Complexity of energy eigenstates as a mechanism for equilibration

• Autores: Masanes, Lluís; Roncaglia, Augusto Jose; Acín, Antonio
• Año de publicación: 2013
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Equilibration; Quantum complexity
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and the complexity of their eigenvectors, provided that a conjecture about the incompressibility of quantum circuits holds. We quantify the complexity by the size of the smallest quantum circuit mapping the local basis onto the energy eigenbasis. Specifically, we consider the set of all Hamiltonians having complexity C, and show that almost all such Hamiltonians equilibrate if C is superquadratic in the system size, which includes the fully random Hamiltonian case in the limit C→∞, and do not equilibrate if C is sublinear. We also provide a simple formula for the equilibration time scale in terms of the Fourier transform of the level density. Our results are statistical and, therefore, do not apply to specific Hamiltonians. Yet they establish a fundamental link between equilibration and complexity theory.
Fil: Masanes, Lluís. ICFO–Institut de Ciències Fotòniques, Mediterranean Technology Park; España;
Fil: Roncaglia, Augusto Jose. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Fisica; Argentina; ICFO–Institut de Ciències Fotòniques, Mediterranean Technology Park; España;
Fil: Acín, Antonio. ICFO–Institut de Ciències Fotòniques, Mediterranean Technology Park; España;