abstract

One of the most important issues of quantum engineering is the construction of low-dimensional structures possessing desirable properties. For example, in different areas of possible applications of the structures containing quantum wells (QW), one often needs a predetermined QW energy spectrum. Then the following question arises: can one reconstruct the shape of QW which supports this spectrum? In this paper we outline a possible strategy of the QW potential shape reconstruction, if the QW spectrum is given in advance. The proposed approach is based on the combination of different techniques such as Inverse Scattering Problem Method, Darboux and Liouville transformation. It enables to take into account the space-variable dependent effective mass of charge carriers and allows the kinetic energy operator to be of non-Hermitian as well as Hermitian form. The proposed technique allows one to construct phase-equivalent potentials, to add the new bounded states to (or remove some of them from) the spectrum supported by an initial potential and provides a systematic procedure for generating new exactly solvable models.

abstract

After a brief summary of the geometry of static multiