Functional Renormalization and Ultracold Quantum Gases

Abstract

Functional renormalization and ultracold quantum gases AbstractThe method of functional renormalization is applied to the theoretical investigation of ultracold quantum gases. Flow equations are derived for a Bose gas with approximately pointlike interaction, for a Fermi gas with two (hyperfine) spin components in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover and for a Fermi gas with three components. The solution of the flow equations determine the properties of these systems both in the few-body regime and in thermal equilibrium.For the Bose gas this covers the quantum phase diagram, the condensate and superfluid fraction, the critical temperature, the correlation length, the specific heat or sound propagation. The properties are discussed both for three and two spatial dimensions. The discussion of the Fermi gas in the BCS-BEC crossover concentrates on the effect of particle-hole fluctuations but addresses the complete phase diagram. For the three component fermions, the flow equations in the few-body regime show a limit-cycle scaling and the Efimov tower of three-body bound states. Applied to the case of Lithium they explain recently observed three-body loss features. Extending the calculations by continuity to nonzero density, it is found that a new trion phase separates a BCS and a BEC phase for three component fermions close to a common resonance.More formal is the derivation of a new exact flow equation for scale dependent composite operators. This equation allows for example a better treatment of bound states.iii

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The $O(N)$ model

“…To this end, we will follow and extend the discussion in Refs. [43,[50][51][52][53] and discuss its technical properties as an alternative way of solving the integrals in Eqs. ( 1) and (2).…”

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part III: Shock and rarefaction waves in RG flows reveal limitations of the $N \rightarrow \infty$ limit in $O(N)$-type models

“…For related works on this toy model QFT, we again refer to Refs. [3,24,[33][34][35][36][37][38][39][40][41][42][43][44][45][48][49][50][51][52][53][54].…”

“…Refs. [3,24,33,[35][36][37][38][39][40][41][42][43][44][45][46][47]. Even a lot of aspects of the large-/infinite-N limit have been discussed already within this setup, cf.…”

Efimov Physics from the Functional Renormalization Group

“…As was discussed in detail in [10,11,12,13], numerous mathematical simplifications appear in fewbody problems compared with more complicated many-body problems. For instance, all Feynman diagrams with loop lines pointing in the same direction necessarily vanish.…”

“…The n-body sector is defined here as the set of one-particle irreducible 2n-point functions expressed in terms of the elementary ψ-fields. For a detailed discussion of the few-body hierarchy as well as a general proof of this feature see[13] 2. Due to the non-relativistic nature of the problem we can assign to the derivatives the scaling dimensions [∇] = 1 and [∂ τ ] = 2 which corresponds to the dynamical critical exponent z = 2.…”