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Thomas Schaefer

Publications and source records attributed to Thomas Schaefer.

At least 37 records · Page 2Linked to original sources
arXiv2021

Dissipative superfluid hydrodynamics for the unitary Fermi gas

In this work we establish constraints on the temperature dependence of the shear viscosity $η$ in the superfluid phase of a dilute Fermi gas in the unitary limit. Our results are based on analyzing experiments that measure the aspect ratio of a deformed cloud after release from an optical trap. We discuss how to apply the two-fluid formalism to the unitary gas, and provide a suitable parametrization of the equation of state. We show that in expansion experiments the difference between the normal and superfluid velocities remains small, and can be treated as a perturbation. We find that expansion experiments favor a shear viscosity that decreases significantly in the superfluid regime. Using an exponential parametrization we find $η(T_c/(2T_F))< 0.37η(T_c/T_F)$, where $T_c$ is the critical temperature, $T_F$ is the local Fermi temperature of the gas.

cond-mat.quant-gas↗
arXiv2020

Multiplicative noise and the diffusion of conserved densities

Stochastic fluid dynamics governs the long time tails of hydrodynamic correlation functions, and the critical slowing down of relaxation phenomena in the vicinity of a critical point in the phase diagram. In this work we study the role of multiplicative noise in stochastic fluid dynamics. Multiplicative noise arises from the dependence of transport coefficients, such as the diffusion constants for charge and momentum, on fluctuating hydrodynamic variables. We study long time tails and relaxation in the diffusion of a conserved density (model B), and a conserved density coupled to the transverse momentum density (model H). Careful attention is paid to fluctuation-dissipation relations. We observe that multiplicative noise contributes at the same order as non-linear interactions in model B, but is a higher order correction to the relaxation of a scalar density and the tail of the stress tensor correlation function in model H.

hep-th↗
arXiv2020

QCD equation of state matched to lattice data and exhibiting a critical point singularity

We construct a family of equations of state for QCD in the temperature range 30 MeV $\leq T\leq$ 800 MeV and in the chemical potential range $0\leq μ_B \leq$ 450 MeV. These equations of state match available lattice QCD results up to $\mathcal{O}(μ_B^4)$ and in each of them we place a critical point in the 3D Ising model universality class. The position of this critical point can be chosen in the range of chemical potentials covered by the second Beam Energy Scan at RHIC. We discuss possible choices for the free parameters, which arise from mapping the Ising model onto QCD. Our results for the pressure, entropy density, baryon density, energy density and speed of sound can be used as inputs in the hydrodynamical simulations of the fireball created in heavy ion collisions. We also show our result for the second cumulant of the baryon number in thermal equilibrium, displaying its divergence at the critical point. In the future, comparisons between RHIC data and the output of the hydrodynamic simulations, including calculations of fluctuation observables, built upon the model equations of state that we have constructed may be used to locate the critical point in the QCD phase diagram, if there is one to be found.

hep-ph↗
arXiv2019

Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories

We investigate the singularity structure of the $(-1)^F$ graded partition function in QCD with $n_f \geq 1$ massive adjoint fermions in the large-$N$ limit. Here, $F$ is fermion number and $N$ is the number of colors. The large $N$ partition function is made reliably calculable by taking space to be a small three-sphere $S^3$. Singularites in the graded partition function are related to phase transitions and to Hagedorn behavior in the $(-1)^F$-graded density of states. We study the flow of the singularities in the complex "inverse temperature" $β$ plane as a function of the quark mass. This analysis is a generalization of the Lee-Yang-Fisher-type analysis for a theory which is always in the thermodynamic limit thanks to the large $N$ limit. We identify two distinct mechanisms for the appearance of physical Hagedorn singularities and center-symmetry changing phase transitions at real positive $β$, inflow of singularities from the $β=0$ point, and collisions of complex conjugate pairs of singularities.

