相关论文: What is the Simplest Linear Ramp?

We compute the spectral form factor of the modular Hamiltonian $K=-\ln\rho_A$ associated to the reduced density matrix of a Haar random state. A ramp is demonstrated and we find an analytic expression for its slope. Our method involves an…

The spectral form factor is believed to exhibit a special type of behavior called ``dip-ramp-plateau'' in chaotic quantum systems that originates from random matrix theory. This suggests that the shape of the spectral form factor could…

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…

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…

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…

We propose a novel indicator for chaotic quantum scattering processes, the scattering form factor (ScFF). It is based on mapping the locations of peaks in the scattering amplitude to random matrix eigenvalues, and computing the analog of…

Consider a hierarchical log-linear model, given by a simplicial complex, $\Gamma$, and integer matrix $A_\Gamma$. We give a new characterization of the rank of $A_\Gamma$ given by a logarithmic transformation on the exponential Hilbert…

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…

We present a way to study the conformal structure of random planar maps. The main idea is to explore the map along an SLE (Schramm--Loewner evolution) process of parameter $ \kappa = 6$ and to combine the locality property of the SLE_{6}…

Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and…

We study of the formation of pattern-forming fronts in the presence of a rigidly-propagating parameter ramp which is slowly-varying in space. In the context of the prototypical supercritical complex Ginzburg-Landau equation, we show that…

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…

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…

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…

Let $M_n$ be a class of symmetric sparse random matrices, with independent entries $M_{ij} = \delta_{ij} \xi_{ij}$ for $i \leq j$. $\delta_{ij}$ are i.i.d. Bernoulli random variables taking the value $1$ with probability $p \geq…

A variant for the Hilbert and Polya spectral interpretation of the Riemann zeta function is proposed. Instead of looking for a self-adjoint linear operator H, whose spectrum coincides with the Riemann zeta zeros, we look for the complex…

We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent…

Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…

We consider scattering theory of the Laplace Beltrami operator on differential forms on a Riemannian manifold that is Euclidean at infinity. The manifold may have several boundary components caused by obstacles at which relative boundary…

Gram's Law describes a pattern that frequently occurs in the distribution of the non-trivial zeros of the Riemann zeta function along the critical line. Whenever Gram's Law holds true, it reduces the difficulty of computing the…