Random matrix theory of the isospectral twirling

Oliviero, Salvatore Francesco Emanuele; Leone, Lorenzo; Caravelli, Francesco; Hamma, Alioscia

doi:10.21468/SciPostPhys.10.3.076

Random matrix theory of the isospectral twirling

Journal Article · Thu Mar 25 00:00:00 EDT 2021 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.10.3.076· OSTI ID:1772675

Oliviero, Salvatore Francesco Emanuele ^[1]; Leone, Lorenzo ^[1]; Caravelli, Francesco ^[2]; Hamma, Alioscia ^[1]

University of Massachusetts Boston
Los Alamos National Laboratory

We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref. [1]. The relevant ensembles of Hamiltonians are those defined by salient spectral probability distributions. The Gaussian Unitary Ensembles (GUE) describes a class of quantum chaotic Hamiltonians, while spectra corresponding to the Poisson and Gaussian Diagonal Ensemble (GDE) describe non chaotic, integrable dynamics. We compute the Isospectral twirling of several classes of important quantities in the analysis of quantum many-body systems: Frame potentials, Loschmidt Echos, OTOCs, Entanglement, Tripartite mutual information, coherence, distance to equilibrium states, work in quantum batteries and extension to CP-maps. Moreover, we perform averages in these ensembles by random matrix theory and show how these quantities clearly separate chaotic quantum dynamics from non chaotic ones.

View Journal Article

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001; AC52-06NA25396

OSTI ID:: 1772675

Alternate ID(s):: OSTI ID: 1835783

Report Number(s):: LA-UR--20-30225; 076

Journal Information:: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 3 Vol. 10; ISSN 2542-4653

Publisher:: Stichting SciPostCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (177)

