24 papers · ranked by Valyu relevance
Rodolphe Garbit, Julien-Bilal Zinoune
This paper presents a family of Fourier eigenfunctions indexed by the space dimension d. These eigenfunctions are radial and built upon some generalized exponential integral function. For d = 1, 2, 3, they are integrable or square integrable and give new explicit examples of Fourier eigenfunctions in the usual or…
Megan Morrison, J. Nathan Kutz
Nonlinear ordinary differential equations can rarely be solved analytically. Koopman operator theory provides a way to solve nonlinear systems by mapping nonlinear dynamics to a linear space using eigenfunctions. Unfortunately, finding such eigenfunctions is difficult. We introduce a method for constructing…
Sigmundur Gudmundsson, Adam Lindström
In this work we find a unifying scheme for the known explicit complex-valued eigenfunctions on the classical compact Riemannian symmetric spaces. For this we employ the well-known Cartan embedding for those spaces. This also leads to the construction of new eigenfunctions on the quaternionic Grassmannians.
B. Zhang, Tuhin Sahai, Youssef Marzouk
We discuss approaches to computing eigenfunctions of the Ornstein–Uhlenbeck (OU) operator in more than two dimensions. While the spectrum of the OU operator and theoretical properties of its eigenfunctions have been well characterized in previous research, the practical computation of general eigenfunctions has not…
Tuba Gulsen, Emrah Yilmaz, Sertac Goktas
We study the conformable fractional (CF) Dirac system with separated boundary conditions on an arbitrary time scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…
Dennis M. Sullivan, Sean Mossman, Mark G. Kuzyk, Timothy Atherton
A method is presented to calculate the eigenenergies and eigenfunctions of quantum wires. This is a true three-dimensional method based on a direct implementation of the time-dependent Schrödinger equation. It makes no approximations to the Schrödinger equation other than the finite-difference approximation of the…
Catherine E. Davey, David B. Grayden, Anthony N. Burkitt
We establish a simple mechanism by which radially oriented simple cells can emerge in the primary visual cortex. In 1986, R. Linsker. proposed a means by which radially symmetric, spatial opponent cells can evolve, driven entirely by noise, from structure in the initial synaptic connectivity distribution. We provide an…
Pär Kurlberg, Alina Ostafe, Zeev Rudnick, Igor E. Shparlinski
We study eigenfunction localization for higher dimensional cat maps, a popular model of quantum chaos. These maps are given by linear symplectic maps in $\operatorname{Sp}2g,{{\mathbb{Z}}}$, which we take to be ergodic. Under some natural assumptions, we show that there is a density one sequence of integers N so that…
G. Abramovici
We revisit the resolution of the one-dimensional Schrödinger hamiltonian with a Coulomb λ/|x| potential. We examine among its self-adjoint extensions those which are compatible with physical conservation laws. In the one-dimensional semi-infinite case, we show that they are classified on a U(1) circle in the attractive…
Ryo Oizumi, Hisashi Inaba, The Anh Han
Various definitions of fitness are essentially based on the number of descendants of an allele or a phenotype after a sufficiently long time. However, these different definitions do not explicate the continuous evolution of life histories. Herein, we focus on the eigenfunction of an age-structured population model as…
Stefan Klus, Feliks Nüske, Boumediene Hamzi
Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential…
Sucheta Ghosh, Shankar Prasad Bhattacharyya
The quantum states of hydrogen atom in one dimension can be obtained by a careful application of the well-known Frobenius method. The exercise is highly educative and brings to focus the subtle aspects of quantum mechanics. The allowed states turn out to be only of odd parity and non-degenerate, having energy given by…
Matthew S. Schmitt, Maciej Koch-Janusz, Michel Fruchart, Daniel S. Seara + 2 more
Model reduction is the construction of simple yet predictive descriptions of the dynamics of many-body systems in terms of a few relevant variables. A prerequisite to model reduction is the identification of these relevant variables, a task for which no general method exists. Here, we develop a systematic approach…
Casper, W. Riley
The eigenvectors of the (N +1)×(N +1) symmetric Pascal matrix T N are analogs of prolate spheroidal wave functions in the discrete setting. The generating functions of the eigenvectors of T N are prolate spheroidal functions in the sense that they are simultaneously eigenfunctions of a third-order differential operator…
Authors not listed
This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we…
Ricardo J. López Candelaria, Yu Qian, Fang Chen, Mansun Law + 2 more
Identifying temporally differentially expressed genes (TDEGs) along pseudotime trajectories from single cell RNA sequencing (scRNA-seq) data helps characterize the cellular states that underlie the dynamic process of cellular development. However, existing tests based on generalized additive models (GAMs) suffer from…
Keisuke Fujii, Naoya Takeishi, Benio Kibushi, Motoki Kouzaki + 1 more
Living organisms dynamically and flexibly operate a great number of components. As one of such redundant control mechanisms, low-dimensional coordinative structures among multiple components have been investigated. However, structures extracted from the conventional statistical dimensionality reduction methods do not…
Bingjie Wu, James Holehouse, Ramon Grima, Chen Jia
In this study, we obtain an exact time-dependent solution of the chemical master equation (CME) of an extension of the two-state telegraph model describing bursty or non-bursty protein expression in the presence of positive or negative autoregulation. Using the method of spectral decomposition, we show that the…
Alex Kasman
> Abstract. A wave function of the N-component KP Hierarchy with continuous flows determined by an invertible matrix H is constructed from the choice of an MN-dimensional space of finitely-supported vector distributions. This wave function is shown to be an eigenfunction for a ring of matrix dif ferential operators in…
Authors not listed
Molecular polaritons are hybrid states formed by the quantum mechanical interaction between light and matter. Recent experiments have shown the ability to drastically modify chemical reactions in both the ground and excited states through the hybridization of the electronic and photonic degrees of freedom. Ab initio…
Sonja Currie, Thomas T. Roth, Bruce A. Watson
Canonical systems in R 2 with absolutely continuous real symmetric π-periodic potentials matrices are considered. A through analysis of the discriminant is given along with the indexing and interlacing of the eigenvalues of the periodic, anti-periodic and Dirichlettype boundary value problems on [0, π]. The periodic…
Pavel Pokhilko, Anna I. Krylov
Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch’s formalism to…
Priya Priya, Mainak Sadhukhan
The quest for an approximate yet accurate kinetic energy density functional is central to the development of orbital-free density functional theory. While a recipe for closed-shell systems has been proposed earlier, we have shown that it cannot be naively extended to open-shell atoms. In this present work, we…
Tomislav Piteša, Severin Polonius, Leticia González, Sebastian Mai
We present the excitonic configuration interaction (ECI) method — a fragment-based analogue of the CI method for electronic-structure calculations of the multichromophoric systems. It can also be viewed as a generalization of the exciton approach which (i) allows embedding via point charges with arbitrary values in the…