84,888 research outputs found
Higher genus partition functions of meromorphic conformal field theories
It is shown that the higher genus vacuum amplitudes of a meromorphic
conformal field theory determine the affine symmetry of the theory uniquely,
and we give arguments that suggest that also the representation content with
respect to this affine symmetry is specified, up to automorphisms of the finite
Lie algebra. We illustrate our findings with the self-dual theories at c=16 and
c=24; in particular, we give an elementary argument that shows that the vacuum
amplitudes of the E_8\times E_8 theory and the Spin(32)/Z_2 theory differ at
genus g=5. The fact that the discrepancy only arises at rather high genus is a
consequence of the modular properties of higher genus amplitudes at small
central charges. In fact, we show that for c\leq 24 the genus one partition
function specifies already the partition functions up to g\leq 4 uniquely.
Finally we explain how our results generalise to non-meromorphic conformal
field theories.Comment: 43 pages, 7 figure
Aspects of stochastic resonance in reaction-diffusion systems: The nonequilibrium-potential approach
We analyze several aspects of the phenomenon of stochastic resonance in
reaction-diffusion systems, exploiting the nonequilibrium potential's
framework. The generalization of this formalism (sketched in the appendix) to
extended systems is first carried out in the context of a simplified scalar
model, for which stationary patterns can be found analytically. We first show
how system-size stochastic resonance arises naturally in this framework, and
then how the phenomenon of array-enhanced stochastic resonance can be further
enhanced by letting the diffusion coefficient depend on the field. A yet less
trivial generalization is exemplified by a stylized version of the
FitzHugh-Nagumo system, a paradigm of the activator-inhibitor class. After
discussing for this system the second aspect enumerated above, we derive from
it -through an adiabatic-like elimination of the inhibitor field- an effective
scalar model that includes a nonlocal contribution. Studying the role played by
the range of the nonlocal kernel and its effect on stochastic resonance, we
find an optimal range that maximizes the system's response.Comment: 16 pages, 15 figures, uses svjour.cls and svepj-spec.clo. Minireview
to appear in The European Physical Journal Special Topics (issue in memory of
Carlos P\'erez-Garc\'{\i}a, edited by H. Mancini
On the use of the proximity force approximation for deriving limits to short-range gravitational-like interactions from sphere-plane Casimir force experiments
We discuss the role of the proximity force approximation in deriving limits
to the existence of Yukawian forces - predicted in the submillimeter range by
many unification models - from Casimir force experiments using the sphere-plane
geometry. Two forms of this approximation are discussed, the first used in most
analyses of the residuals from the Casimir force experiments performed so far,
and the second recently discussed in this context in R. Decca et al. [Phys.
Rev. D 79, 124021 (2009)]. We show that the former form of the proximity force
approximation overestimates the expected Yukawa force and that the relative
deviation from the exact Yukawa force is of the same order of magnitude, in the
realistic experimental settings, as the relative deviation expected between the
exact Casimir force and the Casimir force evaluated in the proximity force
approximation. This implies both a systematic shift making the actual limits to
the Yukawa force weaker than claimed so far, and a degree of uncertainty in the
alpha-lambda plane related to the handling of the various approximations used
in the theory for both the Casimir and the Yukawa forces. We further argue that
the recently discussed form for the proximity force approximation is
equivalent, for a geometry made of a generic object interacting with an
infinite planar slab, to the usual exact integration of any additive two-body
interaction, without any need to invoke approximation schemes. If the planar
slab is of finite size, an additional source of systematic error arises due to
the breaking of the planar translational invariance of the system, and we
finally discuss to what extent this may affect limits obtained on power-law and
Yukawa forces.Comment: 11 page, 5 figure
Comprehensive rate coefficients for electron collision induced transitions in hydrogen
Energy-changing electron-hydrogen atom collisions are crucial to regulating
the energy balance in astrophysical and laboratory plasmas and relevant to the
formation of stellar atmospheres, recombination in H-II clouds, primordial
recombination, three-body recombination and heating in ultracold and fusion
plasmas. Computational modeling of electron-hydrogen collision has been
attempted through quantum mechanical scattering state-to-state calculations of
transitions involving low-lying energy levels in hydrogen (with principal
quantum number n < 7) and at large principal quantum numbers using classical
trajectory techniques. Analytical expressions are proposed which interpolates
the current quantum mechanical and classical trajectory results for
electron-hydrogen scattering in the entire range of energy levels, for nearly
all temperature range of interest in astrophysical environments. An asymptotic
expression for the Born cross-section is interpolated with a modified
expression derived previously for electron-hydrogen scattering in the Rydberg
regime using classical trajectory Monte Carlo simulations. The derived formula
is compared to existing numerical data for transitions involving low principal
quantum numbers, and the dependence of the deviations upon temperature is
discussed.Comment: To appear in The Astrophysical Journa
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