Elements of Information Theory Cover, Thomas M.; Thomas, Joy A. https://doi.org/10.1002/047174882x	book	April 2005
Lyapunov exponents from quantum dynamics Haake, Fritz; Wiedemann, Harald; Życzkowski, Karol Annalen der Physik, Vol. 504, Issue 7 https://doi.org/10.1002/andp.19925040706	journal	January 1992
Representation Theory Fulton, William; Harris, Joe Graduate Texts in Mathematics https://doi.org/10.1007/978-1-4612-0979-9	book	January 2004
Embedded Random Matrix Ensembles in Quantum Physics Kota, V. K. B. Lecture Notes in Physics https://doi.org/10.1007/978-3-319-04567-2	book	January 2014
Chaos in quantum channels Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A. Journal of High Energy Physics, Vol. 2016, Issue 2 https://doi.org/10.1007/JHEP02(2016)004	journal	February 2016
Black holes and the butterfly effect Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)067	journal	March 2014
Localized shocks Roberts, Daniel A.; Stanford, Douglas; Susskind, Leonard Journal of High Energy Physics, Vol. 2015, Issue 3 https://doi.org/10.1007/JHEP03(2015)051	journal	March 2015
Towards the fast scrambling conjecture Lashkari, Nima; Stanford, Douglas; Hastings, Matthew Journal of High Energy Physics, Vol. 2013, Issue 4 https://doi.org/10.1007/JHEP04(2013)022	journal	April 2013
Chaos and complexity by design Roberts, Daniel A.; Yoshida, Beni Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)121	journal	April 2017
Stringy effects in scrambling Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2015, Issue 5 https://doi.org/10.1007/JHEP05(2015)132	journal	May 2015
On entanglement spreading in chaotic systems Mezei, Márk; Stanford, Douglas Journal of High Energy Physics, Vol. 2017, Issue 5 https://doi.org/10.1007/JHEP05(2017)065	journal	May 2017
Black holes and random matrices Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori Journal of High Energy Physics, Vol. 2017, Issue 5 https://doi.org/10.1007/JHEP05(2017)118	journal	May 2017
Entanglement, quantum randomness, and complexity beyond scrambling Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/JHEP07(2018)041	journal	July 2018
Onset of random matrix behavior in scrambling systems Gharibyan, Hrant; Hanada, Masanori; Shenker, Stephen H. Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/JHEP07(2018)124	journal	July 2018
Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one? Romero-Bermúdez, Aurelio; Schalm, Koenraad; Scopelliti, Vincenzo Journal of High Energy Physics, Vol. 2019, Issue 7 https://doi.org/10.1007/JHEP07(2019)107	journal	July 2019
A bound on chaos Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)106	journal	August 2016
Out-of-time-order correlators in quantum mechanics Hashimoto, Koji; Murata, Keiju; Yoshii, Ryosuke Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/JHEP10(2017)138	journal	October 2017
Firewalls vs. scrambling Yoshida, Beni Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/JHEP10(2019)132	journal	October 2019
Chaos, complexity, and random matrices Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu Journal of High Energy Physics, Vol. 2017, Issue 11 https://doi.org/10.1007/JHEP11(2017)048	journal	November 2017
Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator Hashimoto, Koji; Huh, Kyoung-Bum; Kim, Keun-Young Journal of High Energy Physics, Vol. 2020, Issue 11 https://doi.org/10.1007/JHEP11(2020)068	journal	November 2020
Multiple shocks Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)046	journal	December 2014
Conditional mutual information of bipartite unitaries and scrambling Ding, Dawei; Hayden, Patrick; Walter, Michael Journal of High Energy Physics, Vol. 2016, Issue 12 https://doi.org/10.1007/JHEP12(2016)145	journal	December 2016
Eigenvector statistics for the transitions from the orthogonal to the unitary ensemble Życzkowski, Karol; Lenz, Georg Zeitschrift für Physik B Condensed Matter, Vol. 82, Issue 2 https://doi.org/10.1007/bf01324340	journal	June 1991
Aspects of Generic Entanglement Hayden, Patrick; Leung, Debbie W.; Winter, Andreas Communications in Mathematical Physics, Vol. 265, Issue 1 https://doi.org/10.1007/s00220-006-1535-6	journal	March 2006
Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group Collins, Benoît; Śniady, Piotr Communications in Mathematical Physics, Vol. 264, Issue 3 https://doi.org/10.1007/s00220-006-1554-3	journal	March 2006
Random Quantum Circuits are Approximate 2-designs Harrow, Aram W.; Low, Richard A. Communications in Mathematical Physics, Vol. 291, Issue 1 https://doi.org/10.1007/s00220-009-0873-6	journal	July 2009
Local Random Quantum Circuits are Approximate Polynomial-Designs Brandão, Fernando G. S. L.; Harrow, Aram W.; Horodecki, Michał Communications in Mathematical Physics, Vol. 346, Issue 2 https://doi.org/10.1007/s00220-016-2706-8	journal	August 2016
Typicality of Thermal Equilibrium and Thermalization in Isolated Macroscopic Quantum Systems Tasaki, Hal Journal of Statistical Physics, Vol. 163, Issue 5 https://doi.org/10.1007/s10955-016-1511-2	journal	April 2016
