52,960 research outputs found
On the distribution of the total energy of a system on non-interacting fermions: random matrix and semiclassical estimates
We consider a single particle spectrum as given by the eigenvalues of the
Wigner-Dyson ensembles of random matrices, and fill consecutive single particle
levels with n fermions. Assuming that the fermions are non-interacting, we show
that the distribution of the total energy is Gaussian and its variance grows as
n^2 log n in the large-n limit. Next to leading order corrections are computed.
Some related quantities are discussed, in particular the nearest neighbor
spacing autocorrelation function. Canonical and gran canonical approaches are
considered and compared in detail. A semiclassical formula describing, as a
function of n, a non-universal behavior of the variance of the total energy
starting at a critical number of particles is also obtained. It is illustrated
with the particular case of single particle energies given by the imaginary
part of the zeros of the Riemann zeta function on the critical line.Comment: 28 pages in Latex format, 5 figures, submitted for publication to
Physica
ESR study of the single-ion anisotropy in the pyrochlore antiferromagnet Gd2Sn2O7
Single-ion anisotropy is of importance for the magnetic ordering of the
frustrated pyrochlore antiferromagnets Gd2Ti2O7 and Gd2Sn2O7. The anisotropy
parameters for the Gd2Sn2O7 were measured using the electron spin resonance
(ESR) technique. The anisotropy was found to be of the easy plane type, with
the main constant D=140mK. This value is 35% smaller than the value of the
corresponding anisotropy constant in the related compound Gd2Ti2O7.Comment: 8 pages, 3 figure
Black and gray Helmholtz Kerr soliton refraction
efraction of black and gray solitons at boundaries separating different defocusing Kerr media is analyzed within a Helmholtz framework. A universal nonlinear Snell’s law is derived that describes gray soliton refraction, in addition to capturing the behavior of bright and black Kerr solitons at interfaces. Key regimes, defined by beam and interface characteristics, are identified and predictions are verified by full numerical simulations. The existence of a unique total non-refraction angle for gray solitons is reported; both internal and external refraction at a single interface is shown possible (dependent only on incidence angle). This, in turn, leads to the proposal of positive or negative lensing operations on soliton arrays at planar boundaries
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