Dimensional crossover of nonrelativistic bosons

Abstract

We investigate how confining a transverse spatial dimension influences the few- and many-body properties of non-relativistic bosons with pointlike interactions. Our main focus is on the dimensional crossover from three to two dimensions, which is of relevance for ultracold atom experiments. Using Functional Renormalization Group equations and T-matrix calculations we study how the phase transition temperature changes as a function of the spatial extent of the transverse dimension and relate the 3D and 2D s-wave scattering lengths. The analysis reveals how the properties of the lower-dimensional system are inherited from the higher-dimensional one during the renormalization group evolution. We limit the discussion to confinements in a potential well with periodic boundary conditions and argue why this qualitatively captures the physics of other compactifications such as transverse harmonic confinement as in cold atom experiments.

17 pages

References in corpus (22)

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• Weakly bound states of two- and three-boson systems in the crossover from two to three dimension
• Quasi-two-dimensional Fermi gases at finite temperature

Cited by in corpus (21)

• Efimov Physics: a review
• Dimensional crossover for the beyond-mean-field correction in Bose gases
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Dimensional crossovers and Casimir forces for the Bose gas in anisotropic optical lattices
• Strongly-interacting bosons at 2D-1D Dimensional Crossover
• Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one
• Quantum Lifshitz points and fluctuation-induced first-order phase transitions in imbalanced Fermi mixtures
• Confinement of two-body systems and calculations in $d$ dimensions
• Dimensional crossover of Bose-Einstein condensation phenomena in quantum gases confined within slab geometries
• Thermodynamics of Bose gases from functional renormalization with a hydrodynamic low-energy effective action
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Functional renormalization for repulsive Bose-Bose mixtures at zero temperature
• Criticality of the $O(2)$ model with cubic anisotropies from nonperturbative renormalization
• Dimensional crossover in ultracold Fermi gases from Functional Renormalisation
• Causality and dimensionality in geometric scattering
• Superfluid phase transition of nanoscale-confined helium-3
• Dimensional crossover in non-relativistic effective field theory
• Nonuniversal Equation of State of a Quasi-2D Bose Gas in Dimensional Crossover
• Uniaxial modulation and the Berezinskii-Kosterlitz-Thouless transition
• Renormalisation Group Flow and Kaon Condensation
• UV/IR symmetries of the $S$-matrix and RG flow