arXiv subjects

Stefan Floerchinger

Publications and source records attributed to Stefan Floerchinger.

84 records · Page 5Linked to original sources

arXiv2014

Mode-by-mode hydrodynamics: ideas and concepts

The main ideas, technical concepts and perspectives for a mode resolved description of the hydrodynamical regime of relativistic heavy ion collisions are discussed. A background-fluctuation splitting and a Bessel-Fourier expansion for the fluctuating part of the hydrodynamical fields allows for a complete characterization of initial conditions, the fluid dynamical propagation of single modes, the study of interaction effects between modes, the determination of the associated particle spectra and the generalization of the whole program to event-by-event correlations and probability distributions.

nucl-th↗

arXiv2014

Mode-by-mode fluid dynamics for relativistic heavy ion collisions

We propose to study the fluid dynamic propagation of fluctuations in relativistic heavy ion collisions differentially with respect to their azimuthal, radial and longitudinal wavelength. To this end, we introduce a background-fluctuation splitting and a Bessel-Fourier decomposition of the fluctuating modes. We demonstrate how the fluid dynamic evolution of realistic events can be build up from the propagation of individual modes. We describe the main elements of this mode-by-mode fluid dynamics, and we discuss its use in the fluid dynamic analysis of heavy ion collisions. As a first illustration, we quantify to what extent only fluctuations of sufficiently large radial wave length contribute to harmonic flow coefficients. We find that fluctuations of short wave length are suppressed not only due to larger dissipative effects, but also due to a geometrical averaging over the freeze-out hyper surface. In this way, our study further substantiates the picture that harmonic flow coefficients give access to a coarse-grained version of the initial conditions for heavy ion collisions, only.

hep-ph↗

arXiv2013

How (non-) linear is the hydrodynamics of heavy ion collisions?

We provide evidence from full numerical solutions that the hydrodynamical evolution of initial density fluctuations in heavy ion collisions can be understood order-by-order in a perturbative series in deviations from a smooth and azimuthally symmetric background solution. To leading linear order, modes with different azimuthal wave numbers do not mix. Quadratic and higher order corrections are small and can be understood as overtones with corresponding wave numbers.

hep-ph↗

arXiv2013

Characterization of initial fluctuations for the hydrodynamical description of heavy ion collisions

Event-by-event fluctuations in the initial conditions for a hydrodynamical description of heavy-ion collisions are characterized. We propose a Bessel-Fourier decomposition with respect to the azimuthal angle, the radius in the transverse plane and rapidity. This allows for a complete characterization of fluctuations in all hydrodynamical fields including energy density, pressure, fluid velocity, shear stress and bulk viscous pressure. It has the advantage that fluctuations can be ordered with respect to their wave length and that they can be propagated mode-by-mode within the hydrodynamical formalism. Event ensembles can then be characterized in terms of a functional probability distribution. For the event ensemble of a Monte Carlo Glauber model, we provide evidence that the latter is close to Gaussian form, thus allowing for a particularly simple characterization of the event distribution.

hep-ph↗

arXiv2012

Analytic continuation of functional renormalization group equations

Functional renormalization group equations are analytically continued from imaginary Matsubara frequencies to the real frequency axis. On the example of a scalar field with O(N) symmetry we discuss the analytic structure of the flowing action and show how it is possible to derive and solve flow equations for real-time properties such as propagator residues and particle decay widths. The formalism conserves space-time symmetries such as Lorentz or Galilei invariance and allows for improved, self-consistent approximations in terms of derivative expansions in Minkowski space.

hep-th↗

arXiv2012

Fluctuations around Bjorken Flow and the onset of turbulent phenomena

We study how fluctuations in fluid dynamic fields can be dissipated or amplified within the characteristic spatio-temporal structure of a heavy ion collision. The initial conditions for a fluid dynamic evolution of heavy ion collisions may contain significant fluctuations in all fluid dynamical fields, including the velocity field and its vorticity components. We formulate and analyze the theory of local fluctuations around average fluid fields described by Bjorken's model. For conditions of laminar flow, when a linearized treatment of the dynamic evolution applies, we discuss explicitly how fluctuations of large wave number get dissipated while modes of sufficiently long wave-length pass almost unattenuated or can even be amplified. In the opposite case of large Reynold's numbers (which is inverse to viscosity), we establish that (after suitable coordinate transformations) the dynamics is governed by an evolution equation of non-relativistic Navier-Stokes type that becomes essentially two-dimensional at late times. One can then use the theory of Kolmogorov and Kraichnan for an explicit characterization of turbulent phenomena in terms of the wave-mode dependence of correlations of fluid dynamic fields. We note in particular that fluid dynamic correlations introduce characteristic power-law dependences in two-particle correlation functions.

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arXiv2012

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.

cond-mat.quant-gas↗

arXiv2012

Chemical freeze-out in heavy ion collisions at large baryon densities

We argue that the chemical freeze-out in heavy ion collisions at high baryon density is not associated to a phase transition or rapid crossover. We employ the linear nucleon-meson model with parameters fixed by the zero-temperature properties of nuclear matter close to the liquid-gas quantum phase transition. For the parameter region of interest this yields a reliable picture of the thermodynamic and chiral properties at non-zero temperature. The chemical freeze-out observed in low-energy experiments occurs when baryon densities fall below a critical value of about 15 percent of nuclear density. This region in the phase diagram is far away from any phase transition or rapid crossover.

nucl-th↗

arXiv2011

Hydrodynamic collective modes for cold trapped gases

We suggest that collective oscillation frequencies of cold trapped gases can be used to test predictions from quantum many-body physics. Our motivation lies both in rigid experimental tests of theoretical calculations and a possible improvement of measurements of particle number, chemical potential or temperature. We calculate the effects of interaction, dimensionality and thermal fluctuations on the collective modes of a dilute Bose gas in the hydrodynamic limit. The underlying equation of state is provided by non-perturbative Functional Renormalization Group or by Lee--Yang theory. The spectrum of oscillation frequencies could be measured by response techniques. Our findings are generalized to bosonic or fermionic quantum gases with an arbitrary equation of state in the two-fluid hydrodynamic regime. For any given equation of state P(μ,T) and normal fluid density n_n(μ,T) the collective oscillation frequencies in a $d$-dimensional isotropic potential are found to be the eigenvalues of an ordinary differential operator. We suggest a method of numerical solution and discuss the zero-temperature limit. Exact results are provided for harmonic traps and certain special forms of the equation of state. We also present a phenomenological treatment of dissipation effects and discuss the possibility to excite the different eigenmodes individually.

cond-mat.quant-gas↗

arXiv2011

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.

cond-mat.quant-gas↗

arXiv2011

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.

nucl-th↗

arXiv2010

Functional renormalization for the BCS-BEC crossover

We review the functional renormalization group (RG) approach to the BCS-BEC crossover for an ultracold gas of fermionic atoms. Formulated in terms of a scale-dependent effective action, the functional RG interpolates continuously between the atomic or molecular microphysics and the macroscopic physics on large length scales. We concentrate on the discussion of the phase diagram as a function of the scattering length and the temperature which is a paradigm example for the non-perturbative power of the functional RG. A systematic derivative expansion provides for both a description of the many-body physics and its expected universal features as well as an accurate account of the few-body physics and the associated BEC and BCS limits.

cond-mat.quant-gas↗