arXiv subjects

Thomas Schaefer

Publications and source records attributed to Thomas Schaefer.

At least 55 records · Page 3Linked to original sources

arXiv2016

A generalized Theory of Diffusion based on Kinetic Theory

We propose to use spin hydrodynamics, a two-fluid model of spin propagation, as a generalization of the diffusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick's law and the diffusion equation. In the opposite limit spin hydrodynamics is equivalent to a collisionless Boltzmann treatment of spin propagation. Spin hydrodynamics avoids unphysical effects that arise when the diffusion equation is used to describe to a strongly interacting gas with a dilute corona. We apply spin hydrodynamics to the problem of spin diffusion in a trapped atomic gas. We find that the observed spin relaxation rate in the high temperature limit [Sommer et al., Nature 472, 201 (2011)] is consistent with the diffusion constant predicted by kinetic theory.

cond-mat.quant-gas↗

arXiv2016

Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD

We show that there exists a special compactification of QCD on $\mathbb{R}^3 \times S^1$ in which the theory has a domain where continuous chiral symmetry breaking is analytically calculable. We give a microscopic derivation of the chiral lagrangian, the chiral condensate, and the Gell-Mann-Oakes-Renner relation $m_π^2 f_π^2 = m_q \langle \bar{q} q \rangle$. Abelian duality, monopole operators, and flavor-twisted boundary conditions, or a background flavor holonomy, play the main roles. The flavor twisting leads to the new effect of fractional jumping of fermion zero modes among monopole-instantons. Chiral symmetry breaking is induced by monopole-instanton operators, and the Nambu-Goldstone pions arise by color-flavor transmutation from gapless "dual photons". We also give a microscopic picture of the "constituent quark" masses. Our results are consistent with expectations from chiral perturbation theory at large $S^1$, and yield strong support for adiabatic continuity between the small-$S^1$ and large-$S^1$ regimes. We also find concrete microscopic connections between ${\cal N}=1$ and ${\cal N}=2$ supersymmetric gauge theory dynamics and non-supersymmetric QCD dynamics.

hep-th↗

arXiv2016

Model-independent determination of the shear viscosity of a trapped unitary Fermi gas: Application to high temperature data

Determinations of the shear viscosity of trapped ultracold gases suffer from systematic, uncontrolled uncertainties related to the treatment of the dilute part of the gas cloud. In this work we present an analysis of expansion experiments based on a new method, anisotropic fluid dynamics, that interpolates between Navier-Stokes fluid dynamics at the center of the cloud and ballistic behavior in the dilute corona. We validate the method using a comparison between anisotropic fluid dynamics and numerical solutions of the Boltzmann equation. We then apply anisotropic fluid dynamics to the expansion data reported by Cao et al. In the high temperature limit we find $η=0.282(mT)^{3/2}$, which agrees within about 5\% with the theoretical prediction $η=0.269(mT)^{3/2}$.

cond-mat.quant-gas↗

arXiv2016

Properties of hot and dense matter from relativistic heavy ion collisions

We review the progress achieved in extracting the properties of hot and dense matter from relativistic heavy ion collisions at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory and the large hadron collider (LHC) at CERN. We focus on bulk properties of the medium, in particular the evidence for thermalization, aspects of the equation of state, transport properties, as well as fluctuations and correlations. We also discuss the in-medium properties of hadrons with light and heavy quarks, and measurements of dileptons and quarkonia. This review is dedicated to the memory of Gerald E. Brown.

nucl-th↗

arXiv2015

Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence

We show that the semi-classical analysis of generic Euclidean path integrals necessarily requires complexification of the action and measure, and consideration of complex saddle solutions. We demonstrate that complex saddle points have a natural interpretation in terms of the Picard-Lefschetz theory. Motivated in part by the semi-classical expansion of QCD with adjoint matter on ${\mathbb R}^3\times S^1$, we study quantum-mechanical systems with bosonic and fermionic (Grassmann) degrees of freedom with harmonic degenerate minima, as well as (related) purely bosonic systems with harmonic non-degenerate minima. We find exact finite action non-BPS bounce and bion solutions to the holomorphic Newton equations. We find not only real solutions, but also complex solution with non-trivial monodromy, and finally complex multi-valued and singular solutions. Complex bions are necessary for obtaining the correct non-perturbative structure of these models. In the supersymmetric limit the complex solutions govern the ground state properties, and their contribution to the semiclassical expansion is necessary to obtain consistency with the supersymmetry algebra. The multi-valuedness of the action is either related to the hidden topological angle or to the resurgent cancellation of ambiguities. We also show that in the approximate multi-instanton description the integration over the complex quasi-zero mode thimble produces the most salient features of the exact solutions. While exact complex saddles are more difficult to construct in quantum field theory, the relation to the approximate thimble construction suggests that such solutions may be underlying some remarkable features of approximate bion saddles in quantum field theories.

