On Critical Stability of Three Quantum Charges Interacting Through Delta Potentials

Cornean, Horia D.; Duclos, Pierre; Ricaud, Benjamin

doi:10.1007/s00601-005-0125-z

Cited by 11 publications

(16 citation statements)

References 7 publications

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“…It is rigorously proven that m/m 1 = 1 is the exact boundary, above which at least one bound state exists (as conjectured by [21]); the related conclusion is the existence of exactly One should discuss the connection of the present results with those, which take into account the finite interaction radius R e and (quasi)-1D geometry. The determination of the corrections due to finite interaction radius is not a trivial task, however, one expects that the corrections should be small for all calculated values provided R e /a and R e /a 1 are small, where a and a 1 are the two-body scattering lengths.…”

Section: Discussionmentioning

confidence: 55%

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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Section: Discussionmentioning

confidence: 55%

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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“…In addition, few analytical results were presented, in particular, it was shown that exactly one bound state of three equal-mass particles (m/m 1 = 1) exists for arbitrary λ 1 . Next, for two light fermions (in the limit of m/m 1 → 0) three particles are not bound for sufficiently large repulsive interaction between fermions, viz., for λ 1 /|λ| above the critical value ≈ 2.66735 [43], and exactly one bound state exists for λ 1 /|λ| below this value. To elucidate the general features of three one-dimensional particles, both numerical and analytical results were used to construct a schematic "phase" diagram, which shows the number of three-body bound states and a sign of the (2 + 1)-scattering length A in the plane of the parameters m/m 1 and λ 1 /|λ|.…”

Section: F One-dimensional Problemmentioning

confidence: 84%

Recent advances in description of few two-component fermions

Kartavtsev

Malykh

2014

Phys. Atom. Nuclei

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Overview of the recent advances in description of the few two-component fermions is presented.The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass m and a distinct particle of mass m 1 : it turns out that two L P = 1 − three-body bound states emerge if mass ratio m/m 1 increases up to the critical value µ c ≈ 13.607, above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for m/m 1 near µ c , and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.PACS numbers:

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“…Excitonic complexes in CNTs have been studied using many different approaches. 19,20,[48][49][50][51][52][53][54][55][56] In Ref. 19 it was demonstrated that the fractional dimensional model predicts the trion binding energy in CNTs with very high accuracy and therefore we use this as an example.…”

Section: Trions In Carbon Nanotubesmentioning

confidence: 99%

Variational quantum Monte Carlo study of charged excitons in fractional dimensional space

et al. 2011

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In this article we study excitons and trions in fractional dimensional spaces using the model suggested by C. Palmer [J. Phys. A: Math. Gen. 37, 6987 (2004)] through variational quantum Monte Carlo. We present a direct approach for estimating the exciton binding energy and discuss the von Neumann rejection-and Metropolis sampling methods. A simple variational estimate of trions is presented which shows good agreement with previous calculations done within the fractional dimensional model presented by D. R. Herrick and F. H. Stillinger [Phys. Rev. A 11, 42 (1975) and J. Math. Phys. 18, 1224Phys. 18, (1977]. We explain the spatial physics of the positive and negative trions by investigating angular and inter-atomic distances. We then examine the wave function and explain the differences between the positive and negative trions with heavy holes. As applications of the fractional dimensional model we study three systems: First we apply the model to estimate the energy of the hydrogen molecular ion H + 2 . Then we estimate trion binding energies in GaAs-based quantum wells and we demonstrate a good agreement with other theoretical work as well as experimentally observed binding energies. Finally, we apply the results to carbon nanotubes. We find good agreement with recently observed binding energies of the positively charged trion.

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On Critical Stability of Three Quantum Charges Interacting Through Delta Potentials

Abstract: Abstract. We consider three one dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.

Cited by 11 publications

References 7 publications

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

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

Recent advances in description of few two-component fermions

Variational quantum Monte Carlo study of charged excitons in fractional dimensional space

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