Related papers: Krylov state complexity for BMN matrix model
We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state…
We study the spectral properties of two classes of random matrix models: non-Gaussian RMT with quartic and sextic potentials, and RMT with Gaussian noise. We compute and analyze the quantum Krylov complexity and the spectral form factor for…
The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control…
It is well-known that the convergence of Krylov subspace methods to solve linear system depends on the spectrum of the coefficient matrix, moreover, it is widely accepted that for both symmetric and unsymmetric systems Krylov subspace…
We investigate the structure of magnetic field amplified by turbulent velocity fluctuations, in the framework of the kinematic Kazantsev-Kraichnan model. We consider Kolmogorov distribution of velocity fluctuations, and assume that both…
Markov Switching models have had increasing success in time series analysis due to their ability to capture the existence of unobserved discrete states in the dynamics of the variables under study. This result is generally obtained thanks…
Polynomial Krylov subspace methods are among the most widely used methods for approximating $f(A)b$, the action of a matrix function on a vector, in particular when $A$ is large and sparse. When $A$ is Hermitian positive definite, the…
Non-equilibrium Markov State Modeling (MSM) has recently been proposed [Phys. Rev. E 94, 053001 (2016)] as a possible route to construct a physical theory of sliding friction from a long steady state atomistic simulation: the approach…
We consider a matrix model depending on a parameter $\lambda$ which permits the fuzzy sphere as a classical background.By expanding the bosonic matrices around this background ones recovers a U(1) (U(n)) noncommutative gauge theory on the…
Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a…
We provide convergence rates for Krylov subspace solutions to the trust-region and cubic-regularized (nonconvex) quadratic problems. Such solutions may be efficiently computed by the Lanczos method and have long been used in practice. We…
We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to…
On the basis of pure gauge sector of Blaizot-Iancu equation, we derive kinetic equation of Boltzmann type, taking into account 2n+2-colorless plasmon decay processes, n=1,2,.... Using so-called Tsytovich correspondence principle, a direct…
We study quenched dynamics of fully-connected spin models. The system is prepared in a ground state of the initial Hamiltonian and the Hamiltonian is suddenly changed to a different form. We apply the Krylov subspace method to map the…
Reliable adaptive beamforming is critical for large microphone arrays operating in highly dynamic acoustic environments. In scenarios characterized by fast-moving talkers and interferers, the available sample support for estimating the…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
In this work, we explore in detail, the time evolution of Krylov complexity. We demonstrate, through analytical computations, that in finite many-body systems, while ramp and plateau are two generic features of Krylov complexity, the manner…
Krylov complexity has recently been proposed as a quantum probe of chaos. The Krylov exponent characterising the exponential growth of Krylov complexity is conjectured to upper-bound the Lyapunov exponent. We compute the Krylov and the…
This work examines the deformed fuzzy sphere, as an example of a fuzzy space that can be described through a spectral triple, using computer visualisations. We first explore this geometry using an analytic expression for the eigenvalues to…
In an unnormalized Krylov subspace framework for solving symmetric systems of linear equations, the orthogonal vectors that are generated by a Lanczos process are not necessarily on the form of gradients. Associating each orthogonal vector…