hep-th↗

arXiv2015

Complexified path integrals, exact saddles and supersymmetry

In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semi-classical expansion is in conflict with basic properties such as positive-semidefiniteness of the spectrum, and constraints of supersymmetry. Generic saddles are not only complex, but also possibly multi-valued, and even singular. This is in contrast to instanton solutions, which are real, smooth, and single-valued. The multi-valuedness of the action can be interpreted as a hidden topological angle, quantized in units of $π$ in supersymmetric theories. The general ideas also apply to non-supersymmetric theories.

hep-th↗

arXiv2015

Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics

We consider the time evolution of a dilute atomic Fermi gas after release from a trapping potential. A common difficulty with using fluid dynamics to study the expansion of the gas is that the theory is not applicable in the dilute corona, and that a naive treatment of the entire cloud using fluid dynamics leads to unphysical results. We propose to remedy this problem by including certain non-hydrodynamic degrees of freedom, in particular anisotropic components of the pressure tensor, in the theoretical description. We show that, using this method, it is possible to describe the crossover from fluid dynamics to ballistic expansion locally. We illustrate the use of anisotropic fluid dynamics by studying the expansion of the dilute Fermi gas at unitarity using different functional forms of the shear viscosity, including a shear viscosity which is solely a function of temperature, $η\sim (mT)^{3/2}$, as predicted by kinetic theory in the dilute limit.

cond-mat.quant-gas↗

arXiv2015

Bose-Einstein condensates in neutron stars

In the two decades since the appearance of the book "Bose-Einstein Condensation" in 1995, there have been a number of developments in our understanding of dense matter. After a brief overview of neutron star structure and the Bose-Einstein condensed phases that have been proposed, we describe selected topics, including neutron and proton pairing gaps, the physics of the inner crust of neutron stars, where a neutron fluid penetrates a lattice of nuclei, meson condensates, and pairing in dense quark matter. Especial emphasis is placed on basic physical effects and on connections to the physics of cold atomic gases.

nucl-th↗

arXiv2015

Hidden topological angles and Lefschetz thimbles

We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta-parameters in the lagrangian. They arise as invariant angle associated with saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles). Physical effects of HTAs become most transparent upon analytic continuation in $n_f$ to non-integer number of flavors, reducing in the integer $n_f$ limit to a $\mathbb Z_2$ valued phase difference between dominant saddles. In ${\cal N}=1$ super Yang-Mills theory we demonstrate the microscopic mechanism for the vanishing of the gluon condensate. The same effect leads to an anomalously small condensate in a QCD-like $SU(N)$ gauge theory with fermions in the two-index representation. The basic phenomenon is that, contrary to folklore, the gluon condensate can receive both positive and negative contributions in a semi-classical expansion. In quantum mechanics, a HTA leads to a difference in semi-classical expansion of integer and half-integer spin particles.

hep-th↗

arXiv2014

Second order fluid dynamics for the unitary Fermi gas from kinetic theory

We compute second order transport coefficients of the dilute Fermi gas at unitarity. The calculation is based on kinetic theory and the Boltzmann equation at second order in the Knudsen expansion. The second order transport coefficients describe the shear stress relaxation time, non-linear terms in the strain-stress relation, and non-linear couplings between vorticity and strain. An exact calculation in the dilute limit gives $τ_R=η/P$, where $τ_R$ is the shear stress relaxation time, $η$ is the shear viscosity, and $P$ is pressure. This relation is identical to the result obtained using the Bhatnagar-Gross-Krook (BGK) approximation to the collision term, but other transport coefficients are sensitive to the exact collision integral.

cond-mat.quant-gas↗

arXiv2014

Medium effects and the shear viscosity of the dilute Fermi gas away from the conformal limit

We study the shear viscosity of a dilute Fermi gas as a function of the scattering length in the vicinity of the unitarity limit. The calculation is based on kinetic theory, which provides a systematic approach to transport properties in the limit in which the fugacity $z=nλ^3/2$ is small. Here, $n$ is the density of the gas and $λ$ is the thermal wave length of the fermions. At leading order in the fugacity expansion the shear viscosity is independent of density, and the minimum shear viscosity is achieved at unitarity. At the next order medium effects modify the scattering amplitude as well as the quasi-particle energy and velocity. We show that these effects shift the minimum of the shear viscosity to the Bose-Einstein condensation (BEC) side of the resonance, in agreement with the result of recent experiments.

cond-mat.quant-gas↗

arXiv2014

Viscosity spectral function of a scale invariant non-relativistic fluid from holography

We study the viscosity spectral function of a holographic 2+1 dimensional fluid with Schroedinger symmetry. The model is based on a twisted compactification of $Ads_5\times S_5$. We numerically compute the spectral function of the stress tensor correlator for all frequencies, and analytically study the limits of high and low frequency. We compute the shear viscosity, the viscous relaxation time, and the quasi-normal mode spectrum in the shear channel. We find a number of unexpected results: The high frequency behavior is governed by a fractional 1/3 power law, the viscous relaxation time is negative, and the quasi-normal mode spectrum in the shear channel is not doubled.

