Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions

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

doi:10.1134/s002136400722002x

Cited by 27 publications

(60 citation statements)

References 31 publications

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“…The Efimov trimers and KM trimers can also exist with a higher angular momentum L tot , specifically for two fermions plus one particle systems with odd integer L tot , as well as two bosons plus one particle systems with non-zero even integer L tot [17,32]. Therefore, we expect a scenario similar to the one discussed in this paper for these systems as well.…”

Section: Discussionmentioning

confidence: 55%

Crossover trimers connecting continuous and discrete scaling regimes

2012

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For a system of two identical fermions and one distinguishable particle interacting via a short-range potential with a large s-wave scattering length, the Efimov trimers and Kartavtsev-Malykh trimers exist in different regimes of the mass ratio. The Efimov trimers are known to exhibit a discrete scaling invariance, while the Kartavtsev-Malykh trimers feature a continuous one. We point out that a third type of trimers, "crossover trimers", exist universally regardless of short-range details of the potential. These crossover trimers have neither discrete nor continuous scaling invariance. We show that the crossover trimers continuously connect the discrete and continuous scaling regimes as the mass ratio and the scattering length are varied. We identify the regions for the KartavtsevMalykh trimers, Efimov trimers, crossover trimers, and non-universal trimers in terms of the mass ratio and the s-wave scattering length by investigating the scaling property and universality (i.e. independence on short-range details) of the trimers.

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Section: Discussionmentioning

confidence: 55%

Crossover trimers connecting continuous and discrete scaling regimes

2012

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“…which represents the contact interaction between different particles [26,35,37,40]. Taking into account the symmetry requirements, one can consider the variable α within the range 0 ≤ α ≤ π/2 and impose the boundary conditions…”

Section: General Outline and Methodsmentioning

confidence: 99%

“…For large mass ratio m/m 1 , one can use the adiabatic and quasi-classical approximations which provide, e. g., a universal description for the energy spectrum [40]. To describe the three-body properties in the limit of large m/m 1 → ∞ [ω → π/2− m 1 /(2m)], one considers the first eigenvalue ξ 1 (ρ) ≡ iκ(ρ), which large-ρ asymptotic dependence is approximately given by…”

Section: Two Heavy and One Light Particlesmentioning

confidence: 99%

Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement

Kartavtsev

Malykh

Sofianos

2009

J. Exp. Theor. Phys.

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The universal three-body dynamics in ultra-cold binary gases confined to one-dimensional motion are studied. The three-body binding energies and the (2 + 1)-scattering lengths are calculated for two identical particles of mass m and a different one of mass m 1 , which interactions is described in the low-energy limit by zero-range potentials. The critical values of the mass ratio m/m 1 , at which the three-body states arise and the (2 + 1)-scattering length equals zero, are determined both for zero and infinite interaction strength λ 1 of the identical particles. A number of exact results are enlisted and asymptotic dependences both for m/m 1 → ∞ and λ 1 → −∞ are derived.Combining the numerical and analytical results, a schematic diagram showing the number of the three-body bound states and the sign of the (2 + 1)-scattering length in the plane of the mass ratio and interaction-strength ratio is deduced. The results provide a description of the homogeneous and mixed phases of atoms and molecules in dilute binary quantum gases.

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“…We also discuss new and unexpected results for the excited bound states. The three-body problem of interacting atoms with unequal mass has already attracted a lot of attention [23][24][25][26][27][28][29][30] . We will make contact with the corresponding results for the continuum model obtained in Ref.…”

Section: Introductionmentioning

confidence: 99%

Fermionic trimers in spin-dependent optical lattices

Orso¹,

Jolicœur²

2011

Comptes Rendus. Physique

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We investigate the formation of three-body bound states (trimers) in two-component Fermi gases confined in one dimensional optical lattice with spin-dependent tunneling rates. The binding energy and the effective mass of the trimer are obtained from the solution of the Mattis integral equation generalized to the case of unequal Bloch masses. We show that this equation admits multiple solutions corresponding to excited bound states, which are only stable for large mass asymmetry.

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Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions

Cited by 27 publications

References 31 publications

Crossover trimers connecting continuous and discrete scaling regimes

Crossover trimers connecting continuous and discrete scaling regimes

Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement

Fermionic trimers in spin-dependent optical lattices

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