Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0412225

Three-body problem for ultracold atoms in quasi-one-dimensional traps

C. Mora·R. Egger·A. O. Gogolin
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the three-body problem for both fermionic and bosonic cold atom gases in a parabolic transverse trap of lengthscale $a_\perp$. For this quasi-one-dimensional (1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length $a$, and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths, $a_{ad}$ and $b_{ad}$. In the tightly bound `dimer limit', $a_\perp/a\to\infty$, we find $b_{ad}=0$, and $a_{ad}$ is linked to the 3D atom-dimer scattering length. In the weakly bound `BCS limit', $a_\perp/a\to-\infty$, a connection to the Bethe Ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is non-universal: $a_{ad}$ and $b_{ad}$ depend both on $a_\perp/a$ and on a parameter $R^*$ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.

Explore related subjects

cond-mat.stat-mechcond-mat.mes-hallphysics.atom-phquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

C. Mora, R. Egger, A. O. Gogolin. 2005-03-15. Three-body problem for ultracold atoms in quasi-one-dimensional traps. https://doi.org/10.1103/physreva.71.052705

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A General Solution for Network Models with Pairwise Edge Coupling

Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous results obtained for specific interaction structures. We use the Hubbard-Stratonovich transform to show that such higher order models can be decoupled into families of effectively separable random graph models, which might be enhanced with auxiliary, possibly multi-valued, parameters identifying the thermodynamical phase of the system. Moreover, given the diagonalizability of couplings between links, we carry out the full computation of the partition functions and discuss why in some cases they can effectively reduce to the one for the Mean-Field case.

cond-mat.stat-mech↗
arXiv2026

Dynamic Eikonal Attenuation and Mutual Coherence of Quantum Particles due to Equilibrium Coulomb Fluctuations

We develop a dynamic theory of eikonal attenuation and mutual coherence for a quantum particle propagating through equilibrium Coulomb fluctuations. The one-particle length $\ell$ is the attenuation length of the ensemble-averaged retarded propagator, not an Anderson localization length or a transport mean free path. For a collisionless classical one-component plasma (OCP), the potential spectrum follows from the fluctuation--dissipation theorem and the RPA dielectric function. In suitable plasma parameter windows, both fast and slow probe regimes are physically meaningful. Fast probes recover the Coulomb logarithm with the dynamical infrared length $v/ω_{\rm p}$. Slow probes yield $G(v)\propto v$ and, in the controlled weak branch, $\ell\propto k$. We derive an exact finite-thickness mutual-coherence expression and a closed slow-regime transverse scaling function. Within the controlled slow-OCP and thick-slab window, the logarithmic two-ray visibility scales as $v^{-1}$ at fixed transverse separation, in contrast to the $v^{-2}$ dependence for frozen finite-slab fluctuations. For a symmetric diffusive electrolyte, linearized stochastic density functional theory gives the exact on-shell result $G_{\rm el}(v)=(m^2C/\hbar^4)\operatorname{arsinh}[v/(2Dκ)]$, where $C=k_{\mathrm B}Tq_0^2/(4π\varepsilon_b)$. For ordinary liquid electrolytes, the slow diffusive limit is inaccessible within the spatial eikonal regime and is therefore a formal asymptote. The physically relevant electrolyte limit is instead that of a fast probe, $v\gg Dκ$, where the diffusive charge relaxation generates an intrinsic infrared length $v/(Dκ^2)$ absent from the quasi-static theory.

cond-mat.stat-mech↗
arXiv2026

Planckian dissipation from classical hydrodynamics

Hydrodynamics describes the long-time, long-distance dynamics of interacting quantum systems by classical equations, yet at low temperature quantum fluctuations might eventually invalidate this classical picture. Here we ask what it takes for a quantum system to sustain a consistently classical hydrodynamic description. Our starting point is the quantum fluctuation-dissipation theorem which, when read in the time domain, acts as a blurring of the fine details of correlation functions on a Planckian time-scale. We analyse how this blurring interacts with the diffusive large-deviation form of correlators assuming the existence of a hydrodynamic light cone velocity, and show that the interior of the cone splits into a classical region, where correlation and response satisfy the classical fluctuation-dissipation relation, and a quantum region, where they deviate sharply from it. We illustrate the mechanism on three phenomenological hydrodynamic equations - diffusion, telegraph and diffusive-telegraph. Preserving a finite classical region as the temperature is lowered forces the current relaxation rate to be bounded from above by the Planckian rate. This bound connects to bounds on diffusivity, equilibration time and shear viscosity. In this way, a Planckian bound on dissipation emerges not as a quantum constraint on microscopic dynamics, but as the price a system pays to remain describable by classical hydrodynamics down to low temperatures.

cond-mat.stat-mech↗