Quantum Dynamics of Long-Range Interacting Systems Using the Positive-P and Gauge-P Representations

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dc.citation.epage22en_US
dc.citation.issueNumber1en_US
dc.citation.spage1en_US
dc.citation.volumeNumber96en_US
dc.contributor.authorWüster, S.en_US
dc.contributor.authorCorney, J. F.en_US
dc.contributor.authorRost, J. M.en_US
dc.contributor.authorDeuar, P.en_US
dc.date.accessioned2018-04-12T11:03:33Z
dc.date.available2018-04-12T11:03:33Z
dc.date.issued2017en_US
dc.departmentDepartment of Physicsen_US
dc.description.abstractWe provide the necessary framework for carrying out stochastic positive-P and gauge-P simulations of bosonic systems with long-range interactions. In these approaches, the quantum evolution is sampled by trajectories in phase space, allowing calculation of correlations without truncation of the Hilbert space or other approximations to the quantum state. The main drawback is that the simulation time is limited by noise arising from interactions. We show that the long-range character of these interactions does not further increase the limitations of these methods, in contrast to the situation for alternatives such as the density matrix renormalization group. Furthermore, stochastic gauge techniques can also successfully extend simulation times in the long-range-interaction case, by making using of parameters that affect the noise properties of trajectories, without affecting physical observables. We derive essential results that significantly aid the use of these methods: estimates of the available simulation time, optimized stochastic gauges, a general form of the characteristic stochastic variance, and adaptations for very large systems. Testing the performance of particular drift and diffusion gauges for nonlocal interactions, we find that, for small to medium systems, drift gauges are beneficial, whereas for sufficiently large systems, it is optimal to use only a diffusion gauge. The methods are illustrated with direct numerical simulations of interaction quenches in extended Bose-Hubbard lattice systems and the excitation of Rydberg states in a Bose-Einstein condensate, also without the need for the typical frozen gas approximation. We demonstrate that gauges can indeed lengthen the useful simulation time.en_US
dc.identifier.doi10.1103/PhysRevE.96.013309en_US
dc.identifier.issn2470-0045
dc.identifier.urihttp://hdl.handle.net/11693/37129
dc.language.isoEnglishen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1103/PhysRevE.96.013309en_US
dc.source.titlePhysical Review Een_US
dc.subjectBose-Einstein condensationen_US
dc.subjectExchange interactionsen_US
dc.subjectGagesen_US
dc.subjectNumerical methodsen_US
dc.subjectPhase space methodsen_US
dc.subjectQuantum opticsen_US
dc.subjectStatistical mechanicsen_US
dc.subjectStochastic systemsen_US
dc.subjectBose-Einstein condensatesen_US
dc.subjectDensity matrix renormalization groupen_US
dc.subjectInteracting systemen_US
dc.subjectLong range interactionsen_US
dc.subjectNon-local interactionsen_US
dc.subjectQuantum dynamicsen_US
dc.subjectQuantum evolutionen_US
dc.subjectVery large systemsen_US
dc.subjectQuantum theoryen_US
dc.titleQuantum Dynamics of Long-Range Interacting Systems Using the Positive-P and Gauge-P Representationsen_US
dc.typeArticleen_US

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