Classical and quantum dynamics of gyroscopic systems and dark energy

Abstract

Gyroscopic systems in classical and quantum field theory are characterized by the presence of at least two scalar degrees offreedom and by terms that mix fields andtheir time derivatives in the quadratic Lagrangian.In Minkowski spacetime, they naturally appear in the presence of a coupling among fields withtime-dependent vacuum expectation values and fields withspace-dependent vacuum expectation values, breaking spontaneouslyLorentz symmetry; this is the case for a supersolid. In a cosmological backgrounda gyroscopic system can also arise from the time dependence ofnon-diagonal kinetic and mass matrices.We study the classical and quantum dynamics computing the correlationfunctions on the vacuum state that minimizes the energy.Tworegions of stability in parameter space are found: in one region, dubbed normal, theHamiltonian is positive defined, while in the second region, dubbed anomalous, it has no definite sign. Interestingly, in the anomalousregion the 2-point correlation function exhibits a resonant behaviourin a certain region of parameter space. We show that as dynamical a dark energy (with an exact equation of state w = -1)arises naturally as a gyroscopic system.