Chaotic stucture of eigenfunctions in systems with maximal quantum chaos Izrailev, F. M. Physics Letters A, Vol. 125, Issue 5 https://doi.org/10.1016/0375-9601(87)90203-9	journal	November 1987
Random Matrices Mehta, Madan Lal https://doi.org/10.1016/c2009-0-22297-5	book	January 1990
Out-of-time-order operators and the butterfly effect Cotler, Jordan S.; Ding, Dawei; Penington, Geoffrey R. Annals of Physics, Vol. 396 https://doi.org/10.1016/j.aop.2018.07.020	journal	September 2018
Nonperturbative theory of power spectrum in complex systems Riser, Roman; Osipov, Vladimir Al.; Kanzieper, Eugene Annals of Physics, Vol. 413 https://doi.org/10.1016/j.aop.2019.168065	journal	February 2020
Power spectrum and form factor in random diagonal matrices and integrable billiards Riser, Roman; Kanzieper, Eugene Annals of Physics, Vol. 425 https://doi.org/10.1016/j.aop.2020.168393	journal	February 2021
Uncertainty relation on Wigner–Yanase–Dyson skew information Yanagi, Kenjiro Journal of Mathematical Analysis and Applications, Vol. 365, Issue 1 https://doi.org/10.1016/j.jmaa.2009.09.060	journal	May 2010
Quantum chaos and its kinetic stage of evolution Chotorlishvili, L.; Ugulava, A. Physica D: Nonlinear Phenomena, Vol. 239, Issue 3-4 https://doi.org/10.1016/j.physd.2009.08.017	journal	February 2010
Dynamics of Loschmidt echoes and fidelity decay Gorin, Thomas; Prosen, Tomaž; Seligman, Thomas H. Physics Reports, Vol. 435, Issue 2-5 https://doi.org/10.1016/j.physrep.2006.09.003	journal	November 2006
Lyapunov exponent in quantum mechanics. A phase-space approach Man’ko, V. I.; Vilela Mendes, R. Physica D: Nonlinear Phenomena, Vol. 145, Issue 3-4 https://doi.org/10.1016/s0167-2789(00)00117-2	journal	November 2000
Random-matrix theories in quantum physics: common concepts Guhr, Thomas; Müller–Groeling, Axel; Weidenmüller, Hans A. Physics Reports, Vol. 299, Issue 4-6 https://doi.org/10.1016/s0370-1573(97)00088-4	journal	June 1998
The Theory of Quantum Information Watrous, John https://doi.org/10.1017/9781316848142	book	May 2018
Chaos in Dynamical Systems Ott, Edward https://doi.org/10.1017/cbo9780511803260	book	January 2002
On the statistical distribution of the widths and spacings of nuclear resonance levels Wigner, Eugene P. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 47, Issue 4 https://doi.org/10.1017/s0305004100027237	journal	October 1951
Random matrix theory Edelman, Alan; Rao, N. Raj Acta Numerica, Vol. 14 https://doi.org/10.1017/s0962492904000236	journal	April 2005
Thermalization and its mechanism for generic isolated quantum systems Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim Nature, Vol. 452, Issue 7189 https://doi.org/10.1038/nature06838	journal	April 2008
Work extraction and thermodynamics for individual quantum systems Skrzypczyk, Paul; Short, Anthony J.; Popescu, Sandu Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5185	journal	June 2014
Quantum many-body systems out of equilibrium Eisert, J.; Friesdorf, M.; Gogolin, C. Nature Physics, Vol. 11, Issue 2 https://doi.org/10.1038/nphys3215	journal	February 2015
Ergodic dynamics and thermalization in an isolated quantum system Neill, C.; Roushan, P.; Fang, M. Nature Physics, Vol. 12, Issue 11 https://doi.org/10.1038/nphys3830	journal	July 2016
Entanglement and the foundations of statistical mechanics Popescu, Sandu; Short, Anthony J.; Winter, Andreas Nature Physics, Vol. 2, Issue 11 https://doi.org/10.1038/nphys444	journal	October 2006
Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model Lewis-Swan, R. J.; Safavi-Naini, A.; Bollinger, J. J. Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-09436-y	journal	April 2019
Unscrambling the physics of out-of-time-order correlators Swingle, Brian Nature Physics, Vol. 14, Issue 10 https://doi.org/10.1038/s41567-018-0295-5	journal	October 2018
Accessing scrambling using matrix product operators Xu, Shenglong; Swingle, Brian Nature Physics https://doi.org/10.1038/s41567-019-0712-4	journal	November 2019
Verified quantum information scrambling Landsman, K. A.; Figgatt, C.; Schuster, T. Nature, Vol. 567, Issue 7746 https://doi.org/10.1038/s41586-019-0952-6	journal	March 2019
Entropic uncertainty relations for quantum information scrambling Yunger Halpern, Nicole; Bartolotta, Anthony; Pollack, Jason Communications Physics, Vol. 2, Issue 1 https://doi.org/10.1038/s42005-019-0179-8	journal	August 2019
Statistical Theory of the Energy Levels of Complex Systems. I Dyson, Freeman J. Journal of Mathematical Physics, Vol. 3, Issue 1 https://doi.org/10.1063/1.1703773	journal	January 1962
Evenly distributed unitaries: On the structure of unitary designs Gross, D.; Audenaert, K.; Eisert, J. Journal of Mathematical Physics, Vol. 48, Issue 5 https://doi.org/10.1063/1.2716992	journal	May 2007
The Conceptual Foundations of the Statistical Approach in Mechanics Ehrenfest, Paul; Ehrenfest, Tatiana; Moravcsik, Michael J. Physics Today, Vol. 13, Issue 7 https://doi.org/10.1063/1.3057042	journal	July 1960
