Focus on Strongly Correlated Quantum Fluids: from Ultracold Quantum Gases to QCD Plasmas

Strongly correlated quantum fluids are phases of matter that are intrinsically quantum mechanical and that do not have a simple description in terms of weakly interacting quasiparticles. Two systems that have recently attracted a great deal of interest are the quark–gluon plasma, a plasma of strongly interacting quarks and gluons produced in relativistic heavy ion collisions, and ultracold atomic Fermi gases, very dilute clouds of atomic gases confined in optical or magnetic traps. These systems differ by 19 orders of magnitude in temperature, but were shown to exhibit very similar hydrodynamic flows. In particular, both fluids exhibit a robustly low shear viscosity to entropy density ratio, which is characteristic of quantum fluids described by holographic duality, a mapping from strongly correlated quantum field theories to weakly curved higher dimensional classical gravity. This review explores the connection between these fields, and also serves as an introduction to the focus issue of New Journal of Physics on 'Strongly Correlated Quantum Fluids: From Ultracold Quantum Gases to Quantum Chromodynamic Plasmas'. The presentation is accessible to the general physics reader and includes discussions of the latest research developments in all three areas.

The Large Hadron Collider (LHC) at CERN outside Geneva, Switzerland provides Pb + Pb beams at a nucleon–nucleon center-of-mass energy of 2.76 TeV, which is nearly 14 times higher than the energy available at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven (200 GeV). The first LHC heavy ion run ended in December 2010, and already several results are available which give some indications of future directions in heavy ion physics. Results have been released both for bulk observables, the charged particle multiplicity and elliptic flow, as well as for 'hard probes' such as jets and J/ψ. The charged particle multiplicity near mid-rapidity shows no anomalous rise relative to lower energies, although an extrapolation to full phase space using extended longitudinal scaling may be revealing the first known violation of the Landau–Fermi multiplicity formula. Elliptic flow is found to agree surprisingly well with lower-energy data when measured as a function of transverse momentum, agreeing with viscous hydrodynamic calculations that treat the matter at the LHC similarly to that found at RHIC. Despite the similar features found at lower energies, the higher center-of-mass energies provide much higher rates of high-p_T 'hard' probes, to study the medium microscopically. It makes it possible for the first time to study ultrahigh-energy jets, which are found to show dramatic event-by-event asymmetries in their energies, possibly reflecting strong energy loss in the hot, dense medium. Measurements of the spectra of charged tracks within jets are reported, to indicate a softening of fragmentation of the lower-energy jet. J/ψ rates have also been measured, and were found to be suppressed at a similar level as lower-energy results. In total, the medium formed at the LHC appears to be qualitatively similar to that measured at lower energies. However, future measurements will certainly take even more advantage of the particular strengths of the LHC program, in particular the higher multiplicities and higher rates of large-momentum processes, so it is too early to draw strong conclusions.

We explore the phase structure of a holographic toy model of superfluid states in non-relativistic conformal field theories. At low background mass density, we found a familiar second-order transition to a superfluid phase at finite temperature. Increasing the chemical potential for the probe charge density drives this transition strongly first order as the low-temperature superfluid phase merges with a thermodynamically disfavored high-temperature condensed phase. At high background mass density, the system re-enters the normal phase as the temperature is lowered further, hinting at a zero-temperature quantum phase transition as the background density is varied. Given the unusual thermodynamics of the background black hole, however, it seems likely that the true ground state is another configuration altogether.

