相关论文: The Dissipative Spectral Form Factor for I.I.D. Ma…

The Distributed Adaptive Signal Fusion (DASF) framework is a meta-algorithm for computing data-driven spatial filters in a distributed sensing platform with limited bandwidth and computational resources, such as a wireless sensor network.…

In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…

This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…

We compute the spectral form factor of two integrable quantum-critical many body systems in one spatial dimension. The spectral form factor of the quantum Ising chain is periodic in time in the scaling limit described by a conformal field…

Sampling from unnormalised discrete distributions is a fundamental problem across various domains. While Markov chain Monte Carlo offers a principled approach, it often suffers from slow mixing and poor convergence. In this paper, we…

This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…

The Ginibre ensemble of nonhermitean random Hamiltonian matrices $K$ is considered. Each quantum system described by $K$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. The…

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…

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…

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…

The dynamical structure factor (DSF) represents a measure of dynamical density-density correlations in a quantum many-body system. Due to the complexity of many-body correlations and quantum fluctuations in a system of an infinitely large…

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…

In Data Assimilation, observations are fused with simulations to obtain an accurate estimate of the state and parameters for a given physical system. Combining data with a model, however, while accurately estimating uncertainty, is…

The response of dissipative systems to multi-chromatic fields exhibits generic properties which follow from the discrete time-translation symmetry of each driving component. We derive these properties and illustrate them with paradigmatic…

For any finite group $G$, we give an arithmetic algorithm to compute generalized Discrete Fourier Transforms (DFTs) with respect to $G$, using $O(|G|^{\omega/2 + \epsilon})$ operations, for any $\epsilon > 0$. Here, $\omega$ is the exponent…

This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…

Quantum Fisher Information (QFI) is a fundamental quantity in quantum parameter estimation theory, characterizing the ultimate precision bound of parameter estimation. In this work, we investigate QFI for quantum states in non-Hermitian…

This paper proposes a novel approach to the statistical characterization of non-central complex Gaussian quadratic forms (CGQFs). Its key strategy is the generation of an auxiliary random variable (RV) that converges in distribution to the…

We introduce a concept of a fractional-derivatives series and prove that any linear partial differential equation in two independent variables has a fractional-derivatives series solution with coefficients from a differentially closed field…

We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle…