Related papers: On the Spectral Form Factor for Random Matrices
The dynamic structure factor (DSF) is a mathematical function that contains information about inter-particle correlations and their time evolution. Mostly the classical molecular dynamics is used to calculate the DSF of the classical…
As an old and widely used tool, it is still possible to find new insights and applications from Fast Fourier Transform (FFT)-based analyses. The FFT is frequently used to generate the Power Spectral Density (PSD) function, by squaring the…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
We analyze the Double Fourier Sphere (DFS) method on the rotation group $\mathcal{SO}(3)$ in the frequency domain and demonstrate its central role in fast algorithms. Fast Fourier algorithms on $\mathcal{SO}(3)$ are commonly formulated as a…
We develop the uniform sparse Fast Fourier Transform (usFFT), an efficient, non-intrusive, adaptive algorithm for the solution of elliptic partial differential equations with random coefficients. The algorithm is an adaption of the sparse…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…
Motivated by applications in emergency response and experimental design, we consider smooth stochastic optimization problems over probability measures supported on compact subsets of the Euclidean space. With the influence function as the…
Discerning chaos in quantum systems is an important problem as the usual route of Lyapunov exponents in classical systems is not straightforward in quantum systems. A standard route is the comparison of statistics derived from model…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis.Our approach involves utilizing the integral periodic zeros set of Fourier transform to characterize…
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
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…
We present a generic scheme to construct corrected trapezoidal rules with spectral accuracy for integral operators with weakly singular kernels in arbitrary dimensions. We assume that the kernel factorization of the form,…
We extend Fourier analysis to curved spaces by defining a Generalized Fourier Transform (GFT) on any Riemannian manifold $\Sigma$ via spectral decomposition. Under minimal requirements that the transform is an isometric isomorphism and has…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in…
We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n ,\, n \geq 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory.…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…