In this paper, we examine in a unified-fashion dissipative transport in strongly correlated systems. We thereby demonstrate the connection between 'bad metals' (such as high-temperature superconductors) and 'perfect fluids' (such as ultracold Fermi gases, near unitarity). One aim of this paper is to communicate to the high-energy physics community some of the central unsolved problems in high-T_c superconductors. Because of the interest in the nearly perfect fluidity of cold gases and because of new tools such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, the communication may lead to significant progress in a variety of different fields. A second aim is to draw attention to the great power of transport measurements, which reflect the excitation spectrum more directly than, say, thermodynamics, and therefore strongly constrain microscopic theories of correlated fermionic superfluids. Our calculations show that bad metal and perfect fluid behavior is associated with the presence of a normal state excitation gap that suppresses the effective number of carriers leading to anomalously low conductivity and viscosity above the transition temperature T_c. Below T_c, we demonstrate that the condensate collective modes ('phonons') do not couple to transverse probes, such as shear viscosity or conductivity. As a result, our calculated shear viscosity at low T becomes arbitrarily small, as observed in experiments. In both homogeneous and trap calculations, we do not find the upturn in η or η/s (where s is the entropy density) that is found in most theories. In the process of these studies, we demonstrate compatibility with the transverse sum rule and find reasonable agreement with viscosity experiments.

We argue that there exist simple effective field theories describing the long-distance dynamics of holographic liquids. The degrees of freedom responsible for the transport of charge and energy–momentum are Goldstone modes. These modes are coupled to a strongly coupled infrared (IR) sector through emergent gauge and gravitational fields. The IR degrees of freedom are described holographically by the near-horizon part of the metric, whereas the Goldstone bosons are described by a field-theoretical Lagrangian. In the cases where the holographic dual involves a black hole, this picture allows for a direct connection between the holographic prescription where currents live on the boundary and the membrane paradigm where currents live on the horizon. The zero-temperature sound mode in the D3–D7 system is also re-analyzed and re-interpreted within this formalism.

We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T. We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏn is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.

Relativistic heavy-ion collisions have reached energies that enable the creation of a novel state of matter termed the quark–gluon plasma. Many observables point to a picture of the medium as rapidly equilibrating and expanding as a nearly inviscid fluid. In this paper, we explore the evolution of experimental flow observables as a function of collision energy and attempt to reconcile the observed similarities across a broad energy regime in terms of the initial conditions and viscous hydrodynamics. If the initial spatial anisotropies for all collision energies from 39 GeV to 2.76 TeV are very similar, we find that viscous hydrodynamics might be consistent with the level of agreement for v₂ of unidentified hadrons as a function of p_T. However, we predict a strong collision energy dependence for the proton v₂(p_T). The results presented in this paper highlight the need for more systematic studies and for a re-evaluation of previously reported sensitivities to the early time dynamics and properties of the medium.

A quantum chromodynamics (QCD) phase diagram is usually plotted as the temperature (T) versus the chemical potential associated with the conserved baryon number (μ_B). Two fundamental properties of QCD, related to confinement and chiral symmetry, allow for two corresponding phase transitions when T and μ_B are varied. Theoretically, the phase diagram is explored through non-perturbative QCD calculations on a lattice. The energy scale for the phase diagram (Λ_QCD ∼200 MeV) is such that it can be explored experimentally by colliding nuclei at varying beam energies in the laboratory. In this paper, we review some aspects of the QCD phase structure as explored through experimental studies using high-energy nuclear collisions. Specifically, we discuss three observations related to the formation of a strongly coupled plasma of quarks and gluons in the collisions, the experimental search for the QCD critical point on the phase diagram and the freeze-out properties of the hadronic phase.

Spinor ultracold gases in one dimension (1D) represent an interesting example of strongly correlated quantum fluids. They have a rich phase diagram and exhibit a variety of quantum phase transitions. We consider a 1D spinor gas of bosons with a large spin S. A particular example is the gas of chromium atoms (S=3), where the dipolar collisions efficiently change the magnetization and make the system sensitive to the linear Zeeman effect. We argue that in 1D the most interesting effects come from the pairing interaction. If this interaction is negative, it gives rise to a (quasi)condensate of singlet bosonic pairs with an algebraic order at zero temperature, and for (2S+1)≫1 the saddle point approximation leads to physically transparent results. Since in 1D one needs a finite energy to destroy a pair, the spectrum of spin excitations has a gap. Hence, in the absence of a magnetic field, there is only one gapless mode corresponding to phase fluctuations of the pair quasicondensate. Once the magnetic field exceeds the gap, another condensate emerges, namely the quasicondensate of unpaired bosons with spins aligned along the magnetic field. The spectrum then contains two gapless modes corresponding to the singlet-paired and spin-aligned unpaired Bose condensed particles, respectively. At T=0, the corresponding phase transition is of the commensurate–incommensurate type.

