Related papers: A Spectral Canonical Electrostatic Algorithm
Starting from the stochastic thermodynamics description of two coupled underdamped Brownian particles, we showcase and compare three different coarse-graining schemes leading to an effective thermodynamic description for the first of the…
The gravitational $N$-body problem, which is fundamentally important in astrophysics to predict the motion of $N$ celestial bodies under the mutual gravity of each other, is usually solved numerically because there is no known general…
We demonstrate the use of a new algorithm called the Flat Histogram sampling algorithm for the simulation of lattice polymer systems. Thermodynamics properties, such as average energy or entropy and other physical quantities such as…
Hierarchical code coupling strategies make it possible to combine the results of individual numerical solvers into a self-consistent symplectic solution. We explore the possibility of allowing such a coupling strategy to be non-intrusive.…
Understanding the realization of thermal equilibrium through the thermalization process in a many-body system is a fundamental and complex scientific question, bridging thermodynamics and classical dynamics and connecting to a host of…
Strongly interacting fermions underpin some of the most challenging problems in condensed matter physics, such as high-temperature superconductivity. The low-energy states of these systems encode their essential microscopic properties, yet…
We present a nonperturbative recipe for directly computing the $S$-matrix in strongly-coupled QFTs. The method makes use of spectral data obtained in a Hamiltonian framework and can be applied to a wide range of theories, including…
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies…
Accelerated gradient methods have had significant impact in machine learning -- in particular the theoretical side of machine learning -- due to their ability to achieve oracle lower bounds. But their heuristic construction has hindered…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…
The quantum dynamics of two-level systems under classical oscillator heat bath is mapped to the classical one of a charged particle under harmonic oscillator potential plus a magnetic field in a plane. The behavior of eigenstates and…
The concept of guiding center is potent in astrophysics, space plasmas, fusion researches, and arc plasmas to solve the multi-scale dynamics of magnetized plasmas. In this letter, we rigorously prove that the guiding center dynamics can…
The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
Many physical and chemical processes in the condensed phase environment exhibit non-Markovian quantum dynamics. As such simulations are challenging on classical computers, we developed a variational quantum algorithm that is capable of…
A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a…
Most non-relativistic interacting quantum many-body systems, such as atomic and molecular ensembles or materials, are naturally described in terms of continuous-space Hamiltonians. The simulation of their ground-state properties on digital…
We investigate a model of a stochastic engine operating cyclically at constant bath temperature, which consists of an overdamped Brownian harmonic oscillator that plays the role of working substance and is elastically coupled to an active…
Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient relaxation algorithms…