this relaxation dynamics follows a power-law independent of system size.
• Establishing rigorously proven instances of convergence to a generalized Gibbs ensemble.

Conclusions:

• The study provides a powerful framework for understanding equilibration in quantum many-body systems.
• The results offer a new intuition for quantum dynamics, applicable to diverse systems including cold atoms in optical lattices.
• This work bridges theoretical insights with experimental relevance in quantum simulations.