Local realizations of contact interactions in two- and three-body problems

Kruppa, A. T.; Varga, K.; Révai, J.

doi:10.1103/physrevc.63.064301

Cited by 8 publications

(4 citation statements)

References 30 publications

(50 reference statements)

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“…where b is a length scale, m the mass of the identical particles, and C and ǫ are numbers. The potential is a local-potential representation of the contact interaction in the limit ǫ → 0 [36].…”

Section: Finite-range Corrections γ Nmentioning

confidence: 99%

Universality and scaling in theN-body sector of Efimov physics

Gattobigio

Kievsky

2014

Phys. Rev. A

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Universal behaviour has been found inside the window of Efimov physics for systems with N = 4, 5, 6 particles. Efimov physics refers to the emergence of a number of three-body states in systems of identical bosons interacting via a short-range interaction becoming infinite at the verge of binding two particles. These Efimov states display a discrete scale invariance symmetry, with the scaling factor independent of the microscopic interaction. Their energies in the limit of zero-range interaction can be parametrized, as a function of the scattering length, by a universal function. We have found, using the form of finite-range scaling introduced in [A. Kievsky and M. Gattobigio, Phys. Rev A 87, 052719 (2013)], that the same universal function can be used to parametrize the ground-and excited-energy of N ≤ 6 systems inside the Efimov-physics window. Moreover, we show that the same finite-scale analysis reconciles experimental measurements of three-body binding energies with the universal theory.Universality is one of the concepts that have attracted physicists along the years. Different systems, having even different energy scales, share common behaviours. The most celebrated example of universality comes from the investigation of critical phenomena [1,2]: at the critical point, materials that are governed by different microscopic interactions share the same macroscopic laws, for instance the same critical exponents. The theoretical framework to understand universality has been provided by the renormalization group (RG); the critical point is mapped onto a fixed point of a dynamical system, the RG flow, whose phase space is represented by Hamiltonians. At the critical point the systems have scale-invariant (SI) symmetry, forcing all of the observables to be exponential functions of the control parameter. A consequence of SI symmetry is the scaling of the observables: for different materials, in the same class of universality, a selected observable can be represented as a function of the control parameter and, provided that both the observable and the control parameter are scaled by some materialdependent factor, all representations collapse onto a single universal curve [3].

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Section: Finite-range Corrections γ Nmentioning

confidence: 99%

Universality and scaling in theN-body sector of Efimov physics

Gattobigio

Kievsky

2014

Phys. Rev. A

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“…In that respect, it would be quite interesting to reexamine the solution of the Schroedinger equation with a singular α/r 2 potential in conjunction with local realizations of the contact interaction of Ref. 14 implemented by Kruppa, Varga and Revai [21]. Such a study might throw additional light on the corresponding renormalization group flow properties in the 3-body problem.…”

mentioning

confidence: 99%

Singular inverse square potential, limit cycles, and self-adjoint extensions

Bawin

Coon

2003

Phys. Rev. A

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We study the radial Schroedinger equation for a particle of mass m in the field of a singular attractive α/r 2 potential with 2mα > 1/4. This potential is relevant to the fabrication of nanoscale atom optical devices, is said to be the potential describing the dipole-bound anions of polar molecules, and is the effective potential underlying the universal behavior of three-body systems in nuclear physics and atomic physics, including aspects of Bose-Einstein condensates, first described by Efimov. New results in three-body physical systems motivate the present investigation. Using the regularization method of Beane et al., we show that the corresponding "renormalization group flow" equation can be solved analytically. We find that it exhibits a limit cycle behavior and has infinitely many branches. We show that a physical meaning for self-adjoint extensions of the Hamiltonian arises naturally in this framework.

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“…Intuitionally, the coupling strength is proportional to the relative tightness of the fixed force between the plate and the oscillator. The point interaction [ 38 , 39 , 40 ] has attracted much attention in the research of the nuclear [ 41 ], atomic [ 42 ], solid-state [ 43 ], and particle physics [ 44 ]. Furthermore, Šeba [ 45 ] studied the coupling interaction of a delta-function potential in two-dimensional integrable billiards to verify that the strong coupling can cause the transition from integrable to chaotic feature [ 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 ].…”

Section: Coupling Interaction Between Source and Platementioning

confidence: 99%