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Dynamic Monte Carlo method
About: Dynamic Monte Carlo method is a research topic. Over the lifetime, 13294 publications have been published within this topic receiving 371256 citations.
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TL;DR: A review of recent developments in Monte Carlo methods in the field of ultracold gases, including developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and the connection with dynamical mean-field theory.
Abstract: This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons, and spinful bosonic systems. For repulsive fermionic systems determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and show the connection with dynamical mean-field theory. We end the review with diffusion Monte Carlo for the Stoner problem in cold gases.
119 citations
TL;DR: A novel Monte Carlo algorithm for N diffusing finite particles that react on collisions is presented, which is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.
Abstract: We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions Using the theory of first-passage processes and time dependent Green’s functions, we break the di
119 citations
119 citations
TL;DR: In this article, Monte Carlo simulations of a binary mixture simultaneously undergoing spinodal decomposition and the chemical reaction A\ensuremath{\rightleftarrows}B give rise to novel, steady-state pattern formation with domain size scaling with reaction rate to a power.
Abstract: We present Monte Carlo simulations of a binary mixture simultaneously undergoing spinodal decomposition and the chemical reaction A\ensuremath{\rightleftarrows}B. The competing processes give rise to novel, steady-state pattern formation with domain size scaling with reaction rate to a power, s, which equals the domain growth exponent, \ensuremath{\alpha}, in the absence of chemical reactions. Our findings support recent numerical simulations of a Cahn-Hilliard-type model, suggesting that chemical reactions can be used to stabilize and tune patterns arising during phase separation.
119 citations
TL;DR: In this article, the authors compared various theories of dilute coulombic systems with canonical and grand canonical Monte Carlo data on the thermodynamics and structure of this system: HNC, BGY, MPB, and ORPA+B2.
Abstract: Canonical Monte Carlo results are reported for the 2:2 aqueous electrolyte in the primitive model. The various theories of dilute coulombic systems are compared with canonical and grand canonical Monte Carlo data on the thermodynamics and structure of this system: HNC, BGY, MPB, and ORPA+B2 are comparably successful, most other theories less so. The MC results show that there are many triple ions or larger clusters even at low concentrations. The problem of extrapolating experimental thermodynamic data for 2:2 electrolytes is discussed.
119 citations