Classical and quantum dynamics of gyroscopic systems and dark energy

Gyroscopic systems in classical and quantum field theory are characterized by the presence of at least two scalar degrees freedom terms that mix fields their time derivatives quadratic Lagrangian. In Minkowski spacetime, they naturally appear a coupling among with time-dependent vacuum expectation values space-dependent values, breaking spontaneously Lorentz symmetry; this is case for supersolid. cosmological background gyroscopic system can also arise from dependence non-diagonal kinetic mass matrices. We study dynamics computing correlation functions on state minimizes energy. Two regions stability parameter space found: one region, dubbed normal, Hamiltonian positive defined, while second anomalous, it has no definite sign. Interestingly, anomalous region 2-point function exhibits resonant behaviour certain space. show dynamical dark energy models (with exact equation $w=-1$) be realised as system.