Decay of distance autocorrelation and Lyapunov exponents

This work presents numerical evidences that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance autocorrelation are observed for different systems, namely exponential decays for the quadratic map, logarithmic for the H\'enon map and power-law for the conservative standard map. In all these cases the decay exponent is close to the positive Lyapunov exponent. For hyperbolic conservative systems, the power-law decay of the distance autocorrelation tends to be guided by the smallest Lyapunov exponent.Comment: 7 pages, 8 figure

QCD Radiative Corrections to the Leptonic Decay Rate of the B_c Meson

The QCD radiative corrections to the leptonic decay rate of the $B_c$ meson are calculated using the formalism of nonrelativistic QCD (NRQCD) to separate short-distance and long-distance effects. The $B_c$ decay constant is factored into a sum of NRQCD matrix elements each multiplied by a short-distance coefficient. The short-distance coefficient for the leading matrix element is calculated to order $\alpha_s$ by matching a perturbative calculation in full QCD with the corresponding perturbative calculation in NRQCD. This short-distance correction decreases the leptonic decay rate by approximately $15\%$.Comment: Changed Eq. 2 to read 1/(8 \pi), put in a missing i M_{B_c} in Eq. 18, and put in a normalisation factor of 2 M_{B_c} in Eq. 19

Mobility and distance decay at the aggregated and individual level

Most crimes are committed near to where the offender lives; this has been observed both at the aggregate and at the offender level. At the aggregate level, as the distance increases there is a decline in the number of offences committed, and initially this decline is quite slow. This pattern has been described by a number of researchers, and results in a distance decay curve. Near-home offending has also been observed at the level of the individual offender, although it has been debated whether distance decay actually exists at the level of the individual offender. We therefore believe it is important to distinguish near-home offending from decay, i.e. the gradual decline in offences as distances increase. This paper studies mobility patterns and decay curves on serious property crimes in Belgium. First, aggregated patterns are discussed and categorised. Second, individual offenders are analysed. It becomes clear through studying offender patterns that offender mobility and decay are not intertwined at the individual level to the same extent as they are at the aggregate level. This suggests that it is important, particularly when studying individual offenders, to clarify whether (average) distances or decay are being considered

Long distance contribution to B−→K−K−π+B^- \to K^- K^- \pi^+, - a searching ground mode for new physics

The decay $B^- \to K^- K^- \pi^+$ has been sugested as a test for minimal supersymmetric standard model and for supersymmetric models with R-parity violating couplings, in view of its extreme smallnesss in the standard model. We calculate two long distance contributions to this decay, that associated with $DD$ and $D\pi$ intermediate states and that induced by virtual $D$, $\pi$ mesons. The branching ratio due to these contributions is $6 \times 10^{-12}$, which is somewhat smaller than the standard model short distance result, leaving this decay free for the search of new physics.Comment: 13 pages, 2 figures, revised versio

Updated constraints on new physics in rare charm decays

Motivated by recent experimental results on charm physics we investigate implications of the updated constraints of new physics in rare charm meson decays. We first reconsider effects of the MSSM in $c\to u \gamma$ constrained by the recent experimental evidence on $\Delta m_D$ and find, that due to the dominance of long distance physics, $D \to V \gamma$ decay rates cannot be modified by MSSM contributions. Then we consider effects of the extra heavy up vector-like quark models on the decay spectrum of $D^+ \to \pi^+ l^+ l^-$ and $D_s^+ \to K^+ l^+ l^-$ decays. We find a possibility for the tiny increase of the differential decay rate in the region of large dilepton mass. The R-parity violating supersymmetric model can also modify short distance dynamics in $c \to u l^+ l^-$ decays. We constrain relevant parameters using current upper bound on the $D^+ \to \pi^+ l^+ l^-$ decay rate and investigate impact of that constraint on the $D_s^+ \to K^+ l^+ l^-$ differential decay dilepton distribution. Present bounds still allow small modification of the standard model differential decay rate distribution.Comment: 15 pages, 4 figure

Enhanced observability of quantum post-exponential decay using distant detectors

We study the elusive transition from exponential to post-exponential (algebraic) decay of the probability density of a quantum particle emitted by an exponentially decaying source, in one dimension. The main finding is that the probability density at the transition time, and thus its observability, increases with the distance of the detector from the source, up to a critical distance beyond which exponential decay is no longer observed. Solvable models provide explicit expressions for the dependence of the transition on resonance and observational parameters, facilitating the choice of optimal conditions