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Recent work highlighted the importance of higher-order correlations in quantum dynamics for a deeper understanding of quantum chaos and thermalization.
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“Lecture notes on "free probability theory"” (2025)
Roland Speicher · 1908
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“Quasiclassical method in the theory of superconductivity”
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“Planar diagrams”
Edouard Brézin, Claude Itzykson, Giorgio Parisi, and Jean-Bernard Zuber · 1978
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“Planar perturbation expansion”
Predrag Cvitanović · 1981
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“The planar sector of field theories”
Predrag Cvitanović, P G Lauwers, and P N Scharbach · 1982
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“On the multifractal nature of fully developed turbulence and chaotic systems”
Roberto Benzi, Giovanni Paladin, Giorgio Parisi, and Angelo Vulpiani · 1984
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“Intermittency in chaotic systems and rényi entropies”
Giovanni Paladin and Angelo Vulpiani · 1986
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“Classical and quantum chaos for a kicked top”
F. Haake, M. Kuś, and R. Scharf · 1987
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“Symmetry versus degree of level repulsion for kicked quantum systems”
M. Kuś, R. Scharf, and F. Haake · 1987
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“Anomalous scaling laws in multifractal objects”
Giovanni Paladin and Angelo Vulpiani · 1987
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“Generalized lyapunov exponents in high-dimensional chaotic dynamics and products of large random matrices”
Andrea Crisanti, Giovanni Paladin, and Angelo Vulpiani · 1988
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“Spherical codes and designs”
Philippe Delsarte, Jean-Marie Goethals, and Johan Jacob Seidel · 1991
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“Limit laws for random matrices and free products”
Dan Voiculescu · 1991
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“Quantum statistical mechanics in a closed system”
J. M. Deutsch · 1991
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“Free random variables”
Dan V Voiculescu, Ken J Dykema, and Alexandru Nica · 1992
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“Chaos and quantum thermalization”
Mark Srednicki · 1994
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“Free probability theory and non-crossing partitions”
Roland Speicher · 1997
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“The approach to thermal equilibrium in quantized chaotic systems”
Mark Srednicki · 1999
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“Ergodic properties of a generic nonintegrable quantum many-body system in the thermodynamic limit”
Tomaz Prosen · 1999
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“Fluctuations of the inverse participation ratio at the anderson transition”
F. Evers and A. D. Mirlin · 2000
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“Efficient simulation of random quantum states and operators” (2005)
Christoph Dankert · 2005
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“Exact and approximate unitary 2-designs and their application to fidelity estimation”
Christoph Dankert, Richard Cleve, Joseph Emerson, and Etera Livine · 2009
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“Quantum signatures of chaos in a kicked top”
S. Chaudhury, A. Smith, B. E. Anderson, S. Ghose, and P. S. Jessen · 2009
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“Quantum mechanical evolution towards thermal equilibrium”
Noah Linden, Sandu Popescu, Anthony J Short, and Andreas Winter · 2009
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“Random quantum channels i: Graphical calculus and the bell state phenomenon”
Benoît Collins and Ion Nechita · 2010
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“Isotropic entanglement” (2010)
Ramis Movassagh and Alan Edelman · 2010
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“Density of states of quantum spin systems from isotropic entanglement”
Ramis Movassagh and Alan Edelman · 2011
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“Error analysis of free probability approximations to the density of states of disordered systems”
Jiahao Chen, Eric Hontz, Jeremy Moix, Matthew Welborn, Troy Van Voorhis, Alberto Suárez, Ramis Movassagh, and Alan Edelman · 2012
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“Chaos in the black hole s-matrix” (2015)
Joseph Polchinski · 2015
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“A bound on chaos”
Juan Maldacena, Stephen H Shenker, and Douglas Stanford · 2016
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“Chaos in quantum channels”
Pavan Hosur, Xiao-Liang Qi, Daniel A Roberts, and Beni Yoshida · 2016
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“From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics”
Luca D’Alessio, Yariv Kafri, Anatoli Polkovnikov, and Marcos Rigol · 2016
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“Random matrix techniques in quantum information theory”
Benoît Collins and Ion Nechita · 2016
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“Free probability theory”
Roland Speicher · 2016
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“Chaos and complexity by design”
Daniel A Roberts and Beni Yoshida · 2017
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“Chaos, complexity, and random matrices”
Jordan Cotler, Nicholas Hunter-Jones, Junyu Liu, and Beni Yoshida · 2017
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“Eigenstate thermalization in the sachdev-ye- model”
Julian Sonner and Manuel Vielma · 2017
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“Free probability and random matrices”
James A Mingo and Roland Speicher · 2017
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“Black holes and random matrices”
Jordan S Cotler, Guy Gur-Ari, Masanori Hanada, Joseph Polchinski, Phil Saad, Stephen H Shenker, Douglas Stanford, Alexandre Streicher, and Masaki Tezuka · 2017
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“Subsystem eigenstate thermalization hypothesis”
Anatoly Dymarsky, Nima Lashkari, and Hong Liu · 2018
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“Bound on the exponential growth rate of out-of-time-ordered correlators”
Naoto Tsuji, Tomohiro Shitara, and Masahito Ueda · 2018
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“Scrambling and entanglement spreading in long-range spin chains”
