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This paper is concerned with transition paths within the framework of the overdamped Langevin dynamics model of chemical reactions. We aim to give an efficient description of typical transition paths in the small temperature regime. We…

Probability · Mathematics 2017-06-27 Yulong Lu , Andrew M. Stuart , Hendrik Weber

The Principle of Least Action is used with a simple Lagrangian density, involving second-order derivatives of the wave function, to obtain the Schroedinger equation. A Hamiltonian density obtained from this simple Lagrangian density shows…

Quantum Physics · Physics 2007-12-12 Donald H. Kobe

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.

Functional Analysis · Mathematics 2013-03-01 Anna Skripka

Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate the adjoint to that Hausdorff operator of the given function. We find the formulas for the rate of approximation in various metrics in…

Classical Analysis and ODEs · Mathematics 2019-07-31 Alberto Debernardi , Elijah Liflyand

For a large family of real-valued Radon measures m on R^d, including the Kato class, the operators -\Delta + C^2 \Delta^2 + m tend to the Schrodinger operator -\Delta +m in the norm resolvent sense as C tends to zero. If the measure is…

Mathematical Physics · Physics 2007-05-23 J. F. Brasche , K. Ozanova

Let $G$ be a real Lie group, $\Lambda<G$ a lattice and $H<G$ a connected semisimple subgroup without compact factors and with finite center. We define the notion of $H$-expanding measures $\mu$ on $H$ and, applying recent work of…

Dynamical Systems · Mathematics 2023-07-06 Roland Prohaska , Cagri Sert , Ronggang Shi

In this paper, we are concerned with the study of statistical equilibria for focusing nonlinear Schr\"odinger and Hartree equations on the d-dimensional torus when d=1,2,3. Due to the focusing nature of the nonlinearity in these PDEs, Gibbs…

Analysis of PDEs · Mathematics 2024-12-10 Zied Ammari , Andrew Rout , Vedran Sohinger

In this work we introduce and study fractional measure theoretic elliptic operators on the torus and a new stochastic process named W-Brownian motion. We establish some regularity and spectral results related to the operators cited above,…

Analysis of PDEs · Mathematics 2025-12-05 Kelvin J. R. Sousa

Transport in near-integrable, but partially chaotic, $1 1/2$ degree-of-freedom Hamiltonian systems is blocked by invariant tori and is reduced at \emph{almost}-invariant tori, both associated with the invariant tori of a neighboring…

Chaotic Dynamics · Physics 2012-04-03 R. L. Dewar , S. R. Hudson , A. M. Gibson

We study the quasi-periodic Schr\"odinger operator $$ -\psi"(x) + V(x) \psi(x) = E \psi(x), \qquad x \in \mathbb{R} $$ in the regime of "small" $V(x) = \sum_{m\in\mathbb{Z}^\nu}c(m)\exp (2\pi i m\omega x)$, $\omega = (\omega_1, \dots,…

Spectral Theory · Mathematics 2019-02-27 David Damanik , Michael Goldstein , Milivoje Lukic

A Stein operator for the runs is derived as a perturbation of an operator for discrete Gibbs measure. Due to this fact, using perturbation technique, the approximation results for runs arising from identical and non-identical Bernoulli…

Probability · Mathematics 2020-07-16 Amit N Kumar , Neelesh S Upadhye

We investigate U(1)-equivariant deformations of C. LeBrun's self-dual metric with torus action. We explicitly determine all U(1)-subgroups of the torus for which one can obtain U(1)-equivariant deformation that do not preserve semi-free…

Differential Geometry · Mathematics 2007-05-23 Nobuhiro Honda

We apply the Guillemin-Lerman-Sternberg theorem to reprove a formula of Heckman for the Duistermaat-Heckman measure associated to the coadjoint action of $T$, a maximal torus of a compact semisimple Lie group $G$, on a regular coadjoint…

Symplectic Geometry · Mathematics 2007-05-23 Ami Haviv

On va montrer que la densite d etat surfacique de de l operateur de Schrodinger presque periodique discret converge faiblement vers la Densite d etat surfacique continue .

Mathematical Physics · Physics 2007-11-13 souabni boutheina

An ensemble of quasi-periodic discrete Schr\"{o}dinger operators with an arbitrary number of basic frequencies is considered, in a lattice of arbitrary dimension, in which the hull function is a realisation of a stationary Gaussian process…

Mathematical Physics · Physics 2021-09-28 Victor Chulaevsky , Sasha Sodin

We prove many new cases of Zimmer's conjecture for actions by lattices in non-$\mathbb{R}$-split semisimple Lie groups $G$. By prior arguments, Zimmer's conjecture reduces to studying certain probability measures invariant under a minimal…

Dynamical Systems · Mathematics 2024-11-22 Jinpeng An , Aaron Brown , Zhiyuan Zhang

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

Numerical Analysis · Mathematics 2018-08-01 Qingping Zhou , Wenqing Liu , Jinglai Li , Youssef M. Marzouk

We define and prove existence of fractional $P(\phi)_1$-processes as random processes generated by fractional Schr\"odinger semigroups with Kato-decomposable potentials. Also, we show that the measure of such a process is a Gibbs measure…

Probability · Mathematics 2014-03-05 Kamil Kaleta , Jozsef Lorinczi

In this work, we discuss the problem of approximating a multivariate function via $\ell_1$ minimization method, using a random chosen sub-grid of the corresponding tensor grid of Gaussian points. The independent variables of the function…

Numerical Analysis · Mathematics 2016-07-14 Ling Guo , Akil Narayan , Tao Zhou , Yuhang Chen

In this paper we study Lagrangian tori in ${\mathbb C}P^2$. A two-dimensional periodic Schr\"odinger operator is associated with every Lagrangian torus in ${\mathbb C}P^2$. We introduce an energy functional for tori as an integral of the…

Differential Geometry · Mathematics 2017-01-26 Hui Ma , Andrey E. Mironov , Dafeng Zuo