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Spontaneous generation of a crystalline ground state in a higher derivative theory

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  • Ghosh, Subir

Abstract

The possibility of Spontaneous Symmetry Breaking in momentum space in a generic Lifshitz scalar model–a non-relativistic scalar field theory with higher spatial derivative terms–has been studied. We show that the minimum energy state, the ground state, has a lattice structure, where the translation invariance of the continuum theory is reduced to a discrete translation symmetry. The scale of translation symmetry breaking (or induced lattice spacing) is proportional to the inverse of the momentum of the condensate particle. The crystalline ground state is stable under excitations below a certain critical velocity. The small fluctuations above the ground state can have a phonon like dispersion under suitable choice of parameters.

Suggested Citation

  • Ghosh, Subir, 2014. "Spontaneous generation of a crystalline ground state in a higher derivative theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 245-251.
    • Handle: RePEc:eee:phsmap:v:407:y:2014:i:c:p:245-251
    DOI: 10.1016/j.physa.2014.04.012
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    Cited by:

    1. Aerts, Diederik & Czachor, Marek & Kuna, Maciej, 2016. "Crystallization of space: Space-time fractals from fractal arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 201-211.

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