Manuel Valle

Hydrodynamics in 1+1 dimensions with gravitational anomalies

A bstractThe constraints imposed on hydrodynamics by the structure of gauge and gravitational anomalies are studied in two dimensions. By explicit integration of the consistent gravitational anomaly, we derive the equilibrium partition function at second derivative order. This partition function is then used to compute the parity-violating part of the covariant energy-momentum tensor and the transport coefficients.

Analytical approach to relaxation dynamics of condensed Bose gases

Abstract The temporal evolution of a perturbation of the equilibrium distribution of a condensed Bose gas is investigated using the kinetic equation which describes collision between condensate and noncondensate atoms. The dynamics is studied in the low momentum limit where an analytical treatment is feasible. Explicit results are given for the behavior at large times in different temperature regimes.

Parity violating gravitational response and anomalous constitutive relations

A bstractWe compute the parity violating part of the time-dependent gravitational response function of an ideal gas of Weyl fermions up to third order in the derivative expansion and give its full tensorial structure. Our main results are two functions that parametrize the energy-momentum tensor in terms of gauge-invariant combinations of vector and tensor metric perturbations. The zero frequency limit of these functions is related with the anomalous constitutive relations and with the full anomalous partition function in the presence of gauge and mixed anomalies. In particular, our results imply the existence of a previously unknown invariant contribution to the parity-odd partition function at third derivative order that we explicitly construct. Beyond the static limit, the gravitational response function may provide valuable insights into time-dependent phenomena driven by anomalies.

Second-order partition function of a non-interacting chiral fluid in 3+1 dimensions

A bstractWe compute the partition function for non-interacting chiral fermions at second order in a derivative expansion of an arbitrary time-independent gravitational and gauge background. We find that Pauli-Villars regularization of the vacuum part is needed to get consistent results. We use our results to discuss some features of the non-dissipative constitutive relations of second order hydrodynamics.

Hydrodynamic fluctuations in relativistic superfluids

The Hamiltonian formulation of superfluids based on noncanonical Poisson brackets is studied in detail. The assumption that the momentum density is proportional to the flow of the conserved energy is shown to lead to the covariant relativistic theory previously suggested by Khalatnikov, Lebedev, and Carter, and some potentials in this theory are given explicitly. We discuss hydrodynamic fluctuations in the presence of dissipative effects, and we derive the corresponding set of hydrodynamic correlation functions. Kubo relations for the transport coefficients are obtained.

Parity odd equilibrium partition function in 2 + 1 dimensions

A bstractWe use Schwinger’s proper time method to compute the parity odd contributions to the U(1) current and energy-momentum tensor of an ideal gas of fermions in 2 + 1 dimensions in the presence of static gauge and gravitational backgrounds. From these results the equilibrium partition function at first order in the derivative expansion is explicitly obtained by integration. The form of the computed partition function is consistent with general arguments based on Kaluza-Klein and gauge invariance.

Effective theory for the Goldstone field in the BCS–BEC crossover at T=0

Abstract We perform a detailed study of the effective Lagrangian for the Goldstone mode of a superfluid Fermi gas at zero temperature in the whole BCS–BEC crossover. By using a derivative expansion of the response functions, we derive the most general form of this Lagrangian at the next to leading order in the momentum expansion in terms of four coefficient functions. This involves the elimination of all the higher order time derivatives by careful use of the leading order field equations. In the infinite scattering length limit where conformal invariance is realized, we show that the effective Lagrangian must contain an unnoticed invariant combination of higher spatial gradients of the Goldstone mode, while explicit couplings to spatial gradients of the trapping potential are absent. Across the whole crossover, we determine all the coefficient functions at the one-loop level, taking into account the dependence of the gap parameter on the chemical potential in the mean-field approximation. These results are analytically expressed in terms of elliptic integrals of the first and second kind. We discuss the form of these coefficients in the extreme BCS and BEC regimes and around the unitary limit, and compare with recent work by other authors.

Kinetic theory and evolution of cosmological fluctuations with neutrino number asymmetry

We derive a kinetic equation for chiral matter at nonzero chemical potential that governs the response of the parity-odd part of the distribution function to perturbations of the Robertson-Walker metric. The derivation is based on a recent evaluation of the gravitational polarization tensor at nonzero chemical potential. We also provide the equations for gravity waves that follow from the anisotropic stress tensor describing the lepton asymmetry. These equations can be used to assess the effects that a nonzero neutrino chemical potential would have on the evolution of cosmological perturbations.

Instability of the Rayleigh-Jeans spectrum in weak wave turbulence theory

We study the four-wave kinetic equation of weak turbulence linearized around the Rayleigh-Jeans spectrum when the collision integral is associated with short-range interactions between nonrelativistic bosonic quasiparticles. The technique used for the analysis of the stability is based on the properties of the Mellin transform of the kernel in the integral equation. We find that any perturbation of the Rayleigh-Jeans distribution evolves toward low-momentum scales in such a form that when t-->infinity, all the particles occupy a sphere of radius arbitrary small.

Hamiltonian formulation of the effective kinetic theory for superfluid Fermi liquids

Abstract We present in a local form the time dependent effective description of a superfluid Fermi liquid which includes Landau damping effects at T ≠ 0 . This is achieved by the introduction of an additional variable, the quasiparticle distribution function, which obeys a simple kinetic equation. The transport equation is coupled with first order equations for the Goldstone mode and the particle density. We prove that a main feature of this formulation is its Hamiltonian structure relative to a certain Poisson bracket. We construct the Hamiltonian to quadratic order.