Green’s functions and the adiabatic hyperspherical method

Rittenhouse, Seth T.; Mehta, Nirav; Greene, Chris H.

doi:10.1103/physreva.82.022706

Cited by 39 publications

(102 citation statements)

References 40 publications

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“…In summary, we have shown in this section that the running basis is a convenient choice, whose leading order is the usual adiabatic approximation 40,42 and the correction to it is the Berry connection. we have also argued that the Berry connection must be included for physically consistent calculation, thus we will use the exact formalism in our numerical calculation shown later.…”

Section: Running Basismentioning

confidence: 87%

Three-boson bound states in two dimensions

Ren

Aleǐner

2017

Phys. Rev. B

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We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in heterostructures or dihalogenated materials). The bosons are classified in two species (a,b) such that a-a and b-b pairs repel each other and a-b attract each other, forming the two-particle bound state with binding energy (such as bi-exciton). We developed an efficient routine based on the proper choice of basis for analytic and numerical calculations. For zero-angular momentum we found the energies of the three-particle bound statesfor wide ranges of the scattering lengths, and found a universal curve ofwhich depends only on the scattering lengths but not the microscopic details of the interactions.

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Section: Running Basismentioning

confidence: 87%

Three-boson bound states in two dimensions

Ren

Aleǐner

2017

Phys. Rev. B

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“…In the particular case (n, ℓ) = (0, 0), that is for a total degree d = 0 and s = 7/2, there cannot exist a nonzero fermionic polynomial P 0 (x 2 , x 3 ) of degree zero; the expression (46) is a constant, as the change of variable k 2 = x 2 k ′ 2 shows, and so are the contributions to F (0; x 2 , x 3 ) of the pieces f (k 2 ) and f (k 3 ) of D(k 2 , k 3 ), which thus exactly cancel. This was already taken into account in the reasoning above equation (32) and there is no unphysical solution to disregard.…”

Section: For 3 + 1 Fermions This Happens If the Function D Is A Non mentioning

confidence: 99%

“…Everything happens as if the particles absent from the set I, that is the spin ↑ particle i = 1 and the spin ↓ particle j = N ↑ +1, were in fact still there and both prepared in the mode (n, ℓ, m) = (0, 0, 0). This adds an extra constraint to the modes (n i , ℓ i , m i ) i∈I that can be populated by fermions, a constraint not included in the reasoning above equation (32). This immediately leads to the occurrence of three types of unphysical solutions:…”

Section: For 3 + 1 Fermions This Happens If the Function D Is A Non mentioning

confidence: 99%

The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas

Endo¹

2016

J. Phys. A: Math. Theor.

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Abstract. We consider a two-component ideal Fermi gas in an isotropic harmonic potential.Some eigenstates have a wavefunction that vanishes when two distinguishable fermions are at the same location, and would be unaffected by s-wave contact interactions between the two components. We determine the other, interactionsensitive eigenstates, using a Faddeev ansatz. This problem is nontrivial, due to degeneracies and to the existence of unphysical Faddeev solutions. As an application we present a new conjecture for the fourth-order cluster or virial coefficient of the unitary Fermi gas, in good agreement with the numerical results of Blume and coworkers.

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“…Building on earlier work [35][36][37][42][43][44][45][46][47][48][49], we address the following questions: (Q1) Under which conditions do atom-atom-atom resonances occur for the (2, 1) system? (Q2) Under which conditions do atom-atom-atom-atom resonances occur for the (3,1) system?…”

Section: Introductionmentioning

confidence: 99%

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

Blume

Daily

2010

Phys. Rev. A

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Two-component Fermi and Bose gases with infinitely large interspecies s-wave scattering length as exhibit a variety of intriguing properties. Among these are the scale invariance of two-component Fermi gases with equal masses, and the favorable scaling of Efimov features for two-component Bose gases and Bose-Fermi mixtures with unequal masses. This paper builds on our earlier work [D. Blume and K. M. Daily, arXiv:1006.5002] and presents a detailed discussion of our studies of small unequal-mass two-component systems with infinite as in the regime where three-body Efimov physics is absent. We report on non-universal few-body resonances. Just like with twobody systems on resonance, few-body systems have a zero-energy bound state in free space and a diverging generalized scattering length. Our calculations are performed within a non-perturbative microscopic framework and investigate the energetics and structural properties of small unequalmass two-component systems as functions of the mass ratio κ, and the numbers N1 and N2 of heavy and light atoms. For purely attractive Gaussian two-body interactions, we find that the (N1, N2) = (2, 1) and (3, 1) systems exhibit three-body and four-body resonances at mass ratios κ = 12.314(2) and 10.4(2), respectively. The three-and four-particle systems on resonance are found to be large. This suggests that the corresponding wave function has relatively small overlap with deeply-bound dimers, trimers or larger clusters and that the three-and four-body systems on resonance have a comparatively long lifetime. Thus, it seems feasible that the features discussed in this paper can be probed experimentally with present-day technology.

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Green’s functions and the adiabatic hyperspherical method

Cited by 39 publications

References 40 publications

Three-boson bound states in two dimensions

Three-boson bound states in two dimensions

The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas

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

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