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

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      Author
      Wüster, S.
      Corney, J. F.
      Rost, J. M.
      Deuar, P.
      Date
      2017
      Source Title
      Physical Review E
      Print ISSN
      2470-0045
      Publisher
      American Physical Society
      Volume
      96
      Issue
      1
      Pages
      1 - 22
      Language
      English
      Type
      Article
      Item Usage Stats
      117
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      81
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      Abstract
      We 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.
      Keywords
      Bose-Einstein condensation
      Exchange interactions
      Gages
      Numerical methods
      Phase space methods
      Quantum optics
      Statistical mechanics
      Stochastic systems
      Bose-Einstein condensates
      Density matrix renormalization group
      Interacting system
      Long range interactions
      Non-local interactions
      Quantum dynamics
      Quantum evolution
      Very large systems
      Quantum theory
      Permalink
      http://hdl.handle.net/11693/37129
      Published Version (Please cite this version)
      http://dx.doi.org/10.1103/PhysRevE.96.013309
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      • Department of Physics 2299
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