A degenerate three-component Fermi gas of atoms with identical attractive interactions is expected to exhibit superfluidity and magnetic order at low temperature and, for sufficiently strong pairwise interactions, become a Fermi liquid of weakly interacting trimers. The phase diagram of this system is analogous to that of quark matter at low temperature, motivating strong interest in its investigation. We describe how a three-component gas below the superfluid critical temperature can be prepared in an optical lattice. To realize an SU(3)-symmetric system, we show how pairwise interactions in the three-component atomic system can be made equal by applying radiofrequency and microwave radiation. Finally, motivated by the aim to make more accurate models of quark matter, which have color, flavor and spin degrees of freedom, we discuss how an atomic system with SU(2)⊗SU(3) symmetry can be achieved by confining a three-component Fermi gas in the p-orbital band of an optical lattice potential.

Collisions between nuclei at ultrarelativistic energies produce a colour-deconfined plasma that expands explosively and rapidly reverts to the colour-confined (hadronic) state. In non-central collisions, the zone of hot matter is transversely anisotropic and may be 'tilted' relative to the direction of the incoming beams. As the matter cools and expands into the vacuum, the evolution of the system shape depends sensitively on the dynamical response of the plasma under extreme conditions. Two-pion intensity interferometry performed relative to the impact parameter can be used to measure the approximate final shape of the system when pions decouple from the system. We use several transport models to illustrate the dependence of the final shape on the QCD equation of state and late-stage hadronic rescattering. The dependence of the final shape on collision energy may reveal non-trivial structures in the QCD phase diagram. Indeed, the few measurements published to date show an intriguing behaviour in an energy region under intense experimental and theoretical scrutiny, as signatures of a first-order phase transition may appear there. We discuss strong parallels between shape studies in heavy-ion collisions and those in two other strongly coupled systems.

The detailed features of solitons in holographic superfluids are discussed. Using solitons as probes, we study the behavior of holographic superfluids by varying the scaling dimension of the condensing operator and make a comparison to the Bose–Einstein condensate–Bardeen–Cooper–Schrieffer comparison phenomena. Further evidence of this analogy is provided by the behavior of the solitons' length scales as well as by the superfluid critical velocity.

We calculate the ratio of the viscosity to the entropy density for both Bose and Fermi gases in the unitary limit using a new approach to the quantum statistical mechanics of gases based on the S-matrix. In the unitary limit the scattering length diverges and the S-matrix equals − 1. For the fermion case, we obtain η/s>4.7 times the proposed lower bound of ℏ/4πk_B, which came from the anti-Desitter space/conformal field theory correspondence (AdS/CFT) for gauge theories, consistent with the most recent experiments. For the bosonic case, we present evidence that the gas undergoes a phase transition to a strongly interacting Bose–Einstein condensate and is a more perfect fluid, with η/s<1.3 times the bound.

It is quite common that several different phases exist simultaneously in a system of trapped quantum gases of ultra-cold atoms. One example is the strongly interacting Fermi gas with two imbalanced spin species, which has received a great deal of attention owing to the possible occurrence of exotic superfluid phases. By using novel numerical techniques and algorithms, we self-consistently solve the Bogoliubov–de Gennes equations, which describe Fermi superfluids in the mean-field framework. From this study, we investigate the novel phases of spin-imbalanced Fermi gases and examine the validity of local density approximation (LDA), which is often invoked in the extraction of bulk properties from experimental measurements within trapped systems. We show how the validity of the LDA is affected by the trapping geometry, the number of atoms and the spin imbalance.

We study a three-component superfluid Fermi gas in a spherically symmetric harmonic trap using the Bogoliubov–deGennes method. We predict a coexistence phase in which two pairing field order parameters are simultaneously non-zero, in stark contrast to studies performed for trapped gases using local density approximation. We also discuss the role of atom number conservation in the context of a homogeneous system.