Quantum coherence generating power, maximally abelian subalgebras, and Grassmannian geometry Zanardi, Paolo; Campos Venuti, Lorenzo Journal of Mathematical Physics, Vol. 59, Issue 1 https://doi.org/10.1063/1.4997146	journal	January 2018
Asymptotic behavior of group integrals in the limit of infinite rank Weingarten, Don Journal of Mathematical Physics, Vol. 19, Issue 5 https://doi.org/10.1063/1.523807	journal	May 1978
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics D'Alessio, Luca; Kafri, Yariv; Polkovnikov, Anatoli Advances in Physics, Vol. 65, Issue 3 https://doi.org/10.1080/00018732.2016.1198134	journal	May 2016
A Better Bound on the Variance Bhatia, Rajendra; Davis, Chandler The American Mathematical Monthly, Vol. 107, Issue 4 https://doi.org/10.1080/00029890.2000.12005203	journal	April 2000
Universality of eigenvector statistics of kicked tops of different symmetries Kus, M.; Mostowski, J.; Haake, F. Journal of Physics A: Mathematical and General, Vol. 21, Issue 22 https://doi.org/10.1088/0305-4470/21/22/006	journal	November 1988
Indicators of quantum chaos based on eigenvector statistics Zyczkowski, K. Journal of Physics A: Mathematical and General, Vol. 23, Issue 20 https://doi.org/10.1088/0305-4470/23/20/005	journal	October 1990
Entangling power of the quantum baker s map Scott, A. J.; Caves, Carlton M. Journal of Physics A: Mathematical and General, Vol. 36, Issue 36 https://doi.org/10.1088/0305-4470/36/36/308	journal	August 2003
Black holes as mirrors: quantum information in random subsystems Hayden, Patrick; Preskill, John Journal of High Energy Physics, Vol. 2007, Issue 09 https://doi.org/10.1088/1126-6708/2007/09/120	journal	September 2007
Fast scramblers Sekino, Yasuhiro; Susskind, L. Journal of High Energy Physics, Vol. 2008, Issue 10 https://doi.org/10.1088/1126-6708/2008/10/065	journal	October 2008
Thermodynamic entropy of a many-body energy eigenstate Deutsch, J. M. New Journal of Physics, Vol. 12, Issue 7 https://doi.org/10.1088/1367-2630/12/7/075021	journal	July 2010
Equilibration of quantum systems and subsystems Short, Anthony J. New Journal of Physics, Vol. 13, Issue 5 https://doi.org/10.1088/1367-2630/13/5/053009	journal	May 2011
Generating a state t -design by diagonal quantum circuits Nakata, Yoshifumi; Koashi, Masato; Murao, Mio New Journal of Physics, Vol. 16, Issue 5 https://doi.org/10.1088/1367-2630/16/5/053043	journal	May 2014
The extraction of work from quantum coherence Korzekwa, Kamil; Lostaglio, Matteo; Oppenheim, Jonathan New Journal of Physics, Vol. 18, Issue 2 https://doi.org/10.1088/1367-2630/18/2/023045	journal	February 2016
Maximal coherence and the resource theory of purity Streltsov, Alexander; Kampermann, Hermann; Wölk, Sabine New Journal of Physics, Vol. 20, Issue 5 https://doi.org/10.1088/1367-2630/aac484	journal	May 2018
Relaxation, chaos, and thermalization in a three-mode model of a Bose–Einstein condensate Garcia-March, M. A.; Frank, S. van; Bonneau, M. New Journal of Physics, Vol. 20, Issue 11 https://doi.org/10.1088/1367-2630/aaed68	journal	November 2018
Out-of-time-order correlators in the one-dimensional XY model Bao, Jia-Hui; Zhang, Cheng-Yong Communications in Theoretical Physics, Vol. 72, Issue 8 https://doi.org/10.1088/1572-9494/ab8a28	journal	July 2020
Optimizing quantum process tomography with unitary 2 -designs Scott, A. J. Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue 5 https://doi.org/10.1088/1751-8113/41/5/055308	journal	January 2008
Subsystem dynamics under random Hamiltonian evolution No authors listed Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 12 https://doi.org/10.1088/1751-8113/45/12/125204	journal	March 2012
Convex geometry of quantum resource quantification Regula, Bartosz Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 4 https://doi.org/10.1088/1751-8121/aa9100	journal	December 2017
Quantum scrambling and the growth of mutual information Touil, Akram; Deffner, Sebastian Quantum Science and Technology, Vol. 5, Issue 3 https://doi.org/10.1088/2058-9565/ab8ebb	journal	May 2020
Topics in Random Matrix Theory Tao, Terence American Mathematical Society https://doi.org/10.1090/gsm/132	book	January 2012
Large deviation bounds for k -designs Low, Richard A. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 465, Issue 2111 https://doi.org/10.1098/rspa.2009.0232	journal	August 2009
Stability of quantum motion in chaotic and regular systems Peres, Asher Physical Review A, Vol. 30, Issue 4 https://doi.org/10.1103/PhysRevA.30.1610	journal	October 1984
Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model Werner, Reinhard F. Physical Review A, Vol. 40, Issue 8 https://doi.org/10.1103/PhysRevA.40.4277	journal	October 1989
Entangling power of quantum evolutions Zanardi, Paolo; Zalka, Christof; Faoro, Lara Physical Review A, Vol. 62, Issue 3 https://doi.org/10.1103/PhysRevA.62.030301	journal	August 2000
Entanglement of quantum evolutions Zanardi, Paolo Physical Review A, Vol. 63, Issue 4 https://doi.org/10.1103/PhysRevA.63.040304	journal	March 2001
