3,906 research outputs found
Effective Non-Hermitian Hamiltonians for Studying Resonance Statistics in Open Disordered Systems
We briefly discuss construction of energy-dependent effective non-hermitian
hamiltonians for studying resonances in open disordered systemsComment: Latex, 20 pages, 1 fig. Expanded version of a talk at the Workshop on
Pseudo-Hermitian Hamiltonians in Quantum Physics IX, June 21-24 2010,
Zhejiang University, Hangzhou, China. Accepted for publication in the
Internationa Journal of Theoretical Physics (Springer Verlag
Dynamical Generation of Extended Objects in a Dimensional Chiral Field Theory: Non-Perturbative Dirac Operator Resolvent Analysis
We analyze the dimensional Nambu-Jona-Lasinio model non-perturbatively.
In addition to its simple ground state saddle points, the effective action of
this model has a rich collection of non-trivial saddle points in which the
composite fields \sigx=\lag\bar\psi\psi\rag and \pix=\lag\bar\psi
i\gam_5\psi\rag form static space dependent configurations because of
non-trivial dynamics. These configurations may be viewed as one dimensional
chiral bags that trap the original fermions (``quarks") into stable extended
entities (``hadrons"). We provide explicit expressions for the profiles of
these objects and calculate their masses. Our analysis of these saddle points
is based on an explicit representation we find for the diagonal resolvent of
the Dirac operator in a \{\sigx, \pix\} background which produces a
prescribed number of bound states. We analyse in detail the cases of a single
as well as two bound states. We find that bags that trap fermions are the
most stable ones, because they release all the fermion rest mass as binding
energy and become massless. Our explicit construction of the diagonal resolvent
is based on elementary Sturm-Liouville theory and simple dimensional analysis
and does not depend on the large approximation. These facts make it, in our
view, simpler and more direct than the calculations previously done by Shei,
using the inverse scattering method following Dashen, Hasslacher, and Neveu.
Our method of finding such non-trivial static configurations may be applied to
other dimensional field theories
Long range neutrino forces in the cosmic relic neutrino background
Neutrinos mediate long range forces among macroscopic bodies in vacuum. When
the bodies are placed in the neutrino cosmic background, these forces are
modified. Indeed, at distances long compared to the scale , the relic
neutrinos completely screen off the 2-neutrino exchange force, whereas for
small distances the interaction remains unaffected.Comment: 8 pages, 2 figure
"Single Ring Theorem" and the Disk-Annulus Phase Transition
Recently, an analytic method was developed to study in the large limit
non-hermitean random matrices that are drawn from a large class of circularly
symmetric non-Gaussian probability distributions, thus extending the existing
Gaussian non-hermitean literature. One obtains an explicit algebraic equation
for the integrated density of eigenvalues from which the Green's function and
averaged density of eigenvalues could be calculated in a simple manner. Thus,
that formalism may be thought of as the non-hermitean analog of the method due
to Br\'ezin, Itzykson, Parisi and Zuber for analyzing hermitean non-Gaussian
random matrices. A somewhat surprising result is the so called "Single Ring"
theorem, namely, that the domain of the eigenvalue distribution in the complex
plane is either a disk or an annulus. In this paper we extend previous results
and provide simple new explicit expressions for the radii of the eigenvalue
distiobution and for the value of the eigenvalue density at the edges of the
eigenvalue distribution of the non-hermitean matrix in terms of moments of the
eigenvalue distribution of the associated hermitean matrix. We then present
several numerical verifications of the previously obtained analytic results for
the quartic ensemble and its phase transition from a disk shaped eigenvalue
distribution to an annular distribution. Finally, we demonstrate numerically
the "Single Ring" theorem for the sextic potential, namely, the potential of
lowest degree for which the "Single Ring" theorem has non-trivial consequences.Comment: latex, 5 eps figures, 41 page
Constraints on Light Pseudoscalars Implied by Tests of the Gravitational Inverse-Square Law
The exchange of light pseudoscalars between fermions leads to a
spin-independent potential in order g^4, where g is the Yukawa
pseudoscalar-fermion coupling constant. This potential gives rise to detectable
violations of both the weak equivalence principle (WEP) and the gravitational
inverse-square law (ISL), even if g is quite small. We show that when
previously derived WEP constraints are combined with those arisingfrom ISL
tests, a direct experimental limit on the Yukawa coupling of light
pseudoscalars to neutrons can be inferred for the first time (g_n^2/4pi < 1.6
\times 10^-7), along with a new (and significantly improved) limit on the
coupling of light pseudoscalars to protons.Comment: 12 pages, Revtex, with 1 Postscript figure (submitted to Physical
Review Letters
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