44 research outputs found
Grassmann Variables and the Jaynes-Cummings Model
This paper shows that phase space methods using a positive P type
distribution function involving both c-number variables (for the cavity mode)
and Grassmann variables (for the two level atom) can be used to treat the
Jaynes-Cummings model. Although it is a Grassmann function, the distribution
function is equivalent to six c-number functions of the two bosonic variables.
Experimental quantities are given as bosonic phase space integrals involving
the six functions. A Fokker-Planck equation involving both left and right
Grassmann differentiation can be obtained for the distribution function, and is
equivalent to six coupled equations for the six c-number functions.
The approach used involves choosing the canonical form of the (non-unique)
positive P distribution function, where the correspondence rules for bosonic
operators are non-standard and hence the Fokker-Planck equation is also
unusual. Initial conditions, such as for initially uncorrelated states, are
used to determine the initial distribution function. Transformations to new
bosonic variables rotating at the cavity frequency enables the six coupled
equations for the new c-number functions (also equivalent to the canonical
Grassmann distribution function) to be solved analytically, based on an ansatz
from a 1980 paper by Stenholm. It is then shown that the distribution function
is the same as that determined from the well-known solution based on coupled
equations for state vector amplitudes of atomic and n-photon product states.
The treatment of the simple two fermion mode Jaynes-Cummings model is a
useful test case for the future development of phase space Grassmann
distribution functional methods for multi-mode fermionic applications in
quantum-atom optics.Comment: 57 pages, 0 figures. Version
Recurrent dynamical symmetry breaking and restoration by Wilson lines at finite densities on a torus
In this paper we derive the general expression of a one-loop effective
potential of the nonintegrable phases of Wilson lines for an SU(N) gauge theory
with a massless adjoint fermion defined on the spactime manifold
at finite temperature and fermion density. The Phase
structure of the vacuum is presented for the case with and N=2 at zero
temperature. It is found that gauge symmetry is broken and restored alternately
as the fermion density increases, a feature not found in the Higgs mechanism.
It is the manifestation of the quantum effects of the nonintegrable phases.Comment: 17 pages, 2 figure