Functional renormalization for Bose-Einstein Condensation

Abstract

We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three dimensional dilute gases, we find an upper bound on the scattering length a which is of the order of the microphysical scale - typically the range of the Van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density n, and find for the critical temperature T_c a deviation from the free theory, Delta T_c/T_c = 2.1 a n^{1/3}. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.

21 pages, 16 figures. Reference added

References in corpus (25)

• Exact evolution equation for the effective potential
• Critical Phenomena and Renormalization-Group Theory
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Aspects of the Functional Renormalisation Group
• Optimisation of the exact renormalisation group
• Theory of the Weakly Interacting Bose Gas
• Exact Renormalization Group Equations. An Introductory Review
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• The transition temperature of the dilute interacting Bose gas
• Transition temperature of a dilute homogeneous imperfect Bose gas
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Flow Equations for the BCS-BEC Crossover
• Non perturbative renormalisation group and momentum dependence of $n$-point functions (I)
• Two loop results from one loop computations and non perturbative solutions of exact evolution equations
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Renormalization Group Approach to the Infrared Behavior of a Zero-Temperature Bose System
• Infrared Behavior of Interacting Bosons at Zero Temperature
• High-accuracy scaling exponents in the local potential approximation
• Functional renormalization for quantum phase transitions with non-relativistic bosons
• Self-energy and critical temperature of weakly interacting bosons
• Non-perturbative renormalization-group approach to zero-temperature Bose systems
• Application of Renormalization Group Techniques to a Homogeneous Bose Gas at Finite Temperature
• Critical behavior of weakly interacting bosons: A functional renormalization group approach
• Equation of State for Helium-4 from Microphysics

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