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Masanes, L.; Roncaglia, A.J.; Acín, A. "Complexity of energy eigenstates as a mechanism for equilibration" (2013) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 87(3)
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Abstract:

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.

Registro:

Documento: Artículo
Título:Complexity of energy eigenstates as a mechanism for equilibration
Autor:Masanes, L.; Roncaglia, A.J.; Acín, A.
Filiación:ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
Departamento de Física, FCEyN, CONICET, Pabellón 1, 1428 Buenos Aires, Argentina
ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain
Palabras clave: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
Año:2013
Volumen:87
Número:3
DOI: http://dx.doi.org/10.1103/PhysRevE.87.032137
Título revista:Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Título revista abreviado:Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
ISSN:15393755
CODEN:PLEEE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v87_n3_p_Masanes

Referencias:

  • Callen, H.B., (1985) Thermodynamics and An Introduction to Thermostatistics, , John Wiley & Sons, New York
  • Arnold, V.I., Avez, A., (1968) Ergodic Problems of Classical Mechanics, , W. A. Benjamin, New York
  • Schrödinger, E., (1927) Ann. Phys. (Leipzig), 388, p. 956. , ANPYA2 0003-3804 10.1002/andp.19273881504
  • Von Neumann, J., (1929) Z. Phys. A, 57, p. 30. , ZEPYAA 0044-3328 10.1007/BF01339852
  • Gemmer, J., Michel, M., Mahler, G., (2004) Quantum Thermodynamics, , Springer, Berlin
  • Rigol, M., Dunjko, V., Olshanii, M., Thermalization and its mechanism for generic isolated quantum systems (2008) Nature, 452 (7189), pp. 854-858. , DOI 10.1038/nature06838, PII NATURE06838
  • Rigol, M., (2009) Phys. Rev. Lett., 103, p. 100403. , PRLTAO 0031-9007 10.1103/PhysRevLett.103.100403
  • Cassidy, A.C., Clark, C.W., Rigol, M., (2011) Phys. Rev. Lett., 106, p. 140405. , PRLTAO 0031-9007 10.1103/PhysRevLett.106.140405
  • Bañuls, M.C., Cirac, J.I., Hastings, M.B., (2011) Phys. Rev. Lett., 106, p. 050405. , PRLTAO 0031-9007 10.1103/PhysRevLett.106.050405
  • Linden, N., Popescu, S., Short, A.J., Winter, A., (2009) Phys. Rev. e, 79, p. 061103. , PLEEE8 1539-3755 10.1103/PhysRevE.79.061103
  • Cramer, M., Eisert, J., (2010) New J. Phys., 12, p. 055020. , NJOPFM 1367-2630 10.1088/1367-2630/12/5/055020
  • Gogolin, C., Mueller, M.P., Eisert, J., (2011) Phys. Rev. Lett., 106, p. 040401. , PRLTAO 0031-9007 10.1103/PhysRevLett.106.040401
  • Bloch, I., Dalibard, J., Zwerger, W., (2008) Rev. Mod. Phys., 80, p. 885. , RMPHAT 0034-6861 10.1103/RevModPhys.80.885
  • Kinoshita, T., Wenger, T., Weiss, D.S., (2006) Nature (London), 440, p. 900. , NATUAS 0028-0836 10.1038/nature04693
  • Hofferberth, S., Lesanovsky, I., Fischer, B., Schumm, T., Schmiedmayer, J., Non-equilibrium coherence dynamics in one-dimensional Bose gases (2007) Nature, 449 (7160), pp. 324-327. , DOI 10.1038/nature06149, PII NATURE06149
  • Goldstein, S., Lebowitz, J.L., Mastrodonato, C., Tumulka, R., Zanghi, N., (2010) Proc. R. Soc. London, Sect. A, 466, p. 3203. , 1364-5021 10.1098/rspa.2009.0635
  • Reimann, P., (2008) Phys. Rev. Lett., 101, p. 190403. , PRLTAO 0031-9007 10.1103/PhysRevLett.101.190403
  • Short, A.J., Farrelly, T.C., arXiv: 1110.5759; Cramer, M., Dawson, C.M., Eisert, J., Osborne, T.J., Exact relaxation in a class of nonequilibrium quantum lattice systems (2008) Physical Review Letters, 100 (3), p. 030602. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevLett.100.030602&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevLett.100.030602
  • Usha Devi, A.R., Rajagopal, A.K., (2009) Phys. Rev. e, 80, p. 011136. , PLEEE8 1539-3755 10.1103/PhysRevE.80.011136
  • Gong, Z.-X., Duan, L.-M., arXiv: 1109.4696; Nielsen, M.A., Chuang, I.L., (2000) Quantum Information and Quantum Computation, , Cambridge University Press, Cambridge
  • Brandão, F.G.S.L., Harrow, A.W., Horodecki, M., arXiv: 1208.0692; Haar, A., (1933) Ann. Math., 34, p. 147. , ANMAAH 0003-486X 10.2307/1968346
  • Metha, M.L., (1990) Random Matrices, , Academic Press, New York
  • Wigner, E., (1955) Ann. Math., 62, p. 548. , ANMAAH 0003-486X 10.2307/1970079
  • Rosenzweig, N., Porter, C.E., (1960) Phys. Rev., 120, p. 1698. , PHRVAO 0031-899X 10.1103/PhysRev.120.1698
  • Brown, W.G., Viola, L., (2010) Phys. Rev. Lett., 104, p. 250501. , PRLTAO 0031-9007 10.1103/PhysRevLett.104.250501
  • Kastner, M., (2011) Phys. Rev. Lett., 106, p. 130601. , PRLTAO 0031-9007 10.1103/PhysRevLett.106.130601
  • Caux, J.-S., Mossel, J., J. Stat. Mech. Theory Exp., 2011, p. 02023. , 1742-5468 10.1088/1742-5468/2011/02/P02023
  • Vinayak, Znidaric, M., (2012) J. Phys. A, 45, p. 125204. , 1751-8113 10.1088/1751-8113/45/12/125204
  • Brandão, F.G.S.L., Ćwikliński, P., Horodecki, M., Horodecki, P., Korbicz, J., Mozrzymas, M., (2012) Phys. Rev. e, 86, p. 031101. , 1539-3755 10.1103/PhysRevE.86.031101
  • Fulton, W., Harris, J., (2004) Representation Theory, , Springer, New York

Citas:

---------- APA ----------
Masanes, L., Roncaglia, A.J. & Acín, A. (2013) . Complexity of energy eigenstates as a mechanism for equilibration. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 87(3).
http://dx.doi.org/10.1103/PhysRevE.87.032137
---------- CHICAGO ----------
Masanes, L., Roncaglia, A.J., Acín, A. "Complexity of energy eigenstates as a mechanism for equilibration" . Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 87, no. 3 (2013).
http://dx.doi.org/10.1103/PhysRevE.87.032137
---------- MLA ----------
Masanes, L., Roncaglia, A.J., Acín, A. "Complexity of energy eigenstates as a mechanism for equilibration" . Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 87, no. 3, 2013.
http://dx.doi.org/10.1103/PhysRevE.87.032137
---------- VANCOUVER ----------
Masanes, L., Roncaglia, A.J., Acín, A. Complexity of energy eigenstates as a mechanism for equilibration. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2013;87(3).
http://dx.doi.org/10.1103/PhysRevE.87.032137