We develop a Schwinger--Keldysh effective theory for quantum-interference corrections in a two-dimensional electron system in the hydrodynamic regime. Starting from the clean hydrodynamic fixed point, we introduce a minimal random-friction disorder model that generates a finite momentum-relaxation time within the self-consistent Born approximation. The disorder-averaged theory then allows us to construct a hydrodynamic Cooperon and to compute the associated self-energy corrections to the collective modes. Conservation laws protect the density and momentum sectors, so that the leading quantum-coherence correction is forced into the spin-two stress sector. The associated stress self-energy renormalizes the shear viscosity and modifies both the Gurzhi response and its low-field magnetohydrodynamic signatures.
We develop a Schwinger--Keldysh effective theory for quantum-interference corrections in a two-dimensional electron system in the hydrodynamic regime. Starting from the clean hydrodynamic fixed point, we introduce a minimal random-friction disorder model that generates a finite momentum-relaxation time within the self-consistent Born approximation. The disorder-averaged theory then allows us to construct a hydrodynamic Cooperon and to compute the associated self-energy corrections to the collective modes. Conservation laws protect the density and momentum sectors, so that the leading quantum-coherence correction is forced into the spin-two stress sector. The associated stress self-energy renormalizes the shear viscosity and modifies both the Gurzhi response and its low-field magnetohydrodynamic signatures.
In non-diffusive conduction regimes of strongly correlated quantum electron systems, electromagnetic perturbations simultaneously probe the electronic dynamics in time and space: the exchanged energy ℏω excites retarded, i.e., frequency-dependent, many-body interactions, while the probing spatial modulation renders the response spatially nonlocal, i.e., dependent on the external wave vector q. This work derives the nonlocal electrodynamic response of such dynamical quantum fluids assuming local but frequency-dependent self-energies and particle-hole irreducible two-particle vertex functions, and preserving charge/mass conservation. The latter is ensured by Bethe-Salpeter equations for renormalized interaction vertices, entering the Kubo formalism for two-particle correlation functions (e.g., for density, currents, momentum, stress). Within such a framework, exact symmetry criteria for the absence of vertex corrections are inferred. In particular, vertex corrections vanish at q=0 for single-particle dispersions that are even and bare interaction vertices that are odd with respect to specific momentum-space point group transformations, including inversion for vector vertices, and mirror reflections or two- or higher-fold rotations for tensor vertices. If the dispersion is isotropic, vertex corrections vanish from the transverse part (⊥q) of vectorial vertices (such as for electric/particle current) at any finite ℏω and q. These cancellations extend to the full current-current correlation function for quadratic isotropic dispersion. Further symmetry breaking, multiband effects, and the additional imposition of momentum conservation, are discussed, with application to the Hall viscosity of Landau levels. Explicit expressions for generic nonlocal correlation functions are derived for Fermi liquids and non-Fermi liquids.
<!--HTML-->In small colliding systems and near the QCD critical point, the effects due to hydrodynamic fluctuations can be significant. The effective field theory of fluctuating hydrodynamics has recently been formulated on the closed time path (Schwinger-Keldysh formalism) [1]. Such formulation allows for a systematic treatment of non-linear interaction among energy-momentum densities and hydrodynamics noise. We present the first complete leading order analysis of the effects of hydrodynamic fluctuations on stress-energy tensor correlations and show how those fluctuations modify the dispersion of sound and shear modes. We find the contributions of hydrodynamic fluctuations are parametrically more important than those from the second-order terms in hydrodynamics. We discuss the potential implications of our results for heavy-ion collision phenomenology [2]. [1] M. Crossley, P. Glorioso, and H. Liu, Effective field theory of dissipative fluids, JHEP 1709 (2017) 09. [2] P.H.C. Lau, H. Liu and Y. Yin, in preparation.