hep-th↗

arXiv2014

Fluid Dynamics and Viscosity in Strongly Correlated Fluids

We review the modern view of fluid dynamics as an effective low energy, long wavelength theory of many body systems at finite temperature. We introduce the concept of a nearly perfect fluid, defined by a ratio $η/s$ of shear viscosity to entropy density of order $\hbar/k_B$ or less. Nearly perfect fluids exhibit hydrodynamic behavior at all distances down to the microscopic length scale of the fluid. We summarize arguments that suggest that there is fundamental limit to fluidity, and we review the current experimental situation of measurements of $η/s$ in strongly coupled quantum fluids.

hep-ph↗

arXiv2014

Fermi liquid theory: A brief survey in memory of Gerald E. Brown

I present a brief review of Fermi liquid theory, and discuss recent work on Fermi liquid theory in dilute neutron matter and cold atomic gases. I argue that renewed interest in transport properties of quantum fluids provides fresh support for Landau's approach to Fermi liquid theory, which is based on kinetic theory rather than effective field theory and the renormalization group. I also discuss work on non-Fermi liquids, in particular dense quark matter.

nucl-th↗

arXiv2013

Deconfinement transition at weak coupling in Yang-Mills theory on a torus

We describe a weak coupling realization of the deconfinement transition in gauge theory compactified on $R^3\times S^1$. We consider Yang-Mills theory with a single Weyl fermion of mass $m$ in the adjoint representation of the gauge group. The fermion is subject to periodic boundary conditions, $λ(0)=λ(L)$, where $L$ is the size of the circle $S_1$. This theory reduces to thermal Yang-Mills theory in the limit $m\to\infty$. In the limit $m\to 0$ the deconfinement transition can be studied using weak coupling methods. The analysis is based on semi-classical objects characterized by topological and magnetic charges. At leading order the relevant configurations are monopole-instantons and monopole-anti-monopole pairs ("bions"). We argue that in the $m-L$ plane the weak coupling transition is continuously connected to the deconfinement transition in pure gauge theory.

hep-lat↗

arXiv2013

Scale breaking and fluid dynamics in a dilute two-dimensional Fermi gas

We study two observables related to the anomalous breaking of scale invariance in a dilute two dimensional Fermi gas, the frequency shift and damping rate of the monopole mode in a harmonic confinement potential. For this purpose we compute the speed of sound and the bulk viscosity of the two dimensional gas in the high temperature limit. We show that the anomaly in the speed of sound scales as $(2P-ρc_s^2)/P\sim z/[\log(T/E_B)]^2$, and that the bulk viscosity $ζ$ scales as $ζ/η\sim z^2/[\log(T/E_B)]^6$. Here, $P$ is the pressure, $c_s^2$ is the speed of sound, $η$ is the shear viscosity, $z$ is the fugacity, and $E_B$ is the two-body binding energy. We show that our results are consistent with the experimental results of Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)]. Vogt et al. reported a frequency shift $δω/ω$ of the order of a few percent, and a damping rate smaller than the background rate $Γ/ω_0\sim 5%$.

cond-mat.quant-gas↗

arXiv2013

Bulk viscosity and conformal symmetry breaking in the dilute Fermi gas near unitarity

The dilute Fermi gas at unitarity is scale invariant and its bulk viscosity vanishes. We compute the leading contribution to the bulk viscosity when the scattering length is not infinite. A measure of scale breaking is provided by the ratio $(P-\frac{2}{3}{\cal E})/P$, where $P$ is the pressure and ${\cal E}$ is the energy density. In the high temperature limit this ratio scales as $\frac{zλ}{a}$, where $z$ is the fugacity, $λ$ is the thermal wave length, and $a$ is the scattering length. We show that the bulk viscosity $ζ$ scales as the second power of this parameter, $ζ\sim (\frac{zλ}{a})^2 λ^{-3}$.

cond-mat.quant-gas↗

arXiv2013

Universal mechanism of (semi-classical) deconfinement and theta-dependence for all simple groups

Using the twisted partition function on R^3 x S^1, we argue that the deconfinement phase transition in pure Yang-Mills theory for all simple gauge groups is continuously connected to a quantum phase transition that can be studied in a controlled way. We explicitly consider two classes of theories, gauge theories with a center symmetry, such as SU(N_c) gauge theory for arbitrary N_c, and theories without a center symmetry, such as G_2 gauge theory. The mechanism governing the phase transition is universal and valid for all simple groups. The perturbative one-loop potential as well as monopole-instantons generate attraction among the eigenvalues of the Wilson line. This is counter-acted by neutral bions --- topological excitations which generate eigenvalue repulsion for all simple groups. The transition is driven by the competition between these three effects. We study the transition in more detail for the gauge groups SU(N_c), N_c>2, and G_2. In the case of G_2, there is no change of symmetry, but the expectation value of the Wilson line exhibits a discontinuity. We also examine the effect of the theta-angle on the phase transition and critical temperature T_c(theta). The critical temperature is a multi-branched function, which has a minimum at theta=pi as a result of topological intereference.

hep-th↗