The Ginzburg-Pitaevskii equation and microscopic quantum hydrodynamics

L. S. Kuz’menkov, Сергей Геннадьевич Максимов, Владислав Владимирович Федосеев

Luca Salasnich

We discuss the zero-temperature hydrodynamics equations of bosonic and fermionic superfluids and their connection with generalized Gross-Pitaevskii and Ginzburg-Landau equations through a single superfluid nonlinear Schrödinger equation.

R. Eisenschitz

Anton Kapustin, Luke Mrini

We study the hydrodynamics of superconductors within the framework of Schwinger-Keldysh effective field theory (EFT). We show that in the vicinity of the superconducting phase transition the most general leading-order EFT satisfying the local Kubo-Martin-Schwinger condition is described by a version of the time-dependent Ginzburg-Landau (TDGL) equations augmented with stochastic terms. This version of TDGL is applicable in the gapless regime independent of any microscopic details. Within this approach, it is possible to include systematically the effects of nonuniform temperature and heat conductivity, as well as explicit or spontaneous breaking of time reversal. We also introduce a thermal version of the Josephson relation and use it to construct an exotic hydrodynamics describing a phase of matter where heat can flow without dissipation.

K. V. S. Shiv Chaitanya

Makoto Tsubota, Michikazu Kobayashi, Hiromitsu Takeuchi