Efficient algorithm for multiqudit twirling for ensemble quantum computation Tóth, Géza; García-Ripoll, Juan José Physical Review A, Vol. 75, Issue 4 https://doi.org/10.1103/PhysRevA.75.042311	journal	April 2007
Unitary equilibrations: Probability distribution of the Loschmidt echo Campos Venuti, Lorenzo; Zanardi, Paolo Physical Review A, Vol. 81, Issue 2 https://doi.org/10.1103/PhysRevA.81.022113	journal	February 2010
Universality and robustness of revivals in the transverse field X Y model Häppölä, Juho; Halász, Gábor B.; Hamma, Alioscia Physical Review A, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevA.85.032114	journal	March 2012
Conditions for coherence transformations under incoherent operations Du, Shuanping; Bai, Zhaofang; Guo, Yu Physical Review A, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevA.91.052120	journal	May 2015
Quantum speed limits, coherence, and asymmetry Marvian, Iman; Spekkens, Robert W.; Zanardi, Paolo Physical Review A, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevA.93.052331	journal	May 2016
Measuring the scrambling of quantum information Swingle, Brian; Bentsen, Gregory; Schleier-Smith, Monika Physical Review A, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevA.94.040302	journal	October 2016
How to quantify coherence: Distinguishing speakable and unspeakable notions Marvian, Iman; Spekkens, Robert W. Physical Review A, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevA.94.052324	journal	November 2016
Jarzynski-like equality for the out-of-time-ordered correlator Yunger Halpern, Nicole Physical Review A, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevA.95.012120	journal	January 2017
Quantum coherence via skew information and its polygamy Yu, Chang-shui Physical Review A, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevA.95.042337	journal	April 2017
Coherence-generating power of quantum unitary maps and beyond Zanardi, Paolo; Styliaris, Georgios; Campos Venuti, Lorenzo Physical Review A, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevA.95.052306	journal	May 2017
Measures of coherence-generating power for quantum unital operations Zanardi, Paolo; Styliaris, Georgios; Campos Venuti, Lorenzo Physical Review A, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevA.95.052307	journal	May 2017
Multiqubit Clifford groups are unitary 3-designs Zhu, Huangjun Physical Review A, Vol. 96, Issue 6 https://doi.org/10.1103/PhysRevA.96.062336	journal	December 2017
Untangling entanglement and chaos Kumari, Meenu; Ghose, Shohini Physical Review A, Vol. 99, Issue 4 https://doi.org/10.1103/PhysRevA.99.042311	journal	April 2019
Scrambling and complexity in phase space Zhuang, Quntao; Schuster, Thomas; Yoshida, Beni Physical Review A, Vol. 99, Issue 6 https://doi.org/10.1103/PhysRevA.99.062334	journal	June 2019
Many-body localized quantum batteries Rossini, Davide; Andolina, Gian Marcello; Polini, Marco Physical Review B, Vol. 100, Issue 11 https://doi.org/10.1103/PhysRevB.100.115142	journal	September 2019
Quantum coherence and the localization transition Styliaris, Georgios; Anand, Namit; Campos Venuti, Lorenzo Physical Review B, Vol. 100, Issue 22 https://doi.org/10.1103/PhysRevB.100.224204	journal	December 2019
Higher-order level spacings in random matrix theory based on Wigner's conjecture Rao, Wen-Jia Physical Review B, Vol. 102, Issue 5 https://doi.org/10.1103/PhysRevB.102.054202	journal	August 2020
Localization of interacting fermions at high temperature Oganesyan, Vadim; Huse, David A. Physical Review B, Vol. 75, Issue 15 https://doi.org/10.1103/PhysRevB.75.155111	journal	April 2007
Operator entanglement entropy of the time evolution operator in chaotic systems Zhou, Tianci; Luitz, David J. Physical Review B, Vol. 95, Issue 9 https://doi.org/10.1103/PhysRevB.95.094206	journal	March 2017
Information propagation in isolated quantum systems Luitz, David J.; Bar Lev, Yevgeny Physical Review B, Vol. 96, Issue 2 https://doi.org/10.1103/PhysRevB.96.020406	journal	July 2017
Entanglement complexity in quantum many-body dynamics, thermalization, and localization Yang, Zhi-Cheng; Hamma, Alioscia; Giampaolo, Salvatore M. Physical Review B, Vol. 96, Issue 2 https://doi.org/10.1103/PhysRevB.96.020408	journal	July 2017
Out-of-time-ordered correlators in a quantum Ising chain Lin, Cheng-Ju; Motrunich, Olexei I. Physical Review B, Vol. 97, Issue 14 https://doi.org/10.1103/PhysRevB.97.144304	journal	April 2018
Entanglement features of random Hamiltonian dynamics You, Yi-Zhuang; Gu, Yingfei Physical Review B, Vol. 98, Issue 1 https://doi.org/10.1103/PhysRevB.98.014309	journal	July 2018
Scrambling and entanglement spreading in long-range spin chains Pappalardi, Silvia; Russomanno, Angelo; Žunkovič, Bojan Physical Review B, Vol. 98, Issue 13 https://doi.org/10.1103/PhysRevB.98.134303	journal	October 2018
Universal scrambling in gapless quantum spin chains Nakamura, Shunsuke; Iyoda, Eiki; Deguchi, Tetsuo Physical Review B, Vol. 99, Issue 22 https://doi.org/10.1103/PhysRevB.99.224305	journal	June 2019
