41 research outputs found
Theory of the Microscopic Maser Phase Transitions
Phase diagrams of the micromaser system are mapped out in terms of the physical parameters at hand like the atom cavity transit time, the atom-photon frequency detuning, the number of thermal photons and the probability for a pump atom to be in its excited state. Critical fluctuations are studied in terms of correlation measurements on atoms having passed through the micromaser or on the microcavity photons themselves. At sufficiently large values of the detuning we find a ``twinkling'' mode of the micromaser system. Detailed properties of the trapping states are also presented
Macroscopic Interference Effects in Resonant Cavities
We investigate the possibility of interference effects induced by macroscopic
quantum-mechanical superpositions of almost othogonal coherent states - a
Schroedinger cats state - in a resonant microcavity. Despite the fact that a
single atom, used as a probe of the cat state, on the average only change the
mean number of photons by one unit, we show that this single atom can change
the system drastically. Interference between the initial and almost orthogonal
macroscopic quantum states of the radiation field can now take place.
Dissipation under current experimental conditions is taken into account and it
is found that this does not necessarily change the intereference effects
dramatically.Comment: 20 pages, 3 figure
Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect
Our previous ``exotic'' particle, together with the more recent anomalous
anyon model (which has arbitrary gyromagnetic factor ) are reviewed. The
non-relativistic limit of the anyon generalizes the exotic particle which has
to any .When put into planar electric and magnetic fields, the Hall
effect becomes mandatory for all , when the field takes some critical
value.Comment: A new reference added. Talk given by P. Horvathy at the International
Workshop "Nonlinear Physics: Theory and Experiment. III. July'04, Gallipoli
(Lecce, Italy). To be published in Theor. Math. Phys. Latex 9 pages, no
figure
Deconfinement in Matrix Models about the Gross--Witten Point
We study the deconfining phase transition in SU(N) gauge theories at nonzero
temperature using a matrix model of Polyakov loops. The most general effective
action, including all terms up to two spatial derivatives, is presented. At
large N, the action is dominated by the loop potential: following Aharony et
al., we show how the Gross--Witten model represents an ultra-critical point in
this potential. Although masses vanish at the Gross--Witten point, the
transition is of first order, as the fundamental loop jumps only halfway to its
perturbative value. Comparing numerical analysis of the N=3 matrix model to
lattice simulations, for three colors the deconfining transition appears to be
near the Gross--Witten point. To see if this persists for N >= 4, we suggest
measuring within a window ~1/N^2 of the transition temperature.Comment: 22 pages, 7 figures; revtex4. A new Fig. 2 illustrates a strongly
first order transition away from the GW point; discussion added to clarify
relation to hep-th/0310285. Conclusions include a discussion of recent
lattice data for N>3, hep-lat/0411039 and hep-lat/050200
Spin-orbit coupling and the conservation of angular momentum
In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin)
angular momentum of a charged particle with spin that moves in a Coulomb plus
spin-orbit-coupling potential is conserved. In a classical nonrelativistic
treatment of this problem, in which the Lagrange equations determine the
orbital motion and the Thomas equation yields the rate of change of the spin,
the particle's total angular momentum in which the orbital angular momentum is
defined in terms of the kinetic momentum is generally not conserved. However, a
generalized total angular momentum, in which the orbital part is defined in
terms of the canonical momentum, is conserved. This illustrates the fact that
the quantum-mechanical operator of momentum corresponds to the canonical
momentum of classical mechanics.Comment: 10 pages, as published by Eur. J. Phy
A First Principles Estimate of Finite Size Effects in Quark-Gluon Plasma Formation
Using lattice simulations of quenched QCD we estimate the finite size effects
present when a gluon plasma equilibrates in a slab geometry, i.e., finite width
but large transverse dimensions. Significant differences are observed in the
free energy density for the slab when compared with bulk behavior. A small
shift in the critical temperature is also seen. The free energy required to
liberate heavy quarks relative to bulk is measured using Polyakov loops; the
additional free energy required is on the order of 30-40 MeV at 2-3 T_c.Comment: 10 pages, 5 figures, RevTeX; revised version includes comparison with
the Bjorken model and various small improvement
Phenomenological Equations of State for the Quark-Gluon Plasma
Two phenomenological models describing an SU(N) quark-gluon plasma are
presented. The first is obtained from high temperature expansions of the free
energy of a massive gluon, while the second is derived by demanding color
neutrality over a certain length scale. Each model has a single free parameter,
exhibits behavior similar to lattice simulations over the range T_d - 5T_d, and
has the correct blackbody behavior for large temperatures. The N = 2
deconfinement transition is second order in both models, while N = 3,4, and 5
are first order. Both models appear to have a smooth large-N limit. For N >= 4,
it is shown that the trace of the Polyakov loop is insufficient to characterize
the phase structure; the free energy is best described using the eigenvalues of
the Polyakov loop. In both models, the confined phase is characterized by a
mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop
expectation value zero. In the deconfined phase, the rotation of the
eigenvalues in the complex plane towards 1 is responsible for the approach to
the blackbody limit over the range T_d - 5T_d. The addition of massless quarks
in SU(3) breaks Z(3) symmetry weakly and eliminates the deconfining phase
transition. In contrast, a first-order phase transition persists with
sufficiently heavy quarks.Comment: 22 pages, RevTeX, 9 eps file
From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics
In 1990, Dyson published a proof due to Feynman of the Maxwell equations
assuming only the commutation relations between position and velocity. With
this minimal assumption, Feynman never supposed the existence of Hamiltonian or
Lagrangian formalism. In the present communication, we review the study of a
relativistic particle using ``Feynman brackets.'' We show that Poincar\'e's
magnetic angular momentum and Dirac magnetic monopole are the consequences of
the structure of the Lorentz Lie algebra defined by the Feynman's brackets.
Then, we extend these ideas to the dual momentum space by considering
noncommutative quantum mechanics. In this context, we show that the
noncommutativity of the coordinates is responsible for a new effect called the
spin Hall effect. We also show its relation with the Berry phase notion. As a
practical application, we found an unusual spin-orbit contribution of a
nonrelativistic particle that could be experimentally tested. Another practical
application is the Berry phase effect on the propagation of light in
inhomogeneous media.Comment: Presented at the 3rd Feynman Festival (Collage Park, Maryland,
U.S.A., August 2006
Dynamics, correlations and phases of the micromaser
The micromaser possesses a variety of dynamical phase transitions
parametrized by the flux of atoms and the time-of-flight of the atom within the
cavity. We discuss how these phases may be revealed to an observer outside the
cavity using the long-time correlation length in the atomic beam. Some of the
phase transitions are not reflected in the average excitation level of the
outgoing atom, which is the commonly used observable. The correlation length is
directly related to the leading eigenvalue of the time evolution operator,
which we study in order to elucidate the phase structure. We find that as a
function of the time-of-flight the transition from the thermal to the maser
phase is characterized by a sharp peak in the correlation length. For longer
times-of-flight there is a transition to a phase where the correlation length
grows exponentially with the flux. We present a detailed numerical and
analytical treatment of the different phases and discuss the physics behind
them.Comment: 60 pages, 18 figure files, Latex + \special{} for the figures, (some
redundant figures are eliminated and others are changed