abstract

We show analytically that a collective action of two correlated Gaussian white noises, a constant external forcing and a periodic signal leads to a linear stochastic resonance (LSR). The resonance persists for long times, survives averaging over the initial phase of the signal and is characterized by a clear maximum of the signal-to-noise ratio (SNR), unlike other cases of the LSR reported previously. We show that the problem of the LSR is closely related to the behavior of a generalized noisy logistic equation.

abstract

We investigate the mass spectrum of a scalar field in a world with latticized and circular continuum space where background fields take a topological configuration. We find that the mass spectrum is related to the characteristic values of Mathieu functions. The gauge symmetry breaking in a similar spacetime is also discussed.

abstract

The problem of the correct computation of the vacuum energy contribution to cosmological constant is discussed in the context of the relativistic invariant zeta-function approach. This method is shown to yield the value of this quantity proportional to the fourth power of the (small) quantized field mass, while the dependence on the large mass scale is only logarithmic. This value is compared to the result obtained in the dimensional regularization scheme which also satisfies the relativistic invariance condition, and found to be the same up to irrelevant finite terms. The consequences of the renormalization group invariance are also briefly discussed.

abstract

Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite dimensional Hilbert space is studied in detail. The difference between systems with discrete and continuous energy spectra is emphasized. In particular a new scaling law, characteristic for nonlocalized, states is found. Some applications for supersymmetric quantum mechanics are briefly outlined.

abstract

Within the chiral soliton model the SU(3) breaking collective Hamiltonian introduces representation mixing in the baryonic wave functions. We calculate \({\cal {O}}(m_s)\) effects of this mixing on the decay widths of decuplet and antidecuplet baryons. We find importance of the 27-plet admixture in the \({\mit \Theta }^+\) and \({\mit \Xi }_{\overline {10}}\) decays. The role of the \(1/N_{\rm c}\) nonleading terms in \({\cal {O}}(m_s)\) transition matrix elements is discussed.

abstract

We present the comparisons of two independent Monte Carlo event generators, HORACE and WINHAC, for single \(W\)-boson production in hadronic collisions with multiphoton effects in leptonic \(W\) decays. These comparisons were performed first at the parton level with fixed quark-beams energy, and then at the hadron level for proton–proton collisions at the LHC. In general, a good agreement between the two programs has been found. Possible sources of differences in some of the presented results are discussed. We also present and discuss the effects of including non-zero quark masses for the main single \(W\)-boson observables at the LHC.

abstract

Since the 3+1 neutrino models with one light sterile neutrino turn out to be not very effective, at least two light sterile neutrinos may be needed to reconcile the solar and atmospheric neutrino experiments with the LSND result, if this is confirmed by the ongoing MiniBooNE experiment (and when the CPT invariance is assumed to hold for neutrino oscillations). We present an attractive 3+2 neutrino model, where two light sterile neutrinos mix maximally with each other, in analogy to the observed maximal mixing of muon and tauon active neutrinos. But, while the mixing of \(\nu _e\) and \((\nu _\mu - \nu _\tau )~/~\sqrt 2 \) is observed as large (though not maximal), the mixing of \(\nu _e\) with the corresponding combination of two light sterile neutrinos is expected to be only moderate because of the reported smallness of LSND oscillation amplitude. The presented model turns out, however, not to be more effective in explaining the hypothetic LSND result than the simplest 3+1 neutrino model. On the other hand, in the considered 3+2 model, the deviations from conventional oscillations of three active neutrinos appear to be minimal within a larger class of 3+2 models.

abstract

Full one-loop radiative corrections are calculated for low energy neutrino–nucleon quasi-elastic scattering, \(\bar \nu _{e}+p \rightarrow e^+ + n\), which involves both Fermi and Gamow–Teller transitions, in the static limit of nucleons. The calculation is performed for both angular independent and dependent parts. We separate the corrections into the outer and inner parts à la Sirlin. The outer part is infrared and ultraviolet finite, and involves the positron velocity. The calculation of the outer part is straightforward, but that of the inner part requires a scrutiny concerning the continuation of the long-distance hadronic calculation to the short-distance quark treatment and the dependence on the model of hadron structure. We show that the logarithmically divergent parts do not depend on the structure of hadrons not only for the Fermi part, but also for the Gamow–Teller part. This observation enables us to deal with the inner part for the Gamow–Teller transition nearly parallel of that for the Fermi transition. The inner part is universal to weak charged-current processes and can be absorbed into the modification of the coupling constants up to the order of the inverse proton mass \(O(1/m_p)\). The resulting \(O(\alpha )\) corrections to the differential cross section take the form \([1+\delta _{\rm out}(E)][(1+\delta _{\rm in}^{\rm F}) \left \lt 1\right \gt ^2 +g_A^2 (1+\delta _{\rm in}^{\rm GT}) \left \lt {\mathbf \sigma }\right \gt ^2]\), where \(\left \lt 1\right \gt \) and \(\left \lt {\mathbf \sigma }\right \gt \) stand for the Fermi and Gamow–Teller matrix elements; the outer correction \(\delta _{\rm out}\) is positron energy (\(E\)) dependent and takes different functional forms for the angular independent and dependent parts. All factors are explicitly evaluated.

abstract

Using the Landshoff–Nachtmann two-gluon exchange model of the pomeron, the double pomeron exchange contribution to production of gluon pairs in the central region of rapidity is calculated. The results are compared with those for production of quark–antiquark pairs.

abstract

The core/halo model describes the Bose–Einstein correlations in multihadron production taking into account the effects of long-lived resonances. The model contains the combinatorial coefficients \(\alpha _j\) which were originally calculated from a recurrence relation. We show that \(\alpha _j\) is the integer closest to the number \(j!/e\).

abstract

The proposition of micro dynamics, called amplified imitation, is given to explain the property, called deficit in small returns, found in the return distributions of stocks traded on Polish stock market. The micro dynamics is verified in the Cont–Bouchaud model of a stock market.