Scrambling the spectral form factor: Unitarity constraints and exact results del Campo, A.; Molina-Vilaplana, J.; Sonner, J. Physical Review D, Vol. 95, Issue 12 https://doi.org/10.1103/PhysRevD.95.126008	journal	June 2017
Spectral form factors and late time quantum chaos Liu, Junyu Physical Review D, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevD.98.086026	journal	October 2018
Gauging classical and quantum integrability through out-of-time-ordered correlators Fortes, Emiliano M.; García-Mata, Ignacio; Jalabert, Rodolfo A. Physical Review E, Vol. 100, Issue 4 https://doi.org/10.1103/PhysRevE.100.042201	journal	October 2019
Positive quantum Lyapunov exponents in experimental systems with a regular classical limit Pilatowsky-Cameo, Saúl; Chávez-Carlos, Jorge; Bastarrachea-Magnani, Miguel A. Physical Review E, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevE.101.010202	journal	January 2020
Chaos and quantum thermalization Srednicki, Mark Physical Review E, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevE.50.888	journal	August 1994
Misleading signatures of quantum chaos Gómez, J. M. G.; Molina, R. A.; Relaño, A. Physical Review E, Vol. 66, Issue 3 https://doi.org/10.1103/PhysRevE.66.036209	journal	September 2002
Entanglement as a signature of quantum chaos Wang, Xiaoguang; Ghose, Shohini; Sanders, Barry C. Physical Review E, Vol. 70, Issue 1 https://doi.org/10.1103/PhysRevE.70.016217	journal	July 2004
Ground state overlap and quantum phase transitions Zanardi, Paolo; Paunković, Nikola Physical Review E, Vol. 74, Issue 3 https://doi.org/10.1103/PhysRevE.74.031123	journal	September 2006
How complex is quantum motion? Benenti, Giuliano; Casati, Giulio Physical Review E, Vol. 79, Issue 2 https://doi.org/10.1103/PhysRevE.79.025201	journal	February 2009
Quantum mechanical evolution towards thermal equilibrium Linden, Noah; Popescu, Sandu; Short, Anthony J. Physical Review E, Vol. 79, Issue 6 https://doi.org/10.1103/PhysRevE.79.061103	journal	June 2009
Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization Santos, Lea F.; Rigol, Marcos Physical Review E, Vol. 81, Issue 3 https://doi.org/10.1103/PhysRevE.81.036206	journal	March 2010
Onset of chaos and relaxation in isolated systems of interacting spins: Energy shell approach Santos, L. F.; Borgonovi, F.; Izrailev, F. M. Physical Review E, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevE.85.036209	journal	March 2012
Convergence to equilibrium under a random Hamiltonian Brandão, Fernando G. S. L.; Ćwikliński, Piotr; Horodecki, Michał Physical Review E, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevE.86.031101	journal	September 2012
Complexity of energy eigenstates as a mechanism for equilibration Masanes, Lluís; Roncaglia, Augusto J.; Acín, Antonio Physical Review E, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevE.87.032137	journal	March 2013
Entanglement boost for extractable work from ensembles of quantum batteries Alicki, Robert; Fannes, Mark Physical Review E, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevE.87.042123	journal	April 2013
Performance bound for quantum absorption refrigerators Correa, Luis A.; Palao, José P.; Adesso, Gerardo Physical Review E, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevE.87.042131	journal	April 2013
Integrable matrix theory: Level statistics Scaramazza, Jasen A.; Shastry, B. Sriram; Yuzbashyan, Emil A. Physical Review E, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevE.94.032106	journal	September 2016
Timescales in the quench dynamics of many-body quantum systems: Participation ratio versus out-of-time ordered correlator Borgonovi, Fausto; Izrailev, Felix M.; Santos, Lea F. Physical Review E, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevE.99.052143	journal	May 2019
Foundation of Statistical Mechanics under Experimentally Realistic Conditions Reimann, Peter Physical Review Letters, Vol. 101, Issue 19 https://doi.org/10.1103/PhysRevLett.101.190403	journal	November 2008
Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles Atas, Y. Y.; Bogomolny, E.; Giraud, O. Physical Review Letters, Vol. 110, Issue 8 https://doi.org/10.1103/PhysRevLett.110.084101	journal	February 2013
Resource Theory of Quantum States Out of Thermal Equilibrium Brandão, Fernando G. S. L.; Horodecki, Michał; Oppenheim, Jonathan Physical Review Letters, Vol. 111, Issue 25 https://doi.org/10.1103/PhysRevLett.111.250404	journal	December 2013
Emergent Irreversibility and Entanglement Spectrum Statistics Chamon, Claudio; Hamma, Alioscia; Mucciolo, Eduardo R. Physical Review Letters, Vol. 112, Issue 24 https://doi.org/10.1103/PhysRevLett.112.240501	journal	June 2014
Quantifying Coherence Baumgratz, T.; Cramer, M.; Plenio, M. B. Physical Review Letters, Vol. 113, Issue 14 https://doi.org/10.1103/PhysRevLett.113.140401	journal	September 2014
Generalization of von Neumann’s Approach to Thermalization Reimann, Peter Physical Review Letters, Vol. 115, Issue 1 https://doi.org/10.1103/PhysRevLett.115.010403	journal	July 2015
