Universal description of three two-component fermions

Kartavtsev, O. I.; Malykh, A. V.

doi:10.1209/0295-5075/115/36005

Cited by 16 publications

(33 citation statements)

References 43 publications

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“…Also, the explicit form of (81) matches precisely the analogous findings in the physical literature -see, e.g., [34, note 43], and more recently [12,13].…”

Section: Multiplicity Of Extensions and Three-body Boundary Conditionsupporting

confidence: 81%

Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan—Skornyakov type

Michelangeli

Ottolini

2018

Reports on Mathematical Physics

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We reconstruct the whole family of self-adjoint Hamiltonians of Ter-Martirosyan-Skornyakov type for a system of two identical fermions coupled with a third particle of different nature through an interaction of zero range. We proceed through an operator-theoretic approach based on the self-adjoint extension theory of Kreȋn, Višik, and Birman. We identify the explicit 'Kreȋn-Višik-Birman extension parameter' as an operator on the 'space of charges' for this model (the 'Kreȋn space') and we come to formulate a sharp conjecture on the dimensionality of its kernel. Based on our conjecture, for which we also discuss an amount of evidence, we explain the emergence of a multiplicity of extensions in a suitable regime of masses and we reproduce for the first time the previous partial constructions obtained by means of an alternative quadratic form approach.

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“…Also, the explicit form of (81) matches precisely the analogous findings in the physical literature -see, e.g., [34, note 43], and more recently [12,13].…”

Section: Multiplicity Of Extensions and Three-body Boundary Conditionsupporting

confidence: 81%

Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan—Skornyakov type

Michelangeli

Ottolini

2018

Reports on Mathematical Physics

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“…For mass ratios lower than 13.6, Kartavtsev and Malykh pointed out that the system can support another type of trimer state for positive scattering length [34]: Unlike the Efimov trimers, these trimers are universal in the sense that their energies do not depend on the short-range details of the interaction (i.e. a three-body parameter) [35][36][37][38]. However, later studies of finite-range systems show that the universal behavior is only limited to very large scattering lengths [39,40].…”

Section: Exact Solution Of the Three-body Problemmentioning

confidence: 99%

Few-body states of bosons interacting with a heavy quantum impurity

et al. 2018

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We consider the problem of a fixed impurity coupled to a small number N of non-interacting bosons. We focus on impurity-boson interactions that are mediated by a closed-channel molecule, as is the case for tuneable interatomic interactions in cold-atom experiments. We show that this two-channel model can be mapped to a boson model with effective boson-boson repulsion, which enables us to solve the three-body (N = 2) problem analytically and determine the trimer energy for impurity-boson scattering lengths a > 0. By analysing the atom-dimer scattering amplitude, we find a critical scattering length a * at which the atom-dimer scattering length diverges and the trimer merges into the dimer continuum. We furthermore calculate the tetramer energy exactly for a > 0 and show that the tetramer also merges with the continuum at a * . Indeed, since the critical point a * formally resembles the unitary point 1/a = 0, we find that all higher-body bound states (involving the impurity and N > 1 bosons) emerge and disappear at both of these points. We show that the behavior at these "multi-body resonances" is universal, since it occurs for any model with an effective three-body repulsion involving the impurity. Thus, we see that the fixed-impurity problem is strongly affected by a three-body parameter even in the absence of the Efimov effect. arXiv:1807.09992v1 [cond-mat.quant-gas]

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“…At smaller mass ratios this trimer turns into a p-wave atom-dimer resonance, effects of which have been observed in the 40 K- 6 Li mixture (M/m = 6.644) [4]. This manifestly nonperturbative physics has stimulated extensive few-and many-body studies in mass-imbalanced Fermi mixtures [3,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

mentioning

confidence: 94%

“…The non-Efimovian regime appears for s 2 > 0 (s > 0) where, far from few-body resonances, Ψ(R) can be set to be equal to Ψ + (R) (see, however, Ref. [6,16,19]).…”

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confidence: 99%

Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures

Bazak

Petrov

2017

Phys. Rev. Lett.

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We show that four heavy fermions interacting resonantly with a lighter atom (4+1 system) become Efimovian at mass ratio 13.279(2), which is smaller than the corresponding 2+1 and 3+1 thresholds. We thus predict the five-body Efimov effect for this system in the regime where any of its subsystem is non- Efimovian. For smaller mass ratios we show the existence and calculate the energy of a universal 4+1 pentamer state, which continues the series of the 2+1 trimer predicted by Kartavtsev and Malykh and 3+1 tetramer discovered by Blume. We also show that the effective-range correction for the light-heavy interaction has a strong effect on all these states and larger effective ranges increase their tendency to bind

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Universal description of three two-component fermions

Cited by 16 publications

References 43 publications

Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan—Skornyakov type

Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan—Skornyakov type

Few-body states of bosons interacting with a heavy quantum impurity

Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures

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