Related papers: Solving the Wigner Equation for Chemically Relevan…
A system of $N$ non-canonical dynamically free 3D harmonic oscillators is studied. The position and the momentum operators (PM-operators) of the system do not satisfy the canonical commutation relations (CCRs). Instead they obey the weaker…
When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two dimensional systems were predicted to spontaneously break continuous translation symmetry and form a quantum crystal. Efforts to observe this…
We present a systematic approach for the semiclassical treatment of many-body dynamics of interacting, open spin systems. Our approach overcomes some of the shortcomings of the recently developed discrete truncated Wigner approximation…
Quantum simulation of 1D relativistic quantum mechanics has been achieved in well-controlled systems like trapped ions, but properties like spin dynamics and response to external magnetic fields that appear only in higher dimensions remain…
The Direct Simulation Monte Carlo (DSMC) method is the gold standard for non-equilibrium rarefied gas dynamics, yet its computational cost can be prohibitive, especially for near-continuum regimes and high-fidelity \emph{ab initio}…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
We study the Wigner crystal melting in a two dimensional quantum system of particles interacting via the 1/r Coulomb potential. We use quantum Monte Carlo methods to calculate its phase diagram, locate the Wigner crystal region, and analyze…
We present a Monte Carlo wavefunction method for semiclassically modeling spin-$\frac12$ systems in a magnetic field gradient in one dimension. Our model resolves the conflict of determining what classical force an atom should be subjected…
Two-frequency Wigner distribution is introduced to capture the asymptotic behavior of the space-frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
In this paper, we correct a mistake we made in [Phys. Rev. Lett. $\textbf{122}$, 190402 (2019)] and [Phys. Rev. A $\textbf{103}$, 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here…
Dynamical systems in engineering and physics are often subject to irregular excitations that are best modeled as random. Monte Carlo simulations are routinely performed on such random models to obtain statistics on their long-term response.…
Monte-Carlo simulation of physical processes is an important tool for detector development as it allows to predict signal pulse amplitude and timing, time resolution, efficiency ... Yet despite the fact they are very common, full…
Moir\'e materials provide an ideal platform for exploring quantum phases of matter. However, solving the many-electron problem in moir\'e systems is challenging due to strong correlation effects. We introduce a powerful variational…
We introduce a Path Integral Monte Carlo (PIMC) approach that uses the angular momentum representation for the description of interacting rotor systems. Such a choice of representation allows the calculation of momentum properties without…
In plasma edge simulations, kinetic Monte Carlo (MC) is often used to simulate neutral particles and estimate source terms. For large-sized reactors, like ITER and DEMO, high particle collision rates lead to a substantial computational cost…
Quasi-Monte Carlo (QMC) methods for high dimensional integrals over unit cubes and products of spheres are well-studied in literature. We study QMC tractability of integrals of functions defined over the product of $m$ copies of the simplex…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
The Stochastic Weighted Particle Method (SWPM) of Rjasanow and Wagner is a generalization of the Direct Simulation Monte Carlo method for computing the probability density function of the velocities of a system of interacting particles for…
To predict the complex chemical evolution in multicomponent alloys, it is highly desirable to have accurate atomistic simulation methods capable of reaching sufficiently large spatial and temporal scales. In this work, we advance the…