We describe the effects of disorder on the critical temperature of s-wave superfluids from the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein condensate (BEC) regime, with direct application to ultracold fermions. We use the functional integral method and the replica technique to study Gaussian correlated disorder due to impurities, and we discuss how this system can be generated experimentally. In the absence of disorder, the BCS regime is characterized by pair breaking and phase coherence temperature scales that are essentially the same, allowing strong correlations between the amplitude and phase of the order parameter for superfluidity. As non-pair-breaking disorder is introduced, the largely overlapping Cooper pairs seek to maintain phase coherence such that the critical temperature remains essentially unchanged, and Anderson's theorem is satisfied. However, in the BEC regime, the pair breaking and phase coherence temperature scales are very different such that non-pair-breaking disorder can dramatically affect phase coherence, and thus the critical temperature, without the requirement of breaking tightly bound fermion pairs simultaneously. In this case, Anderson's theorem does not apply, and the critical temperature can be more easily reduced in comparison to the BCS limit. Lastly, we find that the superfluid is more robust against disorder in the intermediate region near unitarity between the two regimes.

The metastability associated with the first-order transition from the normal to the superfluid phase is investigated in the phase diagram of two-component polarized Fermi gases. We begin by detailing the dominant decay processes of single quasiparticles, determining the momentum thresholds of each process and calculating their rates. This understanding is then applied to a Fermi sea of polarons, and we predict a region of metastability for the normal partially polarized phase. We propose experiments to observe the threshold of the metastable region, the interaction strength at which the quasiparticle ground state changes character, and the decay rate of polarons.

We present a comprehensive experimental study of Tan's universal contact parameter in a two-component ultracold Fermi gas, using Bragg spectroscopy. The contact uniquely parameterizes a number of universal properties of Fermi gases in the strongly interacting regime. It is linked to the spin-antiparallel component of the static structure factor S_↑↓(k) at high momenta, which can readily be obtained via Bragg scattering. Contact depends upon the relative interaction strength 1/(k_Fa) and temperature T/T_F, where k_F is the Fermi wave vector, a is the s-wave scattering length and T_F is the Fermi temperature. We present measurements of both of these dependencies in a cloud of ⁶Li atoms and compare our findings to theoretical predictions. We also compare Bragg spectroscopic methods based on measuring the energy and momentum transferred to the cloud and examine the conditions under which the energy transfer method provides improved accuracy. Our measurements of the dynamic structure factor and contact are found to be in good agreement with theoretical predictions based on the quantum virial expansion.

We present measurements of spin transport in ultracold gases of fermionic ⁶Li in a mixture of two spin states at a Feshbach resonance. In particular, we study the spin-dipole mode, where the two spin components are displaced from each other against a harmonic restoring force. We prepare a highly imbalanced, or polaronic, spin mixture with a spin-dipole excitation and we observe strong, unitarity-limited damping of the spin-dipole mode. In gases with small spin imbalance, below the Pauli limit for superfluidity, we observe strongly damped spin flow even in the presence of a superfluid core. This indicates strong mutual friction between superfluid and polarized normal spins, possibly involving Andreev reflection at the superfluid–normal interface.

One of the fundamental questions in the field of subatomic physics is the question of what happens to matter at extreme densities and temperatures as may have existed in the first microseconds after the Big Bang and exists, perhaps, in the core of dense neutron stars. The aim of heavy-ion physics is to collide nuclei at very high energies and thereby create such a state of matter in the laboratory. The experimental program began in the 1990s with collisions made available at the Brookhaven Alternating Gradient Synchrotron (AGS) and the CERN Super Proton Synchrotron (SPS), and continued at the Brookhaven Relativistic Heavy-Ion Collider (RHIC) with the maximum center-of-mass energies of , 17.2 and 200 GeV, respectively. Collisions of heavy ions at the unprecedented energy of 2.76 TeV recently became available at the LHC collider at CERN. In this review, I give a brief introduction to the physics of ultrarelativistic heavy-ion collisions and discuss the current status of elliptic flow measurements.

