Classical and relativistic dynamics of supersolids: variational principle

TL;DR

This paper develops a comprehensive hydrodynamic theory of supersolids using a variational approach, unifying thermodynamics and field theory, and extends it to relativistic regimes for potential astrophysical use.

Contribution

It introduces a novel Lagrangian and Poisson brackets framework for supersolids, including relativistic generalization and vortex dynamics.

Findings

Derived nondissipative hydrodynamic equations for supersolids.

Unified thermodynamics and field theory principles in Lagrangian formulation.

Presented relativistic-invariant supersolid hydrodynamics for astrophysical applications.

Abstract

We present a phenomenological Lagrangian and Poisson brackets for obtaining nondissipative hydrodynamic theory of supersolids. A Lagrangian is constructed on the basis of unification of the principles of non-equilibrium thermodynamics and classical field theory. The Poisson brackets, governing the dynamics of supersolids, are uniquely determined by the invariance requirement of the kinematic part of the found Lagrangian. The generalization of Lagrangian is discussed to include the dynamics of vortices. The obtained equations of motion do not account for any dynamic symmetry associated with Galilean or Lorentz invariance. They can be reduced to the original Andreev-Lifshitz equations if to require Galilean invariance. We also present a relativistic-invariant supersolid hydrodynamics, which might be useful in astrophysical applications.