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Classical and relativistic dynamics of supersolids: variational principle. (English) Zbl 1155.74008

Summary: 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 to require Galilean invariance. We also present a relativistic-invariant supersolid hydrodynamics, which might be useful in astrophysical applications.

MSC:

74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
82D20 Statistical mechanics of solids
81T99 Quantum field theory; related classical field theories
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