Recent experiments on atom loss in ultra-cold Fermi gases all show a maximum at a magnetic field below Feshbach resonance, where the s-wave scattering length is large (comparable to inter-particle distance) and positive. These experiments have been performed over a wide range of conditions, with temperatures and trap depths spanning three decades. Different groups have come up with different explanations, including the emergence of Stoner ferromagnetism. Here, we show that this maximum is a consequence of two major steps. The first is the establishment of a population of shallow dimers, which is the combined effect of dimer formation through three-body recombination, and the dissociation of shallow dimers back to atoms through collisions. The dissociation process will be temperature dependent and is affected by Pauli blocking at low temperatures. The second is the relaxation of shallow dimers into tightly bound dimers through atom–dimer and dimer–dimer collisions. In these collisions, a significant amount of energy is released. The reaction products leave the trap, leading to trap loss. We have constructed a simple set of rate equations describing these processes. Remarkably, even with only a few parameters, these equations reproduce the loss rate observed in all recent experiments, despite their widely different experimental conditions. Our studies show that the location of the maximum loss rate depends crucially on experimental parameters such as trap depth and temperature. These extrinsic characters show that this maximum is not a reliable probe of the nature of the underlying quantum states. The physics of our equations also explains some general trends found in current experiments.

We study the low-energy effective action for some collective modes of the color flavor-locked (CFL) phase of QCD. This phase of matter has long been known to be a superfluid because by picking a phase its order parameter breaks the quark-number U(1)_B symmetry spontaneously. We consider the modes describing fluctuations in the magnitude of the condensate, namely the Higgs mode, and in the phase of the condensate, namely the Nambu–Goldstone (NG) (or Anderson–Bogoliubov) mode associated with the breaking of U(1)_B. By employing as microscopic theory the Nambu–Jona-Lasinio model, we reproduce known results for the Lagrangian of the NG field to the leading order in the chemical potential and extend such results evaluating corrections due to the gap parameter. Moreover, we determine the interaction terms between the Higgs and the NG field. This study paves the way for a more reliable study of various dissipative processes in rotating compact stars with a quark matter core in the CFL phase.

In this paper, we discuss the basic elements that should appear in a gravitational system that is dual to a confining gauge theory displaying color superconductivity at large baryon density. We consider a simple system with these minimal elements and show that for a range of parameters, the phase structure of this model as a function of temperature and baryon chemical potential exhibits phases that can be identified with confined, deconfined and color superconducting phases in the dual field theory. We find that the critical temperature at which the superconducting phase disappears is remarkably small (relative to the chemical potential). This small number arises from the dynamics and is unrelated to any small parameter in the model that we study. We discuss similar models that exhibit flavor superconductivity.

The bulk viscosity of cold, dense three-flavor quark matter is studied as a function of temperature and the amplitude of density oscillations. The study is extended to the case of two different types of anharmonic oscillations of density. We point out several qualitative effects due to the anharmonicity, although quantitatively they appear to be relatively small. We found that, in most regions of the parameter space, except for very large amplitudes of density oscillations (i.e. 10% and above), nonlinear effects and anharmonicity have a small effect on the interplay of the nonleptonic and semileptonic processes in the bulk viscosity.

We study the evolution and scaling of the entanglement entropy after two types of quenches for a 2+1 field theory, using a conjectured holographic technique for its computation. We study a thermal quench, dual to the addition of a shell of uncharged matter to four-dimensional anti-de Sitter (AdS₄) spacetime, and study the subsequent formation of a Schwarzschild black hole. We also study an electromagnetic quench, dual to the addition of a shell of charged sources to AdS₄, following the subsequent formation of an extremal dyonic black hole. In these backgrounds, we consider the entanglement entropy of two types of geometries, the infinite strip and the round disc, and find distinct behavior for each. Some of our findings naturally supply results analogous to observations made in the literature for lower dimensions, but we also uncover several new phenomena, such as (in some cases) a discontinuity in the time derivative of the entanglement entropy as it nears saturation, and for the electromagnetic quench, a logarithmic growth in the entanglement entropy with time for both the disc and strip, before settling to saturation. We briefly discuss the possible origin of the new phenomena in terms of the features of the conjectured dual field theory.

