Related papers: Decomposing the Spectral Form Factor
Quantum chaos cannot develop faster than $\lambda \leq 2 \pi/(\hbar \beta)$ for systems in thermal equilibrium [Maldacena, Shenker & Stanford, JHEP (2016)]. This `MSS bound' on the Lyapunov exponent $\lambda$ is set by the width of the…
We consider systems of fermions evolved by non-interacting unitary circuits with correlated on-site potentials. When these potentials are drawn from the eigenvalue distribution of a circular random matrix ensemble, the single-particle…
Recent advances in AdS/CFT holography have suggested that the near-horizon dynamics of black holes can be described by random matrix systems. We study how the energy spectrum of a system with a generic random Hamiltonian matrix affects its…
Spectral statistics such as the level spacing statistics and spectral form factor (SFF) are widely expected to accurately identify ``ergodicity'', including the presence of underlying macroscopic symmetries, in generic quantum systems…
The dynamical signatures of quantum chaos in an isolated system are captured by the spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the ramp being governed by the correlations in the level…
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…
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…
Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle.…
We investigate the appearance of quantum chaos in a single many-body wave function by analyzing the statistical properties of the eigenvalues of its reduced density matrix $\rho_A$ of a spatial subsystem A. We find that the spectrum of…
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…
In this article, using the principles of Random Matrix Theory (RMT), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two-point Out of Time Order Correlation function (OTOC)…
The spectral form factor is a powerful probe of quantum chaos that diagnoses the statistics of energy levels, but is blind to other features of a theory such as matrix elements of operators or OPE coefficients in conformal field theories.…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…
This paper investigates the effects of noise on the diagnostics of quantum chaos, focusing on three primary tools: the spectral form factor (SFF), Krylov complexity, and out-of-time correlators (OTOCs). Utilizing a closed quantum system…
A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well…
One of the central problems in many-body physics, both classical and quantum, is the relations between different notions of chaos. Ergodicity, mixing, operator growth, the eigenstate thermalization hypothesis, and spectral chaos are defined…
The Spectral Form Factor (SFF) is defined as the modulus squared of the partition function in complex temperature for hermitian matrices and a suitable generalisation has been given in the non hermitian case. In this work we compute the…
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…
The notion of scale-invariant dynamics is well established at late times in quantum chaotic systems, as illustrated by the emergence of a ramp in the spectral form factor (SFF). Building on the results of the preceding Letter [Phys. Rev.…
We discuss a number of basic physical mechanisms relevant to the formation of the proximity effect in superconductor/normal metal (SN) systems. Specifically, we review why the proximity effect sharply discriminates between systems with…