Triviality of a model of particles with point interactions in the thermodynamic limit

Moser, Thomas; Seiringer, Robert

doi:10.1007/s11005-016-0915-x

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…The three-body boundary condition introduced in [18] (see also the recent papers [13,17] and the references therein) leads to a Hamiltonian unbounded from below which is unsatisfactory from the physical point of view. Such instability property is known as Thomas effect and it is due to the fact that the interaction becomes too singular when all the three particles are close to each other (we just recall that the situation is rather different for systems made of two species of fermions, see, e.g., [8,9], [20][21][22]). Following a suggestion contained in [18] (see also [2]), it has been recently proposed ( [12], [5, 17, section 9], [13, section 6]) a regularized version of the Hamiltonian for the three-boson system with a different type of three-body boundary condition.…”

Section: Introductionmentioning

confidence: 99%

Zero-Range Hamiltonian for a Bose Gas with an Impurity

Ferretti

Teta

2023

Complex Anal. Oper. Theory

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We study the Hamiltonian for a system of N identical bosons interacting with an impurity, i.e., a different particle, via zero-range forces in dimension three. It is well known that, following the standard approach, one obtains the Ter-Martirosyan Skornyakov Hamiltonian which is unbounded from below. In order to avoid such instability problem, we introduce a three-body force acting at short distances. The effect of this force is to reduce to zero the strength of the zero-range interaction between two particles, i.e., the impurity and a boson, when another boson approaches the common position of the first two particles. We show that the Hamiltonian defined with such regularized interaction is self-adjoint and bounded from below if the strength of the three-body force is sufficiently large. The method of the proof is based on a careful analysis of the corresponding quadratic form.

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Section: Introductionmentioning

confidence: 99%

Zero-Range Hamiltonian for a Bose Gas with an Impurity

Ferretti

Teta

2023

Complex Anal. Oper. Theory

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“…The Thomas effect was first noted by Danilov [10] and then rigorously analyzed by Minlos and Faddeev [28,29], and it makes the Hamiltonian unsatisfactory from the physical point of view (for some recent mathematical contributions see, e.g., [5,6,14,22] with references therein). For other approaches to the construction of many-body contact interactions in R 3 , we refer to [2,31,36].…”

Section: Introductionmentioning

confidence: 99%

Three-Body Hamiltonian with Regularized Zero-Range Interactions in Dimension Three

Basti

Cacciapuoti

Finco

et al. 2022

Ann. Henri Poincaré

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We study the Hamiltonian for a system of three identical bosons in dimension three interacting via zero-range forces. In order to avoid the fall to the center phenomenon emerging in the standard Ter-Martirosyan–Skornyakov (TMS) Hamiltonian, known as Thomas effect, we develop in detail a suggestion given in a seminal paper of Minlos and Faddeev in 1962 and we construct a regularized version of the TMS Hamiltonian which is self-adjoint and bounded from below. The regularization is given by an effective three-body force, acting only at short distance, that reduces to zero the strength of the interactions when the positions of the three particles coincide. The analysis is based on the construction of a suitable quadratic form which is shown to be closed and bounded from below. Then, domain and action of the corresponding Hamiltonian are completely characterized and a regularity result for the elements of the domain is given. Furthermore, we show that the Hamiltonian is the norm resolvent limit of Hamiltonians with rescaled non-local interactions, also called separable potentials, with a suitably renormalized coupling constant.

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Triviality of a model of particles with point interactions in the thermodynamic limit

Cited by 2 publications

References 26 publications

Zero-Range Hamiltonian for a Bose Gas with an Impurity

Zero-Range Hamiltonian for a Bose Gas with an Impurity

Three-Body Hamiltonian with Regularized Zero-Range Interactions in Dimension Three

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