Silvia Pappalardi, Angelo Russomanno, Bojan Žunkovič, Fernando Iemini, Alessandro Silva, and Rosario Fazio · 2018
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“Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos”
Akshay Seshadri, Vaibhav Madhok, and Arul Lakshminarayan · 2018
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“Chaos signatures in the short and long time behavior of the out-of-time ordered correlator”
Ignacio García-Mata, Marcos Saraceno, Rodolfo A. Jalabert, Augusto J. Roncaglia, and Diego A. Wisniacki · 2018
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“Renyi entropy of chaotic eigenstates”
Tsung-Cheng Lu and Tarun Grover · 2019
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“Negativity spectra in random tensor networks and holography”
Jonah Kudler-Flam, Vladimir Narovlansky, and Shinsei Ryu · 2022
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“Replica wormholes and the black hole interior”
Geoff Penington, Stephen H Shenker, Douglas Stanford, and Zhenbin Yang · 2022
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“Thermalisation for wigner matrices”
Giorgio Cipolloni, László Erdős, and Dominik Schröder · 2022
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“Universal behavior beyond multifractality of wave functions at measurement-induced phase transitions”
Piotr Sierant and Xhek Turkeshi · 2022
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“Emergent quantum state designs from individual many-body wave functions”
Jordan S Cotler, Daniel K Mark, Hsin-Yuan Huang, Felipe Hernandez, Joonhee Choi, Adam L Shaw, Manuel Endres, and Soonwon Choi · 2023
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“Preparing random states and benchmarking with many-body quantum chaos”
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“Structure of chaotic eigenstates and their entanglement entropy”
Chaitanya Murthy and Mark Srednicki · 2019
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“Eigenstate thermalization hypothesis and out of time order correlators”
Laura Foini and Jorge Kurchan · 2019
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“Eigenstate thermalization and rotational invariance in ergodic quantum systems”
Laura Foini and Jorge Kurchan · 2019
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“Eigenstate correlations, thermalization, and the butterfly effect”
Amos Chan, Andrea De Luca, and J. T. Chalker · 2019
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“Bounds on chaos from the eigenstate thermalization hypothesis”
Chaitanya Murthy and Mark Srednicki · 2019
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“Towards a full solution of the large n double-scaled syk model”
Micha Berkooz, Mikhail Isachenkov, Vladimir Narovlansky, and Genis Torrents · 2019
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“Multifractal scalings across the many-body localization transition”
Nicolas Macé, Fabien Alet, and Nicolas Laflorencie · 2019
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Joonhee Choi, Adam L. Shaw, Ivaylo S. Madjarov, Xin Xie, Ran Finkelstein, Jacob P. Covey, Jordan S. Cotler, Daniel K. Mark, Hsin-Yuan Huang, Anant Kale, Hannes Pichler, Fernando G. S. L. Brandão, Soonwon Choi, and Manuel Endres · 2023
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“Generalized deep thermalization for free fermions”
Maxime Lucas, Lorenzo Piroli, Jacopo De Nardis, and Andrea De Luca · 2023
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“Deep thermalization in constrained quantum systems”
Tanmay Bhore, Jean-Yves Desaules, and Zlatko Papić · 2023
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“Shadow tomography from emergent state designs in analog quantum simulators”
Max McGinley and Michele Fava · 2023
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“Complete hilbert-space ergodicity in quantum dynamics of generalized fibonacci drives”
Saúl Pilatowsky-Cameo, Ceren B. Dag, Wen Wei Ho, and Soonwon Choi · 2023
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“Local dynamics and the structure of chaotic eigenstates”
Zhengyan Darius Shi, Shreya Vardhan, and Hong Liu · 2023
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“Quantum bounds on the generalized lyapunov exponents”
Silvia Pappalardi and Jorge Kurchan · 2023
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“Quantum chaos without false positives”
Dmitrii A Trunin · 2023
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“Refined quantum lyapunov exponents from replica out-of-time-order correlators”
Dmitrii A Trunin · 2023
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“Full eigenstate thermalization via free cumulants in quantum lattice systems” (2023)
Silvia Pappalardi, Felix Fritzsch, and Tomaž Prosen · 2023
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“Coherent fluctuations in noisy mesoscopic systems, the open quantum SSEP, and free probability”
Ludwig Hruza and Denis Bernard · 2023
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“Bernoulli variables, classical exclusion processes and free probability”
Michel Bauer, Denis Bernard, Philippe Biane, and Ludwig Hruza · 2023
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“Exact entanglement in the driven quantum symmetric simple exclusion process”
Denis Bernard and Ludwig Hruza · 2023
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“Beyond islands: a free probabilistic approach”
Jinzhao Wang · 2023
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“Large n algebras and generalized entropy”
Venkatesa Chandrasekaran, Geoff Penington, and Edward Witten · 2023
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“Classical approach to equilibrium of out-of-time ordered correlators in mixed systems”
Tomás Notenson, Ignacio García-Mata, Augusto J Roncaglia, and Diego A Wisniacki · 2023
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“Operator dynamics in floquet many-body systems” (2023)
Takato Yoshimura, Samuel J Garratt, and J T Chalker · 2023
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“A maximum entropy principle in deep thermalization and in hilbert-space ergodicity” (2024)
Daniel K Mark, Federica Surace, Andreas Elben, Adam L Shaw, Joonhee Choi, Gil Refael, Manuel Endres, and Soonwon Choi · 2024
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Dominik Hahn, David J. Luitz, and J. T. Chalker · 2024
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Siddharth Jindal and Pavan Hosur · 2024
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Elisa Vallini and Silvia Pappalardi · 2026
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