Related papers: Exact potentials in multivariate Langevin equation…
Previously developed ``stochastic representation of deterministic interactions`` enables exact treatment of an open system without leaving its native phase space (Hilbert space) due to peculiar stochastic extension of the Liouville (von…
We discuss a new class of coordinate systems for a plane, which provide an analytical representation of arbitrary straightline, and then define the form of potential on the plane, under which the equations of motion of a mass point are…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases,…
In the field of machine learning coarse-grained potentials in molecular dynamics, many propagators require that the effective Hamiltonian is quadratic in momentum, thus limiting the family of coarse-graining functions. In this paper, we…
An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
Motivated by the observation that all known exactly solvable shape invariant central potentials are inter-related via point canonical transformations, we develop an algebraic framework to show that a similar mapping procedure is also exist…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…
A simple and algorithmic description of matrix shape invariant potentials is presented. The complete lists of generic matrix superpotentials of dimension $2\times2$ and of special superpotentials of dimension $3\times3$ are given…
Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution,…
In this paper, we address exponential ergodicity for L\'{e}vy driven Langevin dynamics with singular potentials, which can be used to model the time evolution of a molecular system consisting of $N$ particles moving in $\R^d$ and subject to…
Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and…
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
We explore conditions for when the gradient of a deep declarative node can be approximated by ignoring constraint terms and still result in a descent direction for the global loss function. This has important practical application when…
The complex Langevin method is a leading candidate for solving the sign problem occurring in various physical situations, notably QCD at finite chemical potential. Its most vexing problem is `convergence to the wrong limit', where the…
Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by…