Critical behavior developed near a quantum phase transition, interesting in its own right, offers exciting opportunities to explore the universality of strongly correlated systems near the ground state. Cold atoms in optical lattices, in particular, represent a paradigmatic system, for which the quantum phase transition between the superfluid and Mott insulator states can be externally induced by tuning the microscopic parameters. In this paper, we describe our approach to study quantum criticality of cesium atoms in a two-dimensional (2D) lattice based on in situ density measurements. Our research agenda involves testing critical scaling of thermodynamic observables and extracting transport properties in the quantum critical regime. We present and discuss experimental progress on both fronts. In particular, the thermodynamic measurement suggests that the equation of state near the critical point follows the predicted scaling law at low temperatures.

We calculate the spin-drag relaxation rate for a two-component ultracold atomic Fermi gas with positive scattering length between the two-spin components. In one dimension, we find that it vanishes linearly with temperature. In three dimensions, the spin-drag relaxation rate vanishes quadratically with temperature for sufficiently weak interactions. This quadratic temperature dependence is present, up to logarithmic corrections, in the two-dimensional (2D) case as well. For stronger interaction, the system exhibits a Stoner ferromagnetic phase transition in two and three dimensions. We show that the spin-drag relaxation rate is enhanced by spin fluctuations as the temperature approaches the critical temperature of this transition from above.

A selfconsistent calculation of heavy-quark (HQ) and quarkonium properties in the quark-gluon plasma (QGP) is conducted to quantify flavor transport and color screening in the medium. The main tool is a thermodynamic T-matrix approach to compute HQ and quarkonium spectral functions in both scattering and bound-state regimes. The T-matrix, in turn, is employed to calculate HQ selfenergies which are implemented into spectral functions beyond the quasiparticle approximation. Charmonium spectral functions are used to evaluate Eulcidean-time correlation functions, which are compared to results from thermal lattice QCD. The comparisons are performed in various hadronic channels, including zero-mode contributions consistently accounting for finite charm-quark width effects. The zero modes are closely related to the charm-quark number susceptibility, which is also compared to existing lattice 'data'. Both the susceptibility and the heavy-light quark T-matrix are applied to calculate the thermal charm-quark relaxation rate, or, equivalently, the charm diffusion constant in the QGP. Implications of our findings in the HQ sector for the viscosity-to-entropy-density ratio of the QGP are briefly discussed.

We find that universal three-body physics extends beyond the threshold regime to non-zero energies. For ultracold atomic gases with a negative two-body s-wave scattering length near a Feshbach resonance, we show that the resonant peaks characteristic of Efimov physics persist in three-body recombination to higher collision energies. For this and other inelastic processes, we use the adiabatic hyperspherical representation to derive universal analytical expressions for their dependence on the scattering length, the collision energy and—for narrow resonances—the effective range. These expressions are supported by full numerical solutions of the Schrödinger equation and display log-periodic dependence on energy characteristic of Efimov physics. This dependence is robust and might be used to experimentally observe several Efimov features.

We study two species of attractively interacting fermion confined to a quasi-one-dimensional geometry, in the presence of a strong scattering potential that can couple, selectively, to one or both species. We show that the fermion density distribution in the presence of such a spin-selective scattering potential reflects the pairing spin gap of the fermions.

We compute the viscosity spectral function of the dilute Fermi gas for different values of the s-wave scattering length a, including the unitarity limit a→∞. We perform the calculation in kinetic theory by studying the response to a non-trivial background metric. We find the expected structure consisting of a diffusive peak in the transverse shear channel and a sound peak in the longitudinal channel. At zero momentum the width of the diffusive peak is ω₀≃(2ε)/(3η) where ε is the energy density and η is the shear viscosity. At finite momentum the spectral function approaches the collisionless limit and the width is of the order of ω₀∼k(T/m)^1/2.

