First-principles quantum dynamics in interacting Bose gases II: stochastic gauges
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Publication:3379379
DOI10.1088/0305-4470/39/11/011zbMATH Open1088.82014arXivcond-mat/0501058OpenAlexW2152177592WikidataQ60033274 ScholiaQ60033274MaRDI QIDQ3379379
Publication date: 6 April 2006
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
Abstract: First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analyzed. In a companion paper, we showed how the positive P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double-, and multi-mode systems in the weak mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant.This could in principle be tested experimentally using Feshbach resonance methods.
Full work available at URL: https://arxiv.org/abs/cond-mat/0501058
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