Stability of the (2+2)-fermionic system with zero-range interaction

Michelangeli, Alessandro; Pfeiffer, Paul

doi:10.1088/1751-8113/49/10/105301

Cited by 21 publications

(18 citation statements)

References 61 publications

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“…Recent progress in cold atom physics made the subject topical, thanks to the possibility of tuning the effective scattering length by means of a magnetically induced Feshbach resonance [28,Section 5.4.2], thus making the zero-range idealisation particularly realistic, above all at unitarity [3,4]. The 2+1 fermionic system is an actual building block for hetheronuclear mixtures with inter-species contact interaction -see [17,Section 1] for an outlook.…”

Section: Introductionmentioning

confidence: 99%

Spectral Analysis of the 2 + 1 Fermionic Trimer with Contact Interactions

Becker

Michelangeli

Ottolini

2018

Math Phys Anal Geom

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We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction of zero range. For arbitrary magnitude of the interaction, and arbitrary value of the mass parameter (the ratio between the mass of the third particle and that of each fermion) above the stability threshold, we identify the essential spectrum, localise the discrete spectrum and prove its finiteness, qualify the angular symmetry of the eigenfunctions, and prove the increasing monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence or absence of bound states in the physically relevant regimes of masses.Date: October 15, 2018. Key words and phrases. Particle systems with zero-range/contact interactions.Ter-Martirosyan-Skornyakov Hamiltonians. Fermonic 2+1 system.

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Section: Introductionmentioning

confidence: 99%

Spectral Analysis of the 2 + 1 Fermionic Trimer with Contact Interactions

Becker

Michelangeli

Ottolini

2018

Math Phys Anal Geom

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“…Models of this kind have been studied extensively in the literature (see, e.g., [6][7][8][9][10][11]13,15,[18][19][20][21][22][23]28,37]) and can be defined via a suitable regularization procedure. More precisely, the formal expression (1.1) can be given a meaning in terms of a suitable quadratic form [7,10,15], which will be introduced in the next section.…”

Section: Introductionmentioning

confidence: 99%

“…For its solution, it is necessary to understand the problem of stability for general systems of N + M particles mutually interacting via point interactions. In the case N = M = 2, a numerical analysis suggests stability, see [19] for the case m = 1 and [12] for the full range of mass ratios where stability for the 2 + 1 problem holds, i.e., for 0.0735 < m < (0.0735) −1 ≈ 13.6 [5].…”

Section: Introductionmentioning

confidence: 99%

Stability of a Fermionic N + 1 Particle System with Point Interactions

Moser

Seiringer

2017

Commun. Math. Phys.

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Abstract:We prove that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m * . The value of m * is independent of N and turns out to be less than 1. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain.

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“…Remark: In Michelamgeli and Pfeiffer [33], positivity of the spectrum was conjectured with the aid of a computer.…”

Section: Propositionmentioning

confidence: 99%

Contact Interactions and Gamma Convergence

Dell’Antonio

2019

Front. Phys.

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We introduce contact interactions defined by boundary conditions at the contact manifold Ŵ ≡ ∪ i,j {x i = x j }. There are two types of contact interactions, weak and strong. Both provide self-adjoint extensions ofĤ 0 the free hamiltonian restricted away from Ŵ. We analyze both of them by "lifting" the system to a space of more singular functions: the map is fractioning and mixing. In the new space we use tools of Functional Analysis. After returning to physical space we use Gamma convergence, a well-known variational tool. We prove that contact interactions are strong resolvent limits of potentials with finite range. Weak contact of one boson with two other bosons leads to the low-density Bose-Einstrin condensate. Simultaneous weak contact of three bosons produces the high-density condensate which has an Efimov sequence of bound states. In Low Energy Physics strong contact of one particle with another two produces an Efimov sequence of bound states (we will comment briefly on the relation with the effect with the same name in Quantum Mechanics). For N bosons strong contact gives a lower bound −CN for the energy. A system of fermions in strong contact (unitary gas) has a positive hamiltonian. We give several examples in dimension 3,2,1. In the Appendix we describe the ground state of the Polaron.

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Stability of the (2+2)-fermionic system with zero-range interaction

Cited by 21 publications

References 61 publications

Spectral Analysis of the 2 + 1 Fermionic Trimer with Contact Interactions

Spectral Analysis of the 2 + 1 Fermionic Trimer with Contact Interactions

Stability of a Fermionic N + 1 Particle System with Point Interactions

Contact Interactions and Gamma Convergence

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