Time-dependent density-functional theory for trapped strongly interacting fermionic atoms

Kim, Yeong E.; Zubarev, Alexander L.

doi:10.1103/physreva.70.033612

Cited by 133 publications

(160 citation statements)

References 56 publications

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“…(27) by the conservation of energy and include an additional term in Eq. (28). We use dimensionless units described in appendix A, setting = k B = m = 1.…”

Section: A the Eigenvalue Problem From Two-fluid Hydrodynamicsmentioning

confidence: 99%

Hydrodynamic collective modes for cold trapped gases

Boettcher¹,

Floerchinger²,

Wetterich³

2011

J. Phys. B: At. Mol. Opt. Phys.

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We suggest that collective oscillation frequencies of cold trapped gases can be used to test predictions from quantum many-body physics. Our motivation lies both in rigid experimental tests of theoretical calculations and a possible improvement of measurements of particle number, chemical potential or temperature. We calculate the effects of interaction, dimensionality and thermal fluctuations on the collective modes of a dilute Bose gas in the hydrodynamic limit. The underlying equation of state is provided by non-perturbative Functional Renormalization Group or by LeeYang theory. The spectrum of oscillation frequencies could be measured by response techniques. Our findings are generalized to bosonic or fermionic quantum gases with an arbitrary equation of state in the two-fluid hydrodynamic regime. For any given equation of state P (µ, T ) and normal fluid density nn(µ, T ) the collective oscillation frequencies in a d-dimensional isotropic potential are found to be the eigenvalues of an ordinary differential operator. We suggest a method of numerical solution and discuss the zero-temperature limit. Exact results are provided for harmonic traps and certain special forms of the equation of state. We also present a phenomenological treatment of dissipation effects and discuss the possibility to excite the different eigenmodes individually.

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“…(27) by the conservation of energy and include an additional term in Eq. (28). We use dimensionless units described in appendix A, setting = k B = m = 1.…”

Section: A the Eigenvalue Problem From Two-fluid Hydrodynamicsmentioning

confidence: 99%

Hydrodynamic collective modes for cold trapped gases

Boettcher¹,

Floerchinger²,

Wetterich³

2011

J. Phys. B: At. Mol. Opt. Phys.

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show abstract

“…For the sake of completeness, in Fig. 1 we also show the dotted curve obtained with the [2,2] Padé approximation of Kim and Zubarev [11], based only on the asymptotes and the Monte-Carlo value [19] at y = 0. Our parametric formula is more accurate, especially around y = 0.…”

Section: Bulk Propertiesmentioning

confidence: 99%

Bulk and collective properties of a dilute Fermi gas in the BCS-BEC crossover

2005

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We investigate the zero-temperature properties of a dilute two-component Fermi gas with attractive interspecies interaction in the BCS-BEC crossover. We build an efficient parametrization of the energy per particle based on Monte Carlo data and asymptotic behavior. This parametrization provides, in turn, analytical expressions for several bulk properties of the system such as the chemical potential, the pressure and the sound velocity. In addition, by using a time-dependent density functional approach, we determine the collective modes of the Fermi gas under harmonic confinement. The calculated collective frequencies are compared to experimental data on confined vapors of 6 Li atoms and with other theoretical predictions.

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“…The developed formalism catches the non-dissipative part of the time-dependent term in the effective action. Thus the evolution equation for the order parameter (when neglecting the second-order time derivatives) is governed by a time-dependent nonlinear Schrödinger equation [40,41] (rather than a time dependent Ginzburg -Landau equation, which must account for the carrier dissipation). Figure 1 shows the difference Ω s − ( Ω s | w=0 ) as a function of temperature for several values of the inverse scattering length 1/a s , for the present approach (full curves) and the standard GL approach (dashed curves).…”

Section: Thermodynamic Potentialmentioning

confidence: 99%

Finite temperature effective field theory and two-band superfluidity in Fermi gases

et al. 2015

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We develop a description of fermionic superfluids in terms of an effective field theory for the pairing order parameter. Our effective field theory improves on the existing Ginzburg -Landau theory for superfluid Fermi gases in that it is not restricted to temperatures close to the critical temperature. This is achieved by taking into account long-range fluctuations to all orders. The results of the present effective field theory compare well with the results obtained in the framework of the Bogoliubov -de Gennes method. The advantage of an effective field theory over Bogoliubov -de Gennes calculations is that much less computation time is required. In the second part of the paper, we extend the effective field theory to the case of a two-band superfluid. The present theory allows us to reveal the presence of two healing lengths in the two-band superfluids, to analyze the finite-temperature vortex structure in the BEC-BCS crossover, and to obtain the ground state parameters and spectra of collective excitations. For the Leggett mode our treatment provides an interpretation of the observation of this mode in two-band superconductors.

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Time-dependent density-functional theory for trapped strongly interacting fermionic atoms

Cited by 133 publications

References 56 publications

Hydrodynamic collective modes for cold trapped gases

Hydrodynamic collective modes for cold trapped gases

Bulk and collective properties of a dilute Fermi gas in the BCS-BEC crossover

Finite temperature effective field theory and two-band superfluidity in Fermi gases

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