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Related papers: Decomposing the Spectral Form Factor

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We numerically study the spectral statistics of open quantum many-body systems (OQMBS) as signatures of quantum chaos (or the lack thereof), using the dissipative spectral form factor (DSFF), a generalization of the spectral form factor to…

Statistical Mechanics · Physics 2024-05-06 Jiachen Li , Stephen Yan , Tomaž Prosen , Amos Chan

In the theory of disordered systems the spectral form factor $S(\tau)$, the Fourier transform of the two-level correlation function with respect to the difference of energies, is linear for $\tau<\tau_c$ and constant for $\tau>\tau_c$. Near…

Condensed Matter · Physics 2009-10-28 E. Brézin , S. Hikami

Signatures of dynamical quantum phase transitions and chaos can be found in the time evolution of generalized partition functions such as spectral form factors (SFF) and Loschmidt echoes. While a lot of work has focused on the nature of…

Strongly Correlated Electrons · Physics 2024-04-12 Anurag Sarkar , Subrata Pachhal , Adhip Agarwala , Diptarka Das

The spectral form factor (SFF) is an important diagnostic of energy level repulsion in random matrix theory (RMT) and quantum chaos. The short-time behavior of the SFF as it approaches the RMT result acts as a diagnostic of the ergodicity…

Chaotic Dynamics · Physics 2023-08-01 Michael Winer , Brian Swingle

In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have…

Mathematical Physics · Physics 2023-07-26 Giorgio Cipolloni , László Erdős , Dominik Schröder

It is well known that the spectral form factor (SFF) of a possibly degenerate many-body Hamiltonian can be identified with a planar random walk taking steps of unequal length. In this paper we push this identification further and propose to…

Quantum Physics · Physics 2026-04-22 Lorenzo Campos Venuti , Jovan Odavić , Alioscia Hamma

While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be…

Quantum Physics · Physics 2025-04-23 Felix Fritzsch , Maximilian F. I. Kieler , Arnd Bäcker

It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF)…

Statistical Mechanics · Physics 2022-04-21 Yunxiang Liao , Victor Galitski

The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…

Quantum Physics · Physics 2026-01-06 Alex Altland , Francisco Divi , Tobias Micklitz , Silvia Pappalardi , Maedeh Rezaei

We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the…

Disordered Systems and Neural Networks · Physics 2023-12-29 Mahaveer Prasad , Abhishodh Prakash , J. H. Pixley , Manas Kulkarni

We show the emergence of random matrix theory (RMT) spectral correlations in the chaotic phase of generic periodically kicked interacting quantum many-body systems by analytically calculating spectral form factor (SFF), $K(t)$, up to two…

Statistical Mechanics · Physics 2025-02-07 Vijay Kumar , Tomaž Prosen , Dibyendu Roy

The spectral form factor (SFF) is a powerful diagnostic of random matrix behavior in quantum many-body systems. We introduce a family of random circuit ensembles whose SFFs can be computed \textit{exactly}. These ensembles describe the…

Statistical Mechanics · Physics 2025-04-24 Tatsuhiko N. Ikeda , Lev Vidmar , Michael O. Flynn

The Sachdev-Ye-Kitaev (SYK) model is a cornerstone in the study of quantum chaos and holographic quantum matter. Real-world implementations, however, deviate from the idealized all-to-all connectivity, raising questions about the robustness…

Statistical Mechanics · Physics 2024-12-20 Andrea Legramandi , Soumik Bandyopadhyay , Philipp Hauke

We discuss conditions under which a deterministic sequence of real numbers, interpreted as the set of eigenvalues of a Hamiltonian, can exhibit features usually associated to random matrix spectra. A key diagnostic is the spectral form…

High Energy Physics - Theory · Physics 2024-01-30 Suman Das , Sumit K. Garg , Chethan Krishnan , Arnab Kundu

In this work, we study the spectral form factor of random matrix models which exhibit a large number of degenerate ground states accompanied by a macroscopic gap in the spectrum. The central aim of this work is to understand how the…

High Energy Physics - Theory · Physics 2026-04-06 Krishan Saraswat

We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding…

High Energy Physics - Theory · Physics 2021-01-14 Jordan Cotler , Nicholas Hunter-Jones

We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the $N>2$…

High Energy Physics - Theory · Physics 2019-06-26 Pak Hang Chris Lau , Chen-Te Ma , Jeff Murugan , Masaki Tezuka

Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells…

chao-dyn · Physics 2016-08-31 Thomas Dittrich , Gert Koboldt , Bernhard Mehlig , Holger Schanz

We consider a non-interacting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model) - a generic model of single-particle quantum chaos. We study the corresponding…

Statistical Mechanics · Physics 2020-12-22 Yunxiang Liao , Amit Vikram , Victor Galitski

We study the onset of RMT dynamics in the mass-deformed SYK model (i.e. an SYK model deformed by a quadratic random interaction) in terms of the strength of the quadratic deformation. We use as chaos probes both the connected unfolded…

High Energy Physics - Theory · Physics 2018-09-26 Tomoki Nosaka , Dario Rosa , Junggi Yoon