One-particle dynamical correlations in the one-dimensional Bose gas

By J. Caux, Pasquale Calabrese, N. Slavnov. 2006

134 citations recorded by the source corpus.

The momentum- and frequency-dependent one-body correlation function of the one-dimensional interacting Bose gas (Lieb–Liniger model) in the repulsive regime is studied using the Algebraic Bethe Ansatz and numerics. We first provide a determinant representation for the field form factor which is well adapted to numerical evaluation. The correlation function is then reconstructed to high accuracy for systems with finite but large numbers of particles, for a wide range of values of the interaction parameter. Our results are extensively discussed, in particular their specialization to the static case.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/abe125205beb3ad83f2dd5baf7d256920215491a

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In Atomic and Molecular Physics, and Optics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Crystallization of strongly interacting photons in a nonlinear optical fibre (2007, methodology): “Solutions based on perturbation theory or classical equations of motion break down and one needs to use non-perturbative approaches such as the Bethe ansatz solution [26, 27, 28, 29] or the Luttinger liquid formalism [30].”
One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm (2011, background): “Recently many new theoretical results were obtained in this direction (Calabrese and Caux, 2007; Caux and Calabrese, 2006; Caux et al., 2007; Cazalilla et al., 2011; Cheianov et al., 2006a,b; Cherny and Brand, 2009; Deuar et al., 2009; Gangardt and Shlyapnikov, 2003a,b; Golovach et al., 2009;…”
Fermi gases in one dimension: From Bethe ansatz to experiments (2013, background): “Further developments in the theoretical study of correlation functions have been reported (Calabrese and Caux, 2007; Caux and Calabrese, 2006; Caux et al., 2007; Gangardt and Shlyapnikov, 2003a,b; Kitanine et al., 2009; Kormos et al., 2009).”
Probing quantum and thermal noise in an interacting many-body system (2007, methodology): “Recent analysis showed [51, 52] that the Luttinger liquid formalism provides extremely accurate description of the correlation functions of the Lieb-Linger model for both long distances and distances just beyond the healing length.”
One dimensional bosons: From condensed matter systems to ultracold gases (2011, methodology): “For the Lieb-Liniger model, Caux and Calabrese (2006) and Caux et al. (2007) computed the dynamic structure factor S(k, ω) = ∫ dxdτ ei(ωτ−kx) 〈ρ̂(x, τ)ρ̂(0, 0)〉 and the single-particle Green’s function G<(k, ω) = ∫ dxdτ ei(ωτ−kx) 〈Ψ̂†(x, τ)Ψ̂(0, 0)〉.”