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Related papers: Spectral form factor in a random matrix theory

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The spectral form factor is a dynamical probe for level statistics of quantum systems. The early-time behaviour is commonly interpreted as a characterization of two-point correlations at large separation. We argue that this interpretation…

Disordered Systems and Neural Networks · Physics 2025-10-07 Wouter Buijsman , Vadim Cheianov , Vladimir Gritsev

The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well…

Chaotic Dynamics · Physics 2019-01-11 Bruno Bertini , Pavel Kos , Tomaz Prosen

We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle number conservation ($U(1)$) symmetry. We analytically…

Statistical Mechanics · Physics 2021-01-04 Dibyendu Roy , Tomaž Prosen

The spectral form factor, k(t), is the Fourier transform of the two level correlation function C(x), which is the averaged probability for finding two energy levels spaced x mean level spacings apart. The average is over a piece of the…

chao-dyn · Physics 2009-10-28 R. E. Prange

The Spectral Form Factor (SFF) measures the fluctuations in the density of states of a Hamiltonian. We consider a generalization of the SFF called the Loschmidt Spectral Form Factor, $\textrm{tr}[e^{iH_1T}]\textrm{tr} [e^{-iH_2T}]$, for…

Statistical Mechanics · Physics 2022-11-09 Michael Winer , Brian Swingle

In quantum chaotic systems, the spectral form factor (SFF), defined as the Fourier transform of the two-level spectral correlation function, is known to follow random matrix theory (RMT), namely a 'ramp' followed by a 'plateau' in…

Quantum Gases · Physics 2023-11-06 Ceren B. Dag , Simeon I. Mistakidis , Amos Chan , H. R. Sadeghpour

We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on…

chao-dyn · Physics 2015-06-24 T. Dittrich , B. Mehlig , H. Schanz , U. Smilansky

We investigate the two-point correlations in the band spectra of spatially periodic systems that exhibit chaotic diffusion in the classical limit. By including level pairs pertaining to non-identical quasimomenta, we define form factors…

chao-dyn · Physics 2009-10-30 T. Dittrich , B. Mehlig , H. Schanz , U. Smilansky

The emergence of quantum chaos in a system of trapped interacting bosons with externally impressed rotation is studied through spectral form factor (SFF) and power spectrum using exact diagonalization. Two distinct interaction regimes are…

Quantum Gases · Physics 2026-03-17 Mohd Talib , M. A. H. Ahsan

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

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

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

We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental…

High Energy Physics - Theory · Physics 2023-12-27 Felix M. Haehl , Wyatt Reeves , Moshe Rozali

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

The spectral form factor of quantum chaotic systems has the familiar `ramp $+$ plateau' form. Techniques to determine its form in the semiclassical or the thermodynamic limit have been devised, in both cases based on the average over an…

Statistical Mechanics · Physics 2024-10-16 Guy Bunin , Laura Foini , Jorge Kurchan

Correlations between the energies of a system's spectrum are one of the defining features of quantum chaos. They can be probed using the Spectral Form Factor (SFF). We investigate how each spectral distance contributes in building this…

Quantum Physics · Physics 2025-05-01 Pablo Martinez-Azcona , Ruth Shir , Aurélia Chenu

We study the behavior of two-time correlation functions at late times for finite system sizes considering observables whose (one-point) average value does not depend on energy. In the long time limit, we show that such correlation functions…

Statistical Mechanics · Physics 2025-08-20 Oscar Bouverot-Dupuis , Silvia Pappalardi , Jorge Kurchan , Anatoli Polkovnikov , Laura Foini

We study spectral form factor in periodically-kicked bosonic chains. We consider a family of models where a Hamiltonian with the terms diagonal in the Fock space basis, including random chemical potentials and pair-wise interactions, is…

Statistical Mechanics · Physics 2022-08-30 Dibyendu Roy , Divij Mishra , Tomaž Prosen

We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown…

Chaotic Dynamics · Physics 2010-03-09 Martin Sieber

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