Parameters of a slightly degenerate plasma

Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay’s angle

“…A simple observation of Hannay's angle is possible for an ellipically orbiting object in celestial mechanics by averaging initial angles of the motion over the torus [35][36][37][38]. Such measurability of Hannay's angle can be extended to more general and complicated systems, such as circular threebody gravitational systems [24,25,39], non-Abellian gauge fields systems [40], interacting many-particle boson systems [41], and systems undergoing noncyclic evolution [42]. In cosmology associated with the theory developed here, the evolution of Hannay's angle given in Eq.…”

“…Hannay's angle is the classical counterpart of the additional quantum phase known as Berry's phase [12][13][14][15]. Among the many areas in which Hannay's angle and Berry's phase play important roles, cosmology [6,8,[16][17][18][19][20][21][22][23] and celestial mechanics [24,25] have been actively investigated so far in connection with them. Hannay's angle (or Berry's phase) can be applied in extracting useful information associated with the theoretical interpretation of observational aspects of inflation-ary perturbations, such as the dynamical evolution of the quantum fluctuations [16], vacuum instability [17], the symmetry breaking of cosmological time [18], and energy conservation in a gravity-scalar system [19].…”

Effect of Bohm potential on a charged gas

“…In a plasma, the above expression is the plasma frequency. Laplace antitransformation of ( 16) is rather involved, however it is not indispensable if interest is focused on the asymptotic solution for large t [10,11,12,13,7], for then the evolution is dominated by the rightmost zero of the denominator in (23), and if its imaginary part is negative this will give rise to a "Landautype" damping. The problem is hence reduced to finding the solutions of the following equation ( )…”

“…Inverse Laplace transformation of Eq. (16) is rather involved, however, it is not indispensable if interest is focused on the asymptotic solution for large t [7,[10][11][12][13]. Then the evolution is dominated by the rightmost zero of the denominator in Eq.…”