14,758 research outputs found
Quantized Non-Abelian Monopoles on S^3
A possible electric-magnetic duality suggests that the confinement of
non-Abelian electric charges manifests itself as a perturbative quantum effect
for the dual magnetic charges. Motivated by this possibility, we study vacuum
fluctuations around a non-Abelian monopole-antimonopole pair treated as point
objects with charges g=\pm n/2 (n=1,2,...), and placed on the antipodes of a
three sphere of radius R. We explicitly find all the fluctuation modes by
linearizing and solving the Yang-Mills equations about this background field on
a three sphere. We recover, generalize and extend earlier results, including
those on the stability analysis of non-Abelian magnetic monopoles. We find that
for g \ge 1 monopoles there is an unstable mode that tends to squeeze magnetic
flux in the angular directions. We sum the vacuum energy contributions of the
fluctuation modes for the g=1/2 case and find oscillatory dependence on the
cutoff scale. Subject to certain assumptions, we find that the contribution of
the fluctuation modes to the quantum zero point energy behaves as -R^{-2/3} and
hence decays more slowly than the classical -R^{-1} Coulomb potential for large
R. However, this correction to the zero point energy does not agree with the
linear growth expected if the monopoles are confined.Comment: 18 pages, 5 figures. Minor changes, reference list update
Magnetoconductance of carbon nanotube p-n junctions
The magnetoconductance of p-n junctions formed in clean single wall carbon
nanotubes is studied in the noninteracting electron approximation and
perturbatively in electron-electron interaction, in the geometry where a
magnetic field is along the tube axis. For long junctions the low temperature
magnetoconductance is anomalously large: the relative change in the conductance
becomes of order unity even when the flux through the tube is much smaller than
the flux quantum. The magnetoconductance is negative for metallic tubes. For
semiconducting and small gap tubes the magnetoconductance is nonmonotonic;
positive at small and negative at large fields.Comment: 5 pages, 2 figure
A Nearly Scale Invariant Spectrum of Gravitational Radiation from Global Phase Transitions
Using a large N sigma model approximation we explicitly calculate the power
spectrum of gravitational waves arising from a global phase transition in the
early universe and we confirm that it is scale invariant, implying an
observation of such a spectrum may not be a unique feature of inflation.
Moreover, the predicted amplitude can be over 3 orders of magnitude larger than
the naive dimensional estimate, implying that even a transition that occurs
after inflation may dominate in Cosmic Microwave Background polarization or
other gravity wave signals.Comment: 4 pages, PRL published versio
Recommended from our members
Numerical modelling of microwave sintering of lunar simulants under near lunar atmospheric condition
Adequacy of the Dicke model in cavity QED: a counter-"no-go" statement
The long-standing debate whether the phase transition in the Dicke model can
be realized with dipoles in electromagnetic fields is yet an unsettled one. The
well-known statement often referred to as the "no-go theorem", asserts that the
so-called A-square term, just in the vicinity of the critical point, becomes
relevant enough to prevent the system from undergoing a phase transition. At
variance with this common belief, in this paper we prove that the Dicke model
does give a consistent description of the interaction of light field with the
internal excitation of atoms, but in the dipole gauge of quantum
electrodynamics. The phase transition cannot be excluded by principle and a
spontaneous transverse-electric mean field may appear. We point out that the
single-mode approximation is crucial: the proper treatment has to be based on
cavity QED, wherefore we present a systematic derivation of the dipole gauge
inside a perfect Fabry-P\'erot cavity from first principles. Besides the impact
on the debate around the Dicke phase transition, such a cleanup of the
theoretical ground of cavity QED is important because currently there are many
emerging experimental approaches to reach strong or even ultrastrong coupling
between dipoles and photons, which demand a correct treatment of the Dicke
model parameters
Resonance modes in a 1D medium with two purely resistive boundaries: calculation methods, orthogonality and completeness
Studying the problem of wave propagation in media with resistive boundaries
can be made by searching for "resonance modes" or free oscillations regimes. In
the present article, a simple case is investigated, which allows one to
enlighten the respective interest of different, classical methods, some of them
being rather delicate. This case is the 1D propagation in a homogeneous medium
having two purely resistive terminations, the calculation of the Green function
being done without any approximation using three methods. The first one is the
straightforward use of the closed-form solution in the frequency domain and the
residue calculus. Then the method of separation of variables (space and time)
leads to a solution depending on the initial conditions. The question of the
orthogonality and completeness of the complex-valued resonance modes is
investigated, leading to the expression of a particular scalar product. The
last method is the expansion in biorthogonal modes in the frequency domain, the
modes having eigenfrequencies depending on the frequency. Results of the three
methods generalize or/and correct some results already existing in the
literature, and exhibit the particular difficulty of the treatment of the
constant mode
Evaluation of exercises taken from the Druker thesis of first grade reading materials of high interest level.
Thesis (Ed.M.)--Boston Universit
Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
We provide Lyapunov-like characterizations of boundedness and convergence of
non-trivial solutions for a class of systems with unstable invariant sets.
Examples of systems to which the results may apply include interconnections of
stable subsystems with one-dimensional unstable dynamics or critically stable
dynamics. Systems of this type arise in problems of nonlinear output
regulation, parameter estimation and adaptive control.
In addition to providing boundedness and convergence criteria the results
allow to derive domains of initial conditions corresponding to solutions
leaving a given neighborhood of the origin at least once. In contrast to other
works addressing convergence issues in unstable systems, our results require
neither input-output characterizations for the stable part nor estimates of
convergence rates. The results are illustrated with examples, including the
analysis of phase synchronization of neural oscillators with heterogenous
coupling
- …