39 research outputs found
A New Expansion of the Heisenberg Equation of Motion with Projection Operator
We derive a new expansion of the Heisenberg equation of motion based on the
projection operator method proposed by Shibata, Hashitsume and Shing\=u. In
their projection operator method, a certain restriction is imposed on the
initial state. As a result, one cannot prepare arbitrary initial states, for
example a coherent state, to calculate the time development of quantum systems.
In this paper, we generalize the projection operator method by relaxing this
restriction. We explain our method in the case of a Hamiltonian both with and
without explicit time dependence. Furthermore, we apply it to an exactly
solvable model called the damped harmonic oscillator model and confirm the
validity of our method.Comment: 16 pages, revtex, no figures, To appear in Prog.Theor.Phy
Projection Operator Approach to Langevin Equations in Theory
We apply the projection operator method (POM) to theory and derive
both quantum and semiclassical equations of motion for the soft modes. These
equations have no time-convolution integral term, in sharp contrast with other
well-known results obtained using the influence functional method (IFM) and the
closed time path method (CTP). However, except for the fluctuation force field
terms, these equations are similar to the corresponding equations obtained
using IFM with the linear harmonic approximation, which was introduced to
remove the time-convolution integral. The quantum equation of motion in POM can
be regarded as a kind of quantum Langevin equation in which the fluctuation
force field is given in terms of the operators of the hard modes. These
operators are then replaced with c-numbers using a certain procedure to obtain
a semiclassical Langevin equation. It is pointed out that there are significant
differences between the fluctuation force fields introduced in this paper and
those introduced in IFM. The arbitrariness of the definition of the fluctuation
force field in IFM is also discussed.Comment: 35pages,2figures, Prog. Theor. Phys. Vol. 107 No. 5 in pres
U(1) symmetry breaking in one-dimensional Mott insulator studied by the Density Matrix Renormalization Group method
A new type of external fields violating the particle number preservation is
studied in one-dimensional strongly correlated systems by the Density Matrix
Renormalization Group method. Due to the U(1) symmetry breaking, the ground
state has fluctuation of the total particle number, which implies injection of
electrons and holes from out of the chain. This charge fluctuation can be
relevant even at half-filling because the particle-hole symmetry is preserved
with the finite effective field. In addition, we discuss a quantum phase
transition obtained by considering the symmetry-breaking fields as a mean field
of interchain-hopping.Comment: 7 pages, 4 figure
Phenomenological approach to the critical dynamics of the QCD phase transition revisited
The phenomenological dynamics of the QCD critical phenomena is revisited.
Recently, Son and Stephanov claimed that the dynamical universality class of
the QCD phase transition belongs to model H. In their discussion, they employed
a time-dependent Ginzburg-Landau equation for the net baryon number density,
which is a conserved quantity. We derive the Langevin equation for the net
baryon number density, i.e., the Cahn-Hilliard equation. Furthermore, they
discussed the mode coupling induced through the {\it irreversible} current.
Here, we show the {\it reversible} coupling can play a dominant role for
describing the QCD critical dynamics and that the dynamical universality class
does not necessarily belong to model H.Comment: 13 pages, the Curie principle is discussed in S.2, to appear in
J.Phys.
Enhancement of Critical Slowing Down in Chiral Phase Transition -- Langevin Dynamics Approach --
We derive the linear Langevin equation that describes the behavior of the
fluctuations of the order parameter of the chiral phase transition above the
critical temperature by applying the projection operator method to the
Nambu-Jona-Lasinio model at finite temperature and density. The Langevin
equation relaxes exhibiting oscillation, reveals thermalization and converges
to the equilibrium state consistent with the mean-field approximation as time
goes on. With the help of this Langevin equation, we further investigate the
relaxation of the critical fluctuations. The relaxation time of the critical
fluctuations increases at speed as the temperature approaches toward the
critical temperature because of the critical slowing down. The critical slowing
down is enhanced as the chemical potential increases because of the Pauli
blocking. Furthermore, we find another enhancement of the critical slowing down
around the tricritical point.Comment: Style file is changed, references are added, 42 pages, 14 figures,
Nucl. Phys. A in pres