14,982 research outputs found
Tunneling with the Lorentz Force and the Friction
We present a semiclassical study of a transport process, the tunneling, in
the presence of a magnetic field and a dissipative environment. We have found
that the problem can be mapped onto an effective one-dimensional one, and the
tunneling rate is strongly affected by the magnetic field, such as a complete
suppression by a large parallel magnetic field, an example of the dynamical
localization. In such case a small perpendicular component of the field, or the
dissipation, can enhance the tunneling rate. In the small parallel field and
finite temperatures the tunneling rate is finite. Explicit expressions will be
presented in those cases. If viewing the tunneling in the presence of a
magnetic field as a dissipative tunneling process, by varying the magnetic
field and the potential one can obtain the dissipative spectral function
between the subohmic and the superohmic . In combination
with a real dissipative spectral function, the effect of the magnetic field can
map the spectral function from to , with mapping to ,
revealing a dual symmetry between the friction and the Lorentz force. Two cases
relevant to experiments, the edge state tunneling in a Hall bar and the
tunneling near the dynamical localization will be discussed in detail.Comment: Late
Approximation formulas for the constant <i>e</i> and an improvement to a Carleman-type inequality
On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas
Inequalities and asymptotic expansions related to the volume of the unit ball in R<sup>n</sup>
Let Ωn=πn/2/Γ(n2+1)(n∈N)Ωn=πn/2/Γ(n2+1)(n∈N) denote the volume of the unit ball in RnRn. In this paper, we present asymptotic expansions and inequalities related to ΩnΩn and the quantities:Ωn−1Ωn,ΩnΩn−1+Ωn+1andΩ1/nnΩ1/(n+1)n+1
On the asymptotics of products related to generalizations of the Wilf and Mortini problems
In this paper, we present the connection between generalized Wilf’sand Mortini’s problems. We also consider the connection betweenanother infinite product formula and limit relation with severalparameters
Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function
In this paper, we present some completely monotonic functions and asymptotic expansions related to the gamma function. Based on the obtained expansions, we provide new bounds for Γ(x + 1)/Γ(x + 1/2) and Γ(x + 1/2)
Non-linear supersymmetric Sigma-Model for Diffusive Scattering of Classical Waves with Resonance Enhancement
We derive a non-linear sigma-model for the transport of light (classical
waves) through a disordered medium. We compare this extension of the model with
the well-established non-linear sigma-model for the transport of electrons
(Schroedinger waves) and display similarities of and differences between both
cases. Motivated by experimental work (M. van Albada et al., Phys. Rev. Lett.
66 (1991) 3132), we then generalize the non-linear sigma-model further to
include resonance scattering. We find that the form of the effective action is
unchanged but that a parameter of the effective action, the mean level density,
is modified in a manner which correctly accounts for the data.Comment: 4 pages, 1 Figure, to be published in Europhysics Letter
Constraints on primordial black holes and primeval density perturbations from the epoch of reionization
We investigate the constraint on the abundance of primordial black holes
(PBHs) and the spectral index of primeval density perturbations given by
the ionizing photon background at the epoch of reionization. Within the
standard inflationary cosmogony, we show that the spectral index of the
power-law power spectrum of primeval density perturbations should be 1.27.
Since the universe is still optical thick at the reionization redshift - 8, this constraint is independent of the unknown parameter of reheating
temperature of the inflation. The ionizing photon background from the PBHs can
be well approximated by a power law spectrum , which is
greatly different from those given by models of massive stars and quasars.Comment: 4 pages, 3 eps figues, to be published in ApJ Letter
Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500
Published in International Economic Review, https://doi.org/10.1111/iere.12132</p
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