hep-th↗
arXiv2019

Critical behavior of the bulk viscosity in QCD

We study the behavior of the bulk viscosity $ζ$ in QCD near a possible critical endpoint in the phase diagram. We verify the expectation that $(ζ/s)\sim a(ξ/ξ_0)^{x_ζ}$, where $s$ is the entropy density, $ξ$ is the correlation length, $ξ_0$ is the non-critical correlation length, $a$ is a constant and $x_ζ\simeq 3$. Using a recently developed equation of state that includes a critical point in the universality class of the Ising model we estimate the constant of proportionality $a$. We find that $a$ is typically quite small, $a\sim O(10^{-4})$. We observe, however, that the result is sensitive to the commonly made assumption that the Ising temperature axis is approximately aligned with the QCD baryon chemical potential axis. If this is not the case, then the critical $ζ/s$ can approach the non-critical value of $η/s$, where $η$ is the shear viscosity, even if the enhancement of the correlation length is modest, $ξ/ξ_0\sim 2$.

hep-ph↗
arXiv2019

Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid

We investigate the impact of hydrodynamic fluctuations on correlation functions in a scale invariant fluid with a conserved $U(1)$ charge. The kinetic equations for the two-point functions of pressure, momentum and heat energy densities are derived within the framework of stochastic hydrodynamics. The leading non-analytic contributions to the energy-momentum tensor as well as the $U(1)$ current are determined from the solutions to these kinetic equations. In the case of a static homogeneous background we show that the long time tails obtained from hydro-kinetic equations reproduce the one-loop results derived from statistical field theory. We use these results to establish bounds on transport coefficients. We generalize the stochastic equation to a background flow undergoing Bjorken expansion. We compute the leading fractional power $\mathcal{O}((τT)^{-3/2})$ correction to the $U(1)$ current and compare with the first order gradient term.

hep-th↗
arXiv2018

Critical Points at Infinity, Non-Gaussian Saddles, and Bions

It has been argued that many non-perturbative phenomena in quantum mechanics (QM) and quantum field theory (QFT) are determined by complex field configurations, and that these contributions should be understood in terms of of Picard-Lefschetz theory. In this work we compute the contribution from non-BPS multi-instanton configurations, such as instanton-anti-instanton $[{I}\bar{I}]$ pairs, and argue that these contributions should be interpreted as exact critical points at infinity. The Lefschetz thimbles associated with such critical points have a specific structure arising from the presence of non-Gaussian, quasi-zero mode (QZM), directions. When fermion degrees of freedom are present, as in supersymmetric theories, the effective bosonic potential can be written as the sum of a classical and a quantum potential. We show that in this case the semi-classical contribution of the critical point at infinity vanishes, but there is a non-trivial contribution that arises from its associated non-Gaussian QZM-thimble. This approach resolves several puzzles in the literature concerning the semi-classical contribution of correlated $[{I}\bar{I}]$ pairs. It has the surprising consequence that the configurations that dominate the expansion of observables, and the critical points that define the Lefschetz thimble decomposition need not be the same, a feature not present in the traditional Picard-Lefschetz approach.

hep-th↗
arXiv2018

Diffusive dynamics of critical fluctuations near the QCD critical point

A quantitatively reliable theoretical description of the dynamics of fluctuations in non-equilibrium is indispensable in the experimental search for the QCD critical point by means of ultra-relativistic heavy-ion collisions. In this work we consider the fluctuations of the net-baryon density which becomes the slow, critical mode near the critical point. Due to net-baryon number conservation the dynamics is described by the fluid dynamical diffusion equation, which we extend to contain a white noise stochastic current. Including nonlinear couplings from the 3d Ising model universality class in the free energy functional, we solve the fully interacting theory in a finite size system. We observe that purely Gaussian white noise generates non-Gaussian fluctuations, but finite size effects and exact net-baryon number conservation lead to significant deviations from the expected behavior in equilibrated systems. In particular the skewness shows a qualitative deviation from infinite volume expectations. With this benchmark established we study the real-time dynamics of the fluctuations. We recover the expected dynamical scaling behavior and observe retardation effects and the impact of critical slowing down near the pseudo-critical temperature.

nucl-th↗
arXiv2018

Fluctuating fluid dynamics for the QGP in the LHC and BES era

In an era of high-precision determinations of QGP properties a full incorporation of fluid dynamical fluctuations into our models has become crucial, in particular, when describing the dynamics of small systems or near the conjectured QCD critical point. In this talk we discuss some effects of the propagation of these fluctuations. For LHC physics we focus on fluctuations in the energy-momentum tensor, while the impact of fluctuations in the diffusive net-baryon density is studied to improve our knowledge on the formation of critical fluctuations being searched in current and future BES programs.

