Landau meets Newton: time translation symmetry breaking in classical mechanics
Aug, 2012Citations per year
Abstract: (arXiv)
Every classical Newtonian mechanical system can be equipped with a nonstandard Hamiltonian structure, in which the Hamiltonian is the square of the canonical Hamiltonian up to a constant shift, and the Poisson bracket is nonlinear. In such a formalism, time translation symmetry can be spontaneously broken, provided the potential function becomes negative. A nice analogy between time translation symmetry breaking and the Landau theory of second order phase transitions is established, together with several example cases illustrating time translation breaking ground states. In particular, the CDM model of FRW cosmology is reformulated as the time translation symmetry breaking ground states.Note:
- 10 pages, 1 figure. V2: minor corrections
- time translation symmetry breaking
- Hamiltonian formalism
- Landau theory of phase transition
- Lambda CDM model
- symmetry breaking: translation
- mechanics
- ground state
- spontaneous symmetry breaking
- critical phenomena
- space-time: Robertson-Walker
References(8)
Figures(1)
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