Numerical solution of the Boltzmann equation for trapped Fermi gases with in-medium effects

Pantel, Pierre-Alexandre; Davesne, D.; Urban, Michael

doi:10.1103/physreva.91.013627

Cited by 18 publications

(36 citation statements)

References 33 publications

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“…Our study is complementary to other realistic simulation approaches, such as those of Refs. [16][17][18][19][20][21]. We believe that comparing and combining these simulation results will open up the possibility of precision determination of transport coefficients from experiments of cold atomic gases, such as the shear and bulk viscosities and heat conductivity.…”

Section: Discussionmentioning

confidence: 99%

“…Compared to Ref. [16], our method has the disadvantage of not accurately describing the non-interacting regime of the cold atom gas on a quantitative level. However, the present approach has the advantage of allowing for arbitrary equations of state, the straightforward simulation of shock waves as well as being considerably cheaper in terms of computational cost.…”

Section: Introductionmentioning

confidence: 99%

“…[16], where the Boltzmann equation was solved numerically using the test particle method. Compared to Ref.…”

Section: Introductionmentioning

confidence: 99%

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Lattice Boltzmann simulations of a strongly interacting two-dimensional Fermi gas

Brewer¹,

Mendoza²,

Young³

et al. 2016

Phys. Rev. A

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We present fully nonlinear dissipative fluid dynamics simulations of a trapped two-dimensional Fermi gas at unitarity using a Lattice Boltzmann algorithm. We are able to simulate non-harmonic trapping potentials, temperature-dependent viscosities as well as a discretized version of the ballistic (non-interacting) behavior. Our approach lends itself to direct comparison with experimental data, opening up the possibility of a precision determination of transport coefficients in the unitary Fermi gas. Furthermore, we predict the presence of a non-hydrodynamic component in the quadrupole mode, which should be observable experimentally.2

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lattice Boltzmann simulations of a strongly interacting two-dimensional Fermi gas

Brewer¹,

Mendoza²,

Young³

et al. 2016

Phys. Rev. A

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“…The situation becomes much simpler for temperatures T > T c where the entire system is in the normal phase. In this case, the transition from collisional hydrodynamic to collisionless behaviour, which is observed experimentally as function of temperature or coupling [256,254], has been theoretically described in the BCS regime up to unitarity in terms of the Boltzmann equation [404,405,254,406,407,408,403]:…”

Section: Collective Modes and Anisotropic Expansionmentioning

confidence: 99%

The BCS–BEC crossover: From ultra-cold Fermi gases to nuclear systems

et al. 2018

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This report adresses topics and questions of common interest in the fields of ultra-cold gases and nuclear physics in the context of the BCS-BEC crossover. By this crossover, the phenomena of Bardeen-Cooper-Schrieffer (BCS) superfluidity and Bose-Einstein condensation (BEC), which share the same kind of spontaneous symmetry breaking, are smoothly connected through the progressive reduction of the size of the fermion pairs involved as the fundamental entities in both phenomena. This size ranges, from large values when Cooper pairs are strongly overlapping in the BCS limit of a weak inter-particle attraction, to small values when composite bosons are non-overlapping in the BEC limit of a strong inter-particle attraction, across the intermediate unitarity limit where the size of the pairs is comparable with the average inter-particle distance.The BCS-BEC crossover has recently been realized experimentally, and essentially in all of its aspects, with ultracold Fermi gases. This realization, in turn, has raised the interest of the nuclear physics community in the crossover problem, since it represents an unprecedented tool to test fundamental and unanswered questions of nuclear manybody theory. Here, we focus on the several aspects of the BCS-BEC crossover, which are of broad joint interest to both ultra-cold Fermi gases and nuclear matter, and which will likely help to solve in the future some open problems in nuclear physics (concerning, for instance, neutron stars). Similarities and differences occurring in ultra-cold Fermi gases and nuclear matter will then be emphasized, not only about the relative phenomenologies but also about the theoretical approaches to be used in the two contexts. Common to both contexts is the fact that at zero temperature the BCS-BEC crossover can be described at the mean-field level with reasonable accuracy. At finite temperature, on the other hand, inclusion of pairing fluctuations beyond mean field represents an essential ingredient of the theory, especially in the normal phase where they account for precursor pairing effects.After an introduction to present the key concepts of the BCS-BEC crossover, this report discusses the mean-field treatment of the superfluid phase, both for homogeneous and inhomogeneous systems, as well as for symmetric (spinor isospin-balanced) and asymmetric (spin-or isospin-imbalanced) matter. Pairing fluctuations in the normal phase are then considered, with their manifestations in thermodynamic and dynamic quantities. The last two Sections provide a more specialized discussion of the BCS-BEC crossover in ultra-cold Fermi gases and nuclear matter, respectively. The separate discussion in the two contexts aims at cross communicating to both communities topics and aspects which, albeit arising in one of the two fields, share a strong common interest.

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“…For a detailed account of the simulation method, we refer the reader to [45], which adjusts the original DSMC approach [48] into a version appropriate to dipolar gases. Similar methods have been employed in the study of ultracold gases, see for instance [49][50][51]. In particular, [49] also studied halo formation in the case of sand d-wave collisional cross sections.…”

Section: Many-body Considerations: Monte-carlo Simulationmentioning

confidence: 99%

Anisotropic collisions of dipolar Bose–Einstein condensates in the universal regime

Burdick¹,

Sykes²,

Tang³

et al. 2016

New J. Phys.

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We report the measurement of collisions between two Bose-Einstein condensates with strong dipolar interactions. The collision velocity is significantly larger than the internal velocity distribution widths of the individual condensates, and thus, with the condensates being sufficiently dilute, a halo corresponding to the two-body differential scattering cross section is observed. The results demonstrate a novel regime of quantum scattering, relevant to dipolar interactions, in which a large number of angular momentum states become coupled during the collision. We perform Monte-Carlo simulations to provide a detailed comparison between theoretical two-body cross sections and the experimental observations.

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Numerical solution of the Boltzmann equation for trapped Fermi gases with in-medium effects

Cited by 18 publications

References 33 publications

Lattice Boltzmann simulations of a strongly interacting two-dimensional Fermi gas

Lattice Boltzmann simulations of a strongly interacting two-dimensional Fermi gas

The BCS–BEC crossover: From ultra-cold Fermi gases to nuclear systems

Anisotropic collisions of dipolar Bose–Einstein condensates in the universal regime

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