Measuring Quantum Coherence with Entanglement Streltsov, Alexander; Singh, Uttam; Dhar, Himadri Shekhar Physical Review Letters, Vol. 115, Issue 2 https://doi.org/10.1103/PhysRevLett.115.020403	journal	July 2015
Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory Roberts, Daniel A.; Stanford, Douglas Physical Review Letters, Vol. 115, Issue 13 https://doi.org/10.1103/PhysRevLett.115.131603	journal	September 2015
Operational Resource Theory of Coherence Winter, Andreas; Yang, Dong Physical Review Letters, Vol. 116, Issue 12 https://doi.org/10.1103/PhysRevLett.116.120404	journal	March 2016
Relating the Resource Theories of Entanglement and Quantum Coherence Chitambar, Eric; Hsieh, Min-Hsiu Physical Review Letters, Vol. 117, Issue 2 https://doi.org/10.1103/PhysRevLett.117.020402	journal	July 2016
Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems Farrelly, Terry; Brandão, Fernando G. S. L.; Cramer, Marcus Physical Review Letters, Vol. 118, Issue 14 https://doi.org/10.1103/PhysRevLett.118.140601	journal	April 2017
Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians Vidmar, Lev; Rigol, Marcos Physical Review Letters, Vol. 119, Issue 22 https://doi.org/10.1103/PhysRevLett.119.220603	journal	November 2017
High-Power Collective Charging of a Solid-State Quantum Battery Ferraro, Dario; Campisi, Michele; Andolina, Gian Marcello Physical Review Letters, Vol. 120, Issue 11 https://doi.org/10.1103/PhysRevLett.120.117702	journal	March 2018
Generalized Entanglement Entropies of Quantum Designs Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Yechao Physical Review Letters, Vol. 120, Issue 13 https://doi.org/10.1103/PhysRevLett.120.130502	journal	March 2018
Chaos Signatures in the Short and Long Time Behavior of the Out-of-Time Ordered Correlator García-Mata, Ignacio; Saraceno, Marcos; Jalabert, Rodolfo A. Physical Review Letters, Vol. 121, Issue 21 https://doi.org/10.1103/PhysRevLett.121.210601	journal	November 2018
Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling González Alonso, José Raúl; Yunger Halpern, Nicole; Dressel, Justin Physical Review Letters, Vol. 122, Issue 4 https://doi.org/10.1103/PhysRevLett.122.040404	journal	February 2019
Extractable Work, the Role of Correlations, and Asymptotic Freedom in Quantum Batteries Andolina, Gian Marcello; Keck, Maximilian; Mari, Andrea Physical Review Letters, Vol. 122, Issue 4 https://doi.org/10.1103/PhysRevLett.122.047702	journal	February 2019
Quantifying the Incompatibility of Quantum Measurements Relative to a Basis Styliaris, Georgios; Zanardi, Paolo Physical Review Letters, Vol. 123, Issue 7 https://doi.org/10.1103/PhysRevLett.123.070401	journal	August 2019
Does Scrambling Equal Chaos? Xu, Tianrui; Scaffidi, Thomas; Cao, Xiangyu Physical Review Letters, Vol. 124, Issue 14 https://doi.org/10.1103/PhysRevLett.124.140602	journal	April 2020
Information Scrambling and Loschmidt Echo Yan, Bin; Cincio, Lukasz; Zurek, Wojciech H. Physical Review Letters, Vol. 124, Issue 16 https://doi.org/10.1103/PhysRevLett.124.160603	journal	April 2020
Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries García-Pintos, Luis Pedro; Hamma, Alioscia; del Campo, Adolfo Physical Review Letters, Vol. 125, Issue 4 https://doi.org/10.1103/PhysRevLett.125.040601	journal	July 2020
Quantum Advantage in the Charging Process of Sachdev-Ye-Kitaev Batteries Rossini, Davide; Andolina, Gian Marcello; Rosa, Dario Physical Review Letters, Vol. 125, Issue 23 https://doi.org/10.1103/PhysRevLett.125.236402	journal	December 2020
Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality Styliaris, Georgios; Anand, Namit; Zanardi, Paolo Physical Review Letters, Vol. 126, Issue 3 https://doi.org/10.1103/PhysRevLett.126.030601	journal	January 2021
Border between Regular and Chaotic Quantum Dynamics Weinstein, Yaakov S.; Lloyd, Seth; Tsallis, Constantino Physical Review Letters, Vol. 89, Issue 21 https://doi.org/10.1103/PhysRevLett.89.214101	journal	November 2002
Fidelity Decay as an Efficient Indicator of Quantum Chaos Emerson, Joseph; Weinstein, Yaakov S.; Lloyd, Seth Physical Review Letters, Vol. 89, Issue 28 https://doi.org/10.1103/PhysRevLett.89.284102	journal	December 2002
Typicality for Generalized Microcanonical Ensembles Reimann, Peter Physical Review Letters, Vol. 99, Issue 16 https://doi.org/10.1103/PhysRevLett.99.160404	journal	October 2007
Random quantum batteries Caravelli, Francesco; Coulter-De Wit, Ghislaine; García-Pintos, Luis Pedro Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023095	journal	April 2020
Bounds on the capacity and power of quantum batteries Julià-Farré, Sergi; Salamon, Tymoteusz; Riera, Arnau Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023113	journal	May 2020
Universal spectral form factor for many-body localization Prakash, Abhishodh; Pixley, J. H.; Kulkarni, Manas Physical Review Research, Vol. 3, Issue 1 https://doi.org/10.1103/PhysRevResearch.3.L012019	journal	February 2021
Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws von Keyserlingk, C. W.; Rakovszky, Tibor; Pollmann, Frank Physical Review X, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevX.8.021013	journal	April 2018
Operator Spreading in Random Unitary Circuits Nahum, Adam; Vijay, Sagar; Haah, Jeongwan Physical Review X, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevX.8.021014	journal	April 2018
Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws Khemani, Vedika; Vishwanath, Ashvin; Huse, David A. Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031057	journal	September 2018
Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation Rakovszky, Tibor; Pollmann, Frank; von Keyserlingk, C. W. Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031058	journal	September 2018
Disentangling Scrambling and Decoherence via Quantum Teleportation Yoshida, Beni; Yao, Norman Y. Physical Review X, Vol. 9, Issue 1 https://doi.org/10.1103/PhysRevX.9.011006	journal	January 2019
Locality, Quantum Fluctuations, and Scrambling Xu, Shenglong; Swingle, Brian Physical Review X, Vol. 9, Issue 3 https://doi.org/10.1103/PhysRevX.9.031048	journal	September 2019
Quantum entanglement Horodecki, Ryszard; Horodecki, Paweł; Horodecki, Michał Reviews of Modern Physics, Vol. 81, Issue 2 https://doi.org/10.1103/RevModPhys.81.865	journal	June 2009
Colloquium : Area laws for the entanglement entropy Eisert, J.; Cramer, M.; Plenio, M. B. Reviews of Modern Physics, Vol. 82, Issue 1 https://doi.org/10.1103/RevModPhys.82.277	journal	February 2010
Colloquium : Nonequilibrium dynamics of closed interacting quantum systems Polkovnikov, Anatoli; Sengupta, Krishnendu; Silva, Alessandro Reviews of Modern Physics, Vol. 83, Issue 3 https://doi.org/10.1103/RevModPhys.83.863	journal	August 2011
Colloquium : Quantum coherence as a resource Streltsov, Alexander; Adesso, Gerardo; Plenio, Martin B. Reviews of Modern Physics, Vol. 89, Issue 4 https://doi.org/10.1103/RevModPhys.89.041003	journal	October 2017
Quantum resource theories Chitambar, Eric; Gour, Gilad Reviews of Modern Physics, Vol. 91, Issue 2 https://doi.org/10.1103/RevModPhys.91.025001	journal	April 2019
Random-matrix theory and eigenmodes of dynamical systems Haake, Fritz; Życzkowski, Karol Physical Review A, Vol. 42, Issue 2 https://doi.org/10.1103/physreva.42.1013	journal	July 1990
Relaxation process in a regime of quantum chaos Casati, Giulio; Maspero, Giulio; Shepelyansky, Dima L. Physical Review E, Vol. 56, Issue 6 https://doi.org/10.1103/physreve.56.r6233	journal	December 1997
Average entropy of a subsystem Page, Don N. Physical Review Letters, Vol. 71, Issue 9 https://doi.org/10.1103/physrevlett.71.1291	journal	August 1993
Moments and cumulants of polynomial random variables on unitarygroups, the Itzykson-Zuber integral, and free probability Collins, Benoît International Mathematics Research Notices, Vol. 2003, Issue 17, p. 953 https://doi.org/10.1155/S107379280320917X	journal	January 2003
Some Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces Dragomir, Silvestru Sever Korean Journal of Mathematics, Vol. 24, Issue 2 https://doi.org/10.11568/kjm.2016.24.2.273	journal	June 2016
Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics Zhou, Shiyu; Yang, Zhicheng; Hamma, Alioscia SciPost Physics, Vol. 9, Issue 6 https://doi.org/10.21468/SciPostPhys.9.6.087	journal	January 2020
Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems Chenu, Aurélia; Molina-Vilaplana, Javier; del Campo, Adolfo Quantum, Vol. 3 https://doi.org/10.22331/q-2019-03-04-127	journal	March 2019
Characteristics Vectors of Bordered Matrices with Infinite Dimensions II Wigner, Eugene P. The Annals of Mathematics, Vol. 65, Issue 2 https://doi.org/10.2307/1969956	journal	March 1957
On the Distribution of the Roots of Certain Symmetric Matrices Wigner, Eugene P. The Annals of Mathematics, Vol. 67, Issue 2 https://doi.org/10.2307/1970008	journal	March 1958
Characteristic Vectors of Bordered Matrices With Infinite Dimensions Wigner, Eugene P. The Annals of Mathematics, Vol. 62, Issue 3 https://doi.org/10.2307/1970079	journal	November 1955
On the Eigenvalues of Random Matrices Diaconis, Persi; Shahshahani, Mehrdad Journal of Applied Probability, Vol. 31 https://doi.org/10.2307/3214948	journal	January 1994
Loschmidt echo Wisniacki, Arseni Scholarpedia, Vol. 7, Issue 8 https://doi.org/10.4249/scholarpedia.11687	journal	January 2012
Chaos and Randomness in Strongly-Interacting Quantum Systems Hunter-Jones, Nicholas R. California Institute of Technology https://doi.org/10.7907/BHZ5-HV76	text	January 2018

Similar Records

Chaos, complexity, and random matrices

Journal Article · Wed Nov 08 19:00:00 EST 2017 · Journal of High Energy Physics (Online) · OSTI ID:1501469

Isometric operators, isospectral Hamiltonians, and supersymmetric quantum mechanics

Journal Article · Mon Apr 14 23:00:00 EST 1986 · Phys. Rev. D; (United States) · OSTI ID:5979627

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Mathematics

Random matrix theory of the isospectral twirling

Citation Formats

References (177)

Similar Records

Related Subjects