Few-body resonances of unequal-mass systems with infinite interspecies two-body<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:math>-wave scattering length

Blume, D.; Daily, K. M.

doi:10.1103/physreva.82.063612

Cited by 21 publications

(34 citation statements)

References 75 publications

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“…We emphasize that the above arguments and results are valid for any number of particles, for both few-and many-body systems, in marked contrast to LDA, which is valid only for systems with large number of particles. From Eq (34), one also finds the upper limit of Z for the uniform system, Z > ≥ Z, where [21,48,51]. The error bars are smaller than the symbol sizes.…”

Section: Uniform Systemsmentioning

confidence: 94%

Universality of the unitary Fermi gas: a few-body perspective

Levinsen¹,

Massignan²,

Endo³

et al. 2017

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

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We revisit the properties of the two-component Fermi gas with short-range interactions in three dimensions, in the limit where the s-wave scattering length diverges. Such a unitary Fermi gas possesses universal thermodynamic and dynamical observables that are independent of any interaction length scale. Focusing on trapped systems of N fermions, where N ≤ 10, we investigate how well we can determine the zero-temperature behavior of the many-body system from published few-body data on the ground-state energy and the contact. For the unpolarized case, we find that the Bertsch parameters extracted from trapped few-body systems all lie within 15% of the established value. Furthermore, the few-body values for the contact are well within the range of values determined in the literature for the many-body system. In the limit of large spin polarization, we obtain a similar accuracy for the polaron energy, and we estimate the polaron's effective mass from the dependence of its energy on N . We also compute an upper bound for the squared wave-function overlap between the unitary Fermi system and the non-interacting ground state, both for the trapped and uniform cases. This allows us to prove that the trapped unpolarized ground state at unitarity has zero overlap with its non-interacting counterpart in the many-body limit N → ∞.

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Section: Uniform Systemsmentioning

confidence: 94%

Universality of the unitary Fermi gas: a few-body perspective

Levinsen¹,

Massignan²,

Endo³

et al. 2017

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

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show abstract

“…The agreement between the two sets of calculations is very good. Column 4 of Table I shows the s ZR 0,unit values obtained earlier [47]; these earlier calculations were restricted to larger r 0 /a ho and are less accurate than the values calculated in this work. Following the discussion of Refs.…”

Section: (31) System With 1 + Symmetrymentioning

confidence: 64%

“…For comparison, column 4 shows the results from Ref. [47]. The κ = 1 entry in the third column is taken from Ref.…”

Section: (31) System With 1 + Symmetrymentioning

confidence: 99%

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Hyperspherical explicitly correlated Gaussian approach for few-body systems with finite angular momentum

Rakshit

Blume

2012

Phys. Rev. A

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Within the hyperspherical framework, the solution of the time-independent Schrödinger equation for a nparticle system is divided into two steps: the solution of a Schrödinger-type equation in the hyperangular degrees of freedom and the solution of a set of coupled Schrödinger-type hyperradial equations. The solutions to the former provide effective potentials and coupling matrix elements that enter into the latter set of equations. This paper develops a theoretical framework to determine the effective potentials, as well as the associated coupling matrix elements, for few-body systems with finite angular momentum L = 1 and negative and positive parity . The hyperangular channel functions are expanded in terms of explicitly correlated Gaussian basis functions, and relatively compact expressions for the matrix elements are derived. The developed formalism is applicable to any n; however, for n 6, the computational demands are likely beyond present-day computational capabilities. A number of calculations relevant to cold-atom physics are presented, demonstrating that the developed approach provides a computationally efficient means to solving four-body bound and scattering problems with finite angular momentum on powerful desktop computers. Details regarding the implementation are discussed.

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“…The uncertainties for the ECG and DMC calculations are, according to Refs. [102,103,104] Figure 13. Symbols show the contact C of the (3, 1) system as a function of τ −1 .…”

Section: Non-interacting Fermi Gas With a Single Impuritymentioning

confidence: 99%

Path integral Monte Carlo ground state approach: formalism, implementation, and applications

Yan

Blume

2017

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

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Abstract. Monte Carlo techniques have played an important role in understanding strongly-correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum mechanical systems, the path integral Monte Carlo approach with its variants has been employed widely. Since semi-classical or classical approaches will not be discussed in this review, path integral based approaches can for our purposes be divided into two categories: approaches applicable to quantum mechanical systems at zero temperature and approaches applicable to quantum mechanical systems at finite temperature. While these two approaches are related to each other, the underlying formulation and aspects of the algorithm differ. This paper reviews the path integral Monte Carlo ground state (PIGS) approach, which solves the time-independent Schrödinger equation. Specifically, the PIGS approach allows for the determination of expectation values with respect to eigen states of the few-or many-body Schrödinger equation provided the system Hamiltonian is known. The theoretical framework behind the PIGS algorithm, implementation details, and sample applications for fermionic systems are presented. : Formalism, implementation, and applications2 Path integral Monte Carlo ground state approach

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Few-body resonances of unequal-mass systems with infinite interspecies two-bodys-wave scattering length

Cited by 21 publications

References 75 publications

Universality of the unitary Fermi gas: a few-body perspective

Universality of the unitary Fermi gas: a few-body perspective

Hyperspherical explicitly correlated Gaussian approach for few-body systems with finite angular momentum

Path integral Monte Carlo ground state approach: formalism, implementation, and applications

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