Related papers: Exact potentials in multivariate Langevin equation…
In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional…
We introduce a novel approach for decomposing and learning every scale of a given multiscale objective function in $\mathbb{R}^d$, where $d\ge 1$. This approach leverages a recently demonstrated implicit bias of the optimization method of…
Characterizing nonequilibrium dynamics in quantum many-body systems is a challenging frontier of physics. In this Letter, we systematically construct solvable nonintegrable quantum circuits that exhibit exact hidden Markovian subsystem…
We propose a scheme for extending the model Hamiltonian method developed originally for studying the equilibrium properties of complex perovskite systems to include Langevin dynamics. The extension is based on Zwanzig's treatment of…
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the…
This paper studies convergence to equilibrium for second-order Langevin dynamics under general growth conditions on the potential. Although we are principally motivated by the case when the potential is singular, e.g. when the dynamics has…
The complex Langevin approach is a promising method for the numerical treatment of systems with a sign problem, for which conventional lattice field theory techniques based on importance sampling cannot be applied. However, complex Langevin…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that…
This work addresses the exact characterization of the covariance dynamics related to linear discrete-time systems subject to both additive and parametric stochastic uncertainties that are potentially unbounded. Using this characterization,…
This article is concerned with sampling from Gibbs distributions $\pi(x)\propto e^{-U(x)}$ using Markov chain Monte Carlo methods. In particular, we investigate Langevin dynamics in the continuous- and the discrete-time setting for such…
Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is…
Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C,…
System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…
We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure exponentially fast in…
A family of collective variables is proposed to perform exact dynamical coarse-graining even in systems without time scale separation. More precisely, it is shown that these variables are not slow in general but they satisfy an overdamped…
The construction of effective and informative landscapes for stochastic dynamical systems has proven a long-standing and complex problem. In many situations, the dynamics may be described by a Langevin equation while constructing a…
Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…
We consider the problem of equilibration of a single oscillator system with dynamics given by the generalized Langevin equation. It is well-known that this dynamics can be obtained if one considers a model where the single oscillator is…
A many particle Hamiltonian, where the interaction term conserves the number of particles, is considered. A master equation for the populations of the different levels is derived in an exact way. It results in a local equation with…