nucl-th↗
arXiv2018

Baryon number diffusion with critical fluctuations

The description of dynamical fluctuations near the QCD critical point in heavy-ion collisions is crucial for understanding the existing and upcoming experimental data from the beam energy scan programs. In this talk we discuss the evolution of fluctuations of the net-baryon density as given by a stochastic diffusion equation. We study equilibrium as well as dynamical systems for which we can show the impact of nonequilibrium effects on the second-order moment.

nucl-th↗
arXiv2017

Hydrodynamic tails and a fluctuation bound on the bulk viscosity

We study the small frequency behavior of the bulk viscosity spectral function using stochastic fluid dynamics. We obtain a number of model independent results, including the long-time tail of the bulk stress correlation function, and the leading non-analyticity of the spectral function at small frequency. We also establish a lower bound on the bulk viscosity which is weakly dependent on assumptions regarding the range of applicability of fluid dynamics. The bound on the bulk viscosity $ζ$ scales as $ζ_{\it min} \sim (P-\frac{2}{3}{\cal E})^2 \sum_i D_i^{-2}$, where $D_i$ are the diffusion constants for energy and momentum, and $P-\frac{2}{3}{\cal E}$, where $P$ is the pressure and ${\cal E}$ is the energy density, is a measure of scale breaking. Applied to the cold Fermi gas near unitarity, $|λ/a_s|\geq 1$ where $λ$ is the thermal de Broglie wave length and $a_s$ is the $s$-wave scattering length, this bound implies that the ratio of bulk viscosity to entropy density satisfies $ζ/s \geq 0.1\hbar/k_B$. Here, $\hbar$ is Planck's constant and $k_B$ is Boltzmann's constant.

cond-mat.quant-gas↗
arXiv2017

Determination of the density and temperature dependence of the shear viscosity of a unitary Fermi gas based on hydrodynamic flow

We determine the shear viscosity of the ultracold Fermi gas at unitarity in the normal phase using hydrodynamic expansion data. The analysis is based on a generalized fluid dynamic framework which ensures a smooth transition between the fluid dynamic core of the cloud and the ballistic corona. We use expansion data taken by Joseph et al. and measurements of the equation of state by Ku et al. We find that the shear viscosity to particle density ratio just above the critical temperature is $η/n|_{T_c}=0.41\pm 0.11$. We also obtain evidence that the shear viscosity to entropy density ratio has a minimum slightly above $T_c$ with $η/s |_{\it min}=0.50\pm 0.10$.

cond-mat.quant-gas↗
arXiv2017

From cold Fermi fluids to the hot QGP

Strongly coupled quantum fluids are found in different forms, including ultracold Fermi gases or tiny droplets of extremely hot Quark-Gluon Plasma. Although the systems differ in temperature by many orders of magnitude, they exhibit a similar almost inviscid fluid dynamical behavior. In this work, we summarize some of the recent theoretical developments toward better understanding this property in cold Fermi gases at and near unitarity.

cond-mat.quant-gas↗
arXiv2016

Behavior of universal critical parameters in the QCD phase diagram

We determine the dependence of important parameters for critical fluctuations on temperature and baryon chemical potential in the QCD phase diagram. The analysis is based on an identification of the fluctuations of the order parameter obtained from the Ising model equation of state and the Ginzburg-Landau effective potential approach. The impact of the mapping from Ising model variables to QCD thermodynamics is discussed.

nucl-th↗
arXiv2016

Quantum Chromodynamics: Computational Aspects

We present a brief introduction to QCD, the QCD phase diagram, and non-equilibrium phenomena in QCD. We emphasize aspects of the theory that can be addressed using computational methods, in particular euclidean path integral Monte Carlo, fluid dynamics, kinetic theory, classical field theory and holographic duality.

nucl-th↗
arXiv2016

Impact of resonance decays on critical point signals in net-proton fluctuations

The non-monotonic beam energy dependence of the higher cumulants of net-proton fluctuations is a widely studied signature of the conjectured presence of a critical point in the QCD phase diagram. In this work we study the effect of resonance decays on critical fluctuations. We show that resonance effects reduce the signatures of critical fluctuations, but that for reasonable parameter choices critical effects in the net-proton cumulants survive. The relative role of resonance decays has a weak dependence on the order of the cumulants studied with a slightly stronger suppression of critical effects for higher-order cumulants.

nucl-th↗