Complexity of energy eigenstates as a mechanism for equilibration

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 conje...

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Autor principal:	Roncaglia, Augusto José
Publicado:	2013
Materias:	Complexity theory Energy eigenstates Equilibration time Level density Quantum circuit Quantum many-body systems Statistical relationship System size Eigenvalues and eigenfunctions Logic circuits Quantum theory Hamiltonians
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v87_n3_p_Masanes http://hdl.handle.net/20.500.12110/paper_15393755_v87_n3_p_Masanes
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_15393755_v87_n3_p_Masanes
record_format	dspace
spelling	paper:paper_15393755_v87_n3_p_Masanes2023-06-08T16:20:57Z Complexity of energy eigenstates as a mechanism for equilibration Roncaglia, Augusto José Complexity theory Energy eigenstates Equilibration time Level density Quantum circuit Quantum many-body systems Statistical relationship System size Eigenvalues and eigenfunctions Logic circuits Quantum theory Hamiltonians 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. © 2013 American Physical Society. Fil:Roncaglia, A.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v87_n3_p_Masanes http://hdl.handle.net/20.500.12110/paper_15393755_v87_n3_p_Masanes
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Complexity theory Energy eigenstates Equilibration time Level density Quantum circuit Quantum many-body systems Statistical relationship System size Eigenvalues and eigenfunctions Logic circuits Quantum theory Hamiltonians
spellingShingle	Complexity theory Energy eigenstates Equilibration time Level density Quantum circuit Quantum many-body systems Statistical relationship System size Eigenvalues and eigenfunctions Logic circuits Quantum theory Hamiltonians Roncaglia, Augusto José Complexity of energy eigenstates as a mechanism for equilibration
topic_facet	Complexity theory Energy eigenstates Equilibration time Level density Quantum circuit Quantum many-body systems Statistical relationship System size Eigenvalues and eigenfunctions Logic circuits Quantum theory Hamiltonians
description	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. © 2013 American Physical Society.
author	Roncaglia, Augusto José
author_facet	Roncaglia, Augusto José
author_sort	Roncaglia, Augusto José
title	Complexity of energy eigenstates as a mechanism for equilibration
title_short	Complexity of energy eigenstates as a mechanism for equilibration
title_full	Complexity of energy eigenstates as a mechanism for equilibration
title_fullStr	Complexity of energy eigenstates as a mechanism for equilibration
title_full_unstemmed	Complexity of energy eigenstates as a mechanism for equilibration
title_sort	complexity of energy eigenstates as a mechanism for equilibration
publishDate	2013
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v87_n3_p_Masanes http://hdl.handle.net/20.500.12110/paper_15393755_v87_n3_p_Masanes
work_keys_str_mv	AT roncagliaaugustojose complexityofenergyeigenstatesasamechanismforequilibration
_version_	1768545992080097280

Complexity of energy eigenstates as a mechanism for equilibration

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