We study the electrical transport of a two-dimensional non-Fermi-liquid with disorder, and we determine the first quantum correction to the semiclassical dc conductivity due to quantum interference. We consider a system with N flavors of fermions coupled to SU(N) critical matrix bosons. Motivated by the SYK model, we employ the bilocal field formalism and derive a set of finite-temperature saddle-point equations governing the fermionic and bosonic self-energies in the large-N limit. Interestingly, disorder smearing induces a marginal Fermi-liquid (MFL) self-energy for the fermions. We next consider fluctuations around the saddle points and derive a MFL-Finkel'stein nonlinear sigma model. We find that the Altshuler-Aronov quantum conductance correction gives linear-T resistivity that can dominate over the Drude result at low temperatures. The strong temperature dependence of the quantum correction arises due to rapid relaxation of the mediating quantum-critical bosons. We verify that our calculations explicitly satisfy the Ward identity at the semiclassical and quantum levels. Our results establish that quantum interference persists in two-particle hydrodynamic modes, even when quasiparticles are subject to strong (Planckian) dissipation.
We construct a quantum Schwinger-Keldysh (SK) effective field theory for the diffusive hydrodynamics of a conserved scalar field. Quantum corrections within the SK framework are guided by fluctuation-dissipation relations, enforced via a dynamical Kubo-Martin-Schwinger (KMS) symmetry. We find that the KMS symmetry necessarily generates fluctuation contributions in the SK effective action at all orders in the noise field, thereby giving rise to intrinsically non-Gaussian noise. We use our results to compute one-loop quantum corrections to the two-point density-density retarded correlation function, leading to a quantum generalization of hydrodynamic long-time tails. Our results apply at arbitrarily high orders in ℏ. The one-loop results for retarded correlation functions have been expressed in terms of a family of polynomials. We also provide a closed-form expression for the one-loop results at leading order in the wavevector expansion.
We develop the theory of hydrodynamic fluctuations for one-dimensional quantum liquids. At low temperatures the relaxation of interacting electrons in a single-channel wire separates into two classes: equilibration, which changes the numbers of right and left movers through backscattering and is exponentially slow, and thermalization, which redistributes energy and momentum at a fixed number of movers at a power-law rate. This separation of time scales gives the electron liquid a two-fluid description analogous to superfluid 4He, with the zero mode of the Luttinger liquid as the superfluid component and the gas of thermal excitations as the normal component. Using Onsager reciprocity and the fluctuation-dissipation theorem, we add Langevin fluxes to the two-fluid hydrodynamic equations, including a mutual-friction noise generated by rare backscattering events that has no counterpart in helium. We apply the theory to Coulomb-coupled quantum wires and calculate the dynamic structure factors, which contain a second-sound peak next to the plasmon doublet; the Coulomb drag resistivity, where intrawire equilibration acts as a bottleneck and turns the hydrodynamic drag into an activated temperature dependence; and the near-field heat transfer between the wires. Mode frequencies, spectral weights, linewidths, and the crossover scales of the transport coefficients are expressed through the thermodynamic properties of the liquid and a few dissipative coefficients, providing spectroscopic and transport probes of two-fluid behavior in one-dimensional quantum systems.
The hydrodynamic regime of electron transport has been recently realized in conductors with ultralow densities of defects. Although relaxation processes in two-dimensional (2D) fluids have been studied in many theoretical works, the viscosity of the realistic Fermi gas of 2D electrons having a quadratic energy spectrum and interacting by Coulomb's law has not been reliably determined either in theory or in experiment. Here, we construct a theory of viscosity and thermal conductivity in such a system. We compare the calculated viscosity of the 2D electron Fermi gas and the previously known viscosity of a 2D Fermi liquid with available experimental data extracted from the hydrodynamic negative magnetoresistance of the best-quality GaAs quantum wells. Based on this comparison, we argue that measurements of the temperature dependence of the viscosity can allow us to trace the transition between an electron Fermi liquid and a Fermi gas.