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Advances in non-relativistic matter via complex Langevin approaches

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 نشر من قبل Joaquin E. Drut
 تاريخ النشر 2017
  مجال البحث فيزياء
والبحث باللغة English
 تأليف J. E. Drut




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The recent progress in understanding the mathematics of complex stochastic quantization, as well as its application to quantum chromodynamics in situations that have a complex phase problem (e.g. finite quark density, real time), has opened up an intriguing possibility for non-relativistic many-body physics which has so far remained largely unexplored. In this brief contribution, I review a few specific examples of advances in the characterization of the thermodynamics of non-relativistic matter in a variety of one-dimensional cases affected by the sign problem: repulsive interactions, finite polarization, finite mass imbalance, and projection to finite systems to obtain virial coefficients.



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We review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign problem, incl uding the classic reweighting method, alternative Hubbard-Stratonovich transformations, dual variables (for bosons and fermions), Majorana fermions, density-of-states methods, imaginary asymmetry approaches, and Lefschetz thimbles. We discuss some aspects of the mathematical underpinnings of conventional stochastic quantization, provide a few pedagogical examples, and summarize open challenges and practical solutions for the complex case. Finally, we review the recent applications of complex Langevin to quantum field theory in relativistic and nonrelativistic quantum matter, with an emphasis on the nonrelativistic case.
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