Functional renormalization and ultracold quantum gases

The 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.Comment: doctoral thesis, 187 pages, 60 figure

Effective description of dark matter as a viscous fluid

Treating dark matter at large scales as an effectively viscous fluid provides an improved framework for the calculation of the density and velocity power spectra compared to the standard assumption of an ideal pressureless fluid. We discuss how this framework can be made concrete through an appropriate coarse-graining procedure. We also review results that demonstrate that it improves the convergence of cosmological perturbation theory.Comment: 8 pages, 3 figures, talk by N. Tetradis at Quarks-2016, includes unpublished materia

Exact flow equation for composite operators

We propose an exact flow equation for composite operators and their correlation functions. This can be used for a scale-dependent partial bosonization or "flowing bosonization" of fermionic interactions, or for an effective change of degrees of freedom in dependence on the momentum scale. The flow keeps track of the scale dependent relation between effective composite fields and corresponding composite operators in terms of the fundamental fields.Comment: 7 pages, 1 figure, minor changes, published versio

Efimov physics from the functional renormalization group

Few-body physics related to the Efimov effect is discussed using the functional renormalization group method. After a short review of renormalization in its modern formulation we apply this formalism to the description of scattering and bound states in few-body systems of identical bosons and distinguishable fermions with two and three components. The Efimov effect leads to a limit cycle in the renormalization group flow. Recently measured three-body loss rates in an ultracold Fermi gas $^6$Li atoms are explained within this framework. We also discuss briefly the relation to the many-body physics of the BCS-BEC crossover for two-component fermions and the formation of a trion phase for the case of three species.Comment: 28 pages, 13 figures, invited contribution to a special issue of "Few-Body Systems" devoted to Efimov physics, published versio

Turbulent fluctuations around Bjorken flow

We study the evolution of local event-by-event deviations from smooth average fluid dynamic fields, as they can arise in heavy ion collisions from the propagation of fluctuating initial conditions. Local fluctuations around Bjorken flow are found to be governed by non-linear equations whose solutions can be characterized qualitatively in terms of Reynolds numbers. Perturbations at different rapidities decouple quickly, and satisfy (after suitable coordinate transformations) an effectively two-dimensional Navier-Stokes equation of non-relativistic form. We discuss the conditions under which non-linearities in these equations cannot be neglected and turbulent behavior is expected to set in.Comment: 4 pages, 2 figures - To appear in the conference proceedings for Quark Matter 2011, May 23 - May 28, Annecy, Franc

Quantum phase transition in Bose-Fermi mixtures

We study a quantum Bose-Fermi mixture near a broad Feshbach resonance at zero temperature. Within a quantum field theoretical model a two-step Gaussian approximation allows to capture the main features of the quantum phase diagram. We show that a repulsive boson-boson interaction is necessary for thermodynamic stability. The quantum phase diagram is mapped in chemical potential and density space, and both first and second order quantum phase transitions are found. We discuss typical characteristics of the first order transition, such as hysteresis or a droplet formation of the condensate which may be searched for experimentally.Comment: 16 pages, 17 figures; typos corrected, one figure adde

Functional renormalization for Bose-Einstein Condensation

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.Comment: 21 pages, 16 figures. Reference adde