Fermion-Boson Duality of One-Dimensional Quantum Particles with Generalized Contact Interactions

Cheon, Taksu; Shigehara, Takaomi

doi:10.1103/physrevlett.82.2536

Cited by 222 publications

(347 citation statements)

References 29 publications

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“…However, after mapping to the bosonic Hilbert space one has the usual Lieb-Liniger interaction g B 1D δ(z jℓ ) which is well-behaved in all perturbation orders and in second quantization. This generalization of the Fermi-Bose mapping theorem, due to Cheon and Shigehara [26], extends the useful domain of the mapping of Eqs. (55) and (56) to the whole range of coupling constants g B 1D and g F 1D .…”

Section: B Magnetically Trapped Spin-aligned Fermionsmentioning

confidence: 99%

“…Although a discontinuity in the derivative is a wellknown consequence of the zero-range delta function pseudopotential and plays a crucial role in the solution of the Lieb-Liniger model [23], discontinuities of ψ itself have received little attention, although they have been discussed previously by Cheon and Shigehara [26] and are implicit in the recent work of Granger and Blume [21]. For a fermionic wave function ψ F the discontinuity 2ψ F (0+) is a trivial consequence of antisymmetry together with the fact that a nonzero odd-wave scattering length cannot be obtained in the limit z 0 → 0 unless ψ F (0±) = 0.…”

Section: Spin-aligned Fermionsmentioning

confidence: 99%

“…This will be done first for the original mapping for impenetrable bosons (γ ≫ 1) [1,2], then for a very powerful generalization to arbitrary values of γ due to Cheon and Shigehara [26], and finishing with a further generalization to the case of spinor Fermi and Bose gases, important for applications to optically trapped fermionic atoms whose spins are unconstrained.…”

Section: Fermi-bose Mapping Methods and N-atom Ground Statesmentioning

confidence: 99%

“…In Sec. III B a very powerful generalization of this mapping to arbitrary coupling strength [26] will be described and its application to determination of the ground state of the magnetically trapped, spinaligned Fermi gas will be reviewed, and in Sec. III C application of two further generalizations of the mapping to determination of the ground state of the optically trapped spinor Fermi gas will be described.…”

Section: Introductionmentioning

confidence: 99%

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Effective interactions, Fermi–Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides

Girardeau

Nguyen

Olshanii

2004

Optics Communications

141

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Derivation of effective zero-range one-dimensional (1D) interactions between atoms in tight waveguides is reviewed, as is the Fermi-Bose mapping method for determination of exact and stronglycorrelated many-body ground states of ultracold bosonic and fermionic atomic vapors in such waveguides, including spin degrees of freedom. Odd-wave 1D interactions derived from 3D p-wave scattering are included as well as the usual even-wave interactions derived from 3D s-wave scattering, with emphasis on the role of 3D Feshbach resonances for selectively enhancing s-wave or p-wave scattering so as to reach 1D confinement-induced resonances of the even and odd-wave interactions. A duality between 1D fermions and bosons with zero-range interactions suggested by Cheon and Shigehara is shown to hold for the effective 1D dynamics of a spinor Fermi gas with both even and odd-wave interactions and that of a spinor Bose gas with even and odd-wave interactions, with even(odd)-wave Bose coupling constants inversely related to odd(even)-wave Fermi coupling constants. Some recent applications of Fermi-Bose mapping to determination of many-body ground states of Bose gases and of both magnetically trapped, spin-aligned and optically trapped, spin-free Fermi gases are described, and a new generalized Fermi-Bose mapping is used to determine the phase diagram of ground-state total spin of the spinor Fermi gas as a function of its even and odd-wave coupling constants.

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Section: B Magnetically Trapped Spin-aligned Fermionsmentioning

confidence: 99%

Section: Spin-aligned Fermionsmentioning

confidence: 99%

Section: Fermi-bose Mapping Methods and N-atom Ground Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effective interactions, Fermi–Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides

Girardeau

Nguyen

Olshanii

2004

Optics Communications

141

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“…In dimension one, on the other hand, the larger family U (2) of allowed interactions admits a number of more intriguing features. These include the 'fermion-boson duality', which is the phenomenon that two systems with distinct point interactions related by coupling inversion shares an identical spectrum with symmetric and antisymmetric states interchanged [10]. The other notable feature is the spectral anholonomy [11], which is the appearance of a double spiral structure of the energy levels when the subfamily of parity invariant point interactions is considered.…”

Section: Introductionmentioning

confidence: 99%

Symmetry, Duality, and Anholonomy of Point Interactions in One Dimension

Cheon¹,

Fülöp²,

Tsutsui³

2001

Annals of Physics

Self Cite

148

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Abstract. We analyze the spectral structure of the one dimensional quantum mechanical system with point interaction, which is known to be parametrized by the group U (2). Based on the classification of the interactions in terms of symmetries, we show, on a general ground, how the fermion-boson duality and the spectral anholonomy recently discovered can arise. A vital role is played by a hidden su(2) formed by a certain set of discrete transformations, which becomes a symmetry if the point interaction belongs to a distinguished U (1) subfamily in which all states are doubly degenerate. Within the U (1), there is a particular interaction which admits the interpretation of the system as a supersymmetric Witten model.

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Fermi-Bose mapping for one-dimensional Bose gases

Yukalov¹,

Girardeau²

2005

Laser Phys. Lett.

173

207

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One-dimensional Bose gases are considered, interacting either through the hard-core potentials or through the contact delta potentials. Interest in these gases gained momentum because of the recent experimental realization of quasi-one-dimensional Bose gases in traps with tightly confined radial motion, achieving the Tonks-Girardeau (TG) regime of strongly interacting atoms. For such gases the Fermi-Bose mapping of wavefunctions is applicable. The aim of the present communication is to give a brief survey of the problem and to demonstrate the generality of this mapping by emphasizing that: (i) It is valid for nonequilibrium wavefunctions, described by the time-dependent Schr\"odinger equation, not merely for stationary wavefunctions. (ii) It gives the whole spectrum of all excited states, not merely the ground state. (iii) It applies to the Lieb-Liniger gas with the contact interaction, not merely to the TG gas of impenetrable bosons.Comment: Brief review, Latex file, 15 page

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Fermion-Boson Duality of One-Dimensional Quantum Particles with Generalized Contact Interactions

Cited by 222 publications

References 29 publications

Effective interactions, Fermi–Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides

Effective interactions, Fermi–Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides

Symmetry, Duality, and Anholonomy of Point Interactions in One Dimension

Fermi-Bose mapping for one-dimensional Bose gases

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