We study the phase diagram of an SU(3)-symmetric mixture of three-component ultracold fermions with attractive interactions in an optical lattice, including the additional effect on the mixture of an effective three-body constraint induced by three-body losses. We address the properties of the system in D⩾2 by using dynamical mean-field theory and variational Monte Carlo techniques. The phase diagram of the model shows a strong interplay between magnetism and superfluidity. In the absence of the three-body constraint (no losses), the system undergoes a phase transition from a color superfluid (c-SF) phase to a trionic phase, which shows additional particle density modulations at half-filling. Away from the particle–hole symmetric point the c-SF phase is always spontaneously magnetized, leading to the formation of different c-SF domains in systems where the total number of particles of each species is conserved. This can be seen as the SU(3) symmetric realization of a more general tendency for phase separation in three-component Fermi mixtures. The three-body constraint strongly disfavors the trionic phase, stabilizing a (fully magnetized) c-SF also at strong coupling. With increasing temperature we observe a transition to a non-magnetized SU(3) Fermi liquid phase.

Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semicircle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the dc ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero dc conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semicircle transitions between them. The model can be regarded as a strongly coupled analogue of the old 'composite boson' picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model. In particular, the model indicates the value for low-temperature scaling exponents for transitions among quantum Hall plateaux, in agreement with the measured value 0.42±0.01.

In this paper, we study how quantum fluctuations modify the quantum evolution of an initially classical field theory. We consider a scalar ϕ⁴ theory coupled to an external source as a toy model for the color glass condensate description of the early time dynamics of heavy-ion collisions. We demonstrate that quantum fluctuations considerably modify the time evolution driving the system to evolve in accordance with ideal hydrodynamics. We attempt to understand the mechanism behind this relaxation to ideal hydrodynamics by using modified initial spectra and studying the particle content of the theory.

The Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover problem is solved for stationary gray solitons via the Boguliubov–de Gennes equations at zero temperature. These crossover solitons exhibit a localized notch in the gap and a characteristic phase difference across the notch for all interaction strengths, from BEC to BCS regimes. However, they do not follow the well-known Josephson-like sinusoidal relationship between velocity and phase difference except in the far BEC limit: at unitarity, the velocity has a nearly linear dependence on phase difference over an extended range. For a fixed phase difference, the soliton is of nearly constant depth from the BEC limit to unitarity and then grows progressively shallower into the BCS limit, and on the BCS side, Friedel oscillations are apparent in both gap amplitude and phase. The crossover soliton appears fundamentally in the gap; we show, however, that the density closely follows the gap, and the soliton is therefore observable. We develop an approximate power-law relationship to express this fact: the density of gray crossover solitons varies as the square of the gap amplitude in the BEC limit and as a power of about 1.5 at unitarity.

In a clean Fermi liquid, due to spin up/spin down symmetry, the dc spin current driven by a magnetic field gradient is finite even in the absence of impurities. Hence, the spin conductivity σ_s assumes a well-defined collision-dominated value in the disorder-free limit, providing a direct measure of the inverse strength of electron–electron interactions. In neutral graphene, with Fermi energy at the Dirac point, the Coulomb interactions remain unusually strong, such that the inelastic scattering rate comes close to a conjectured upper bound τ_inel⁻¹≲k_BT/ℏ, similar to the case of strongly coupled quantum critical systems. The strong scattering is reflected by a minimum of spin conductivity at the Dirac point, where it reaches at weak Coulomb coupling α, μ_s≈μ_B being the magnetic moment of the electronic spins. Up to the replacement of quantum units, e²/ℏ→μ_s²/ℏ, this result equals the collision-dominated electrical conductivity obtained previously. This accidental symmetry is, however, broken to higher orders in the interaction strength. For gated graphene and two-dimensional metals in general, we show that the transport time is parametrically smaller than the collision time. We exploit this fact to compute the collision-limited σ_s analytically as , with for weak Coulomb coupling α.

