Related papers: Classical Langevin Dynamics for Model Hamiltonians
When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon…
A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. As in standard projection operator methods, a set of resolved variables is…
A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian…
A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occur in a pairwise fashion. It is also…
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…
Complex microscopic many-body processes are often interpreted in terms of so-called `reaction coordinates', i.e. in terms of the evolution of a small set of coarse-grained observables. A rigorous method to produce the equation of motion of…
Optical micro-manipulation techniques has evolved into powerful tools to efficiently steer the motion of microscopical particles on periodic and quasi-periodic potentials, driven by the external electromagnetic field. Here, the dynamics of…
The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the…
We introduce a constructive framework to learn effective Langevin equations from stationary time series. Unlike conventional approaches that require iterative calibration to match target statistics, our construction guarantees the observed…
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…
We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce…
Sometimes the dynamics of a physical system is described by non-Hamiltonian equations of motion, and additionally, the system is characterized by long-range interactions. A concrete example is that of particles interacting with light as…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
We build upon recent work on using Machine Learning models to estimate Hamiltonian parameters using continuous weak measurement of qubits as input. We consider two settings for the training of our model: (1) supervised learning where the…
After a short review of one of proposals to avoid complex stochastic processes in Complex Langevin studies, the recent progress in the former is reported. In particular, the new developments allow now to construct positive and normalizable…
We present an approach for carrying out non-adiabatic molecular dynamics simulations of systems in which non-adiabatic transitions arise from the coupling between the classical atomic motions and a quasi-continuum of electronic quantum…
A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
The paper begins with a novel variational formulation of Duffing equation using the extended framework of Hamilton's principle (EHP). This formulation properly accounts for initial conditions, and it recovers all the governing differential…