Unlike the Berry phase, orbital angular momentum (OAM) of magnons with two-dimensional wavevector k in band n is not gauge invariant for arbitrary phase lambda_n(k). However, by integrating OAM over orientation $\phi $ k, we construct a gauge-invariant function F_n(k). Like F_n(k), average magnon circle radius also invariant. We demonstrate these results ferromagnet on honeycomb lattice Dzyallo...

We investigate properties of the invariant measure for the A0 gauge field in finite temperature gauge theories both on the lattice and in the continuum theory. We have found the cancellation of the naive measure in both cases. The result is quite general and holds at any finite temperature. We demonstrate, however, that there is no cancellation at any temperature for the invariant measure contr...

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show that as the forcing and dissipation are removed a unique limit of the deterministic system is selected. The exact structure of the limiting measure depends on...

Abstract: We provide a Hamiltonian analysis of the Mixmaster Universe dynamics showing the covariant nature of its chaotic behavior with respect to any choice of time variable. We construct the appropriate invariant measure for the system (which relies on the existence of an “energy-like” constant of motion) without fixing the time gauge, i.e. the corresponding lapse function. The key point in ...

A technique to measure microscopic rotational motion is presented. When a small fluorescent polystyrene microsphere is attached to a larger polystyrene microsphere, the larger sphere acts as a lens for the smaller microsphere and provides an optical signal that is a strong function of the azimuthal angle. We demonstrate the technique by measuring the rotational diffusion constant of the microsp...