In the high-temperature phase of QCD, the heavy-quark momentum diffusion constant determines, via a fluctuation–dissipation relation, how fast a heavy quark kinetically equilibrates. This transport coefficient can be extracted from thermal correlators via a Kubo formula. We present a lattice calculation of the relevant Euclidean correlators in the gluon plasma, based on a recent formulation of the problem in heavy-quark effective field theory (HQET). We find a ≈20% enhancement of the Euclidean correlator at maximal time separation as the temperature is lowered from 6T_c to 2T_c, pointing to stronger interactions at lower temperatures. At the same time, the correlator becomes flatter from 6T_c down to 2T_c, indicating a relative shift of the spectral weight to lower frequencies. A recent next-to-leading order perturbative calculation of the correlator agrees with the time dependence of the lattice data at the few-per cent level. We estimate how much additional contribution from the ω≲T region of the perturbative spectral function would be required to bring it in agreement with the lattice data at 3.1T_c.

The recently discovered universal thermodynamic behavior of dilute, strongly interacting Fermi gases also implies a universal structure in the many-body pair-correlation function at short distances, as quantified by the contact . Here, we theoretically calculate the temperature dependence of this universal contact for a Fermi gas in free space and in a harmonic trap. At high temperatures above the Fermi degeneracy temperature, T≳T_F, we obtain a reliable non-perturbative quantum virial expansion up to third order. At low temperatures, we compare different approximate strong-coupling theories. These make different predictions, which need to be tested either by future experiments or by advanced quantum Monte Carlo simulations. We conjecture that in the universal unitarity limit, the contact or correlation decreases monotonically with increasing temperature, unless the temperature is significantly lower than the critical temperature, T≪T_c∼0.2T_F. We also discuss briefly how to measure the universal contact in either homogeneous or harmonically trapped Fermi gases.

We propose a new and simple method of estimating the radiation due to an accelerated quark in a strongly coupled medium, within the framework of the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. In particular, we offer a heuristic explanation of the collimated nature of synchrotron radiation produced by a circling quark, which was recently studied by Athanasiou et al (2010 Phys. Rev. D 81 26001). The gravitational dual of such a quark is a coiling string in AdS, whose backreaction on the spacetime geometry remains tightly confined, as if 'beamed' towards the boundary. While this appears to contradict conventional expectations from the scale/radius duality, we resolve the issue by observing that the backreaction of a relativistic string is reproduced by a superposition of gravitational shock waves. We further demonstrate that this proposal allows us to reduce the problem of computing the boundary stress tensor to merely calculating geodesics in AdS, as opposed to solving linearized Einstein's equations.

We examine spin diffusion in a two-component homogeneous Fermi gas in the normal phase. Using a variational approach, analytical results are presented for the spin diffusion coefficient and the related spin relaxation time as a function of temperature and interaction strength. For low temperatures, strong correlation effects are included through the Landau parameters, which we extract from Monte Carlo results. We show that the spin diffusion coefficient has a minimum for a temperature somewhat below the Fermi temperature with a value that approaches the quantum limit ∼ℏ/m in the unitarity regime, where m is the particle mass. Finally, we derive a value for the low-temperature shear viscosity in the normal phase from the Landau parameters.

We abstract the essential features of holographic dimer models, and develop several new applications of these models. Firstly, semi-holographically coupling free band fermions to holographic dimers, we uncover novel phase transitions between conventional Fermi liquids and non-Fermi liquids, accompanied by a change in the structure of the Fermi surface. Secondly, we make dimer vibrations propagate through the whole crystal by way of double trace deformations, obtaining nontrivial band structure. In a simple toy model, the topology of the band structure experiences an interesting reorganization as we vary the strength of the double trace deformations. Finally, we develop tools that would allow one to build, in a bottom-up fashion, a holographic avatar of the Hubbard model.

We report on the observation of a quenched moment of inertia resulting from superfluidity in a strongly interacting Fermi gas. Our method is based on setting the hydrodynamic gas in slow rotation and determining its angular momentum by detecting the precession of a radial quadrupole excitation. The measurements distinguish between the superfluid and collisional origins of hydrodynamic behavior, and show the phase transition.