Universal Phase Diagram and Scaling Functions of Imbalanced Fermi Gases

FRANK, B.; LANG, J.; ZWERGER, W.

doi:10.1134/s0044451018110020

Cited by 7 publications

(10 citation statements)

References 58 publications

(114 reference statements)

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“…We have verified that in the mass-balanced case our results agree with those obtained by a similar approach in Ref. [45].…”

Section: Numerical Results For the Homogeneous Systemsupporting

confidence: 90%

Beyond-mean-field description of a trapped unitary Fermi gas with mass and population imbalance

Pini,

Pieri,

Grimm

et al. 2020

Preprint

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“…We have verified that in the mass-balanced case our results agree with those obtained by a similar approach in Ref. [45].…”

Section: Numerical Results For the Homogeneous Systemsupporting

confidence: 90%

Beyond-mean-field description of a trapped unitary Fermi gas with mass and population imbalance

Pini,

Pieri,

Grimm

et al. 2020

Preprint

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“…Chevy [29]. Recall that µ ↑ = E F and µ ↓ = E Proceeding one step further, it is possible to construct the so-called self-consistent Tmatrix approach (SCTMA) [52,83,84] which deploys the many-body T -matrix Γ S composed of dressed propagators as schematically shown in Fig. 1(e).…”

Section: A T -Matrix Approach To Fermi Polaron Problemsmentioning

confidence: 99%

Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

Tajima,

Takahashi,

Mistakidis

et al. 2021

Preprint

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The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments and in particular we exemplify the modifications of the medium either in the presence of Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two-and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom.Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.

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“…On the other hand, the phase transition to the superfluid is signaled by an instability of the pair propagator in the low-momentum limit. In this system, the LFT has been applied to study the phase diagram in the presence of a finite spin imbalance 17 . Furthermore, similar challenges arise in the efficient simulation of analog low/high pass filters 18 , in the context of signal processing as well as in the numerical solution of differential equations 19 .…”

Section: B Numerical Implementationmentioning

confidence: 99%

“…Next, one has to investigate the convergence properties of the remaining sum over the auxiliary variable s in (17). First, we focus on the properties of the exact integral…”

Section: A Theoretical Perspectivementioning

confidence: 99%

See 1 more Smart Citation

Fast logarithmic Fourier-Laplace transform of nonintegrable functions

Lang

Frank

2019

Phys. Rev. E

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We present an efficient and very flexible numerical fast Fourier-Laplace transform, that extends the logarithmic Fourier transform (LFT) introduced by Haines and Jones [Geophys. J. Int. 92(1):171 (1988)] for functions varying over many scales to nonintegrable functions. In particular, these include cases of the asymptotic form f (ν → 0) ∼ ν a and f (|ν| → ∞) ∼ ν b with arbitrary real a > b. Furthermore, we prove that the numerical transform converges exponentially fast in the number of data points, provided that the function is analytic in a cone | ν| < θ| ν| with a finite opening angle θ around the real axis and satisfies |f (ν)f (1/ν)| < ν c as ν → 0 with a positive constant c, which is the case for the class of functions with power-law tails. Based on these properties we derive ideal transformation parameters and discuss how the logarithmic Fourier transform can be applied to convolutions. The ability of the logarithmic Fourier transform to perform these operations on multiscale (non-integrable) functions with power-law tails with exponentially small errors makes it the method of choice for many physical applications, which we demonstrate on typical examples. These include benchmarks against known analytical results inaccessible to other numerical methods, as well as physical models near criticality.

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Universal Phase Diagram and Scaling Functions of Imbalanced Fermi Gases

Cited by 7 publications

References 58 publications

Beyond-mean-field description of a trapped unitary Fermi gas with mass and population imbalance

Beyond-mean-field description of a trapped unitary Fermi gas with mass and population imbalance

Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

Fast logarithmic Fourier-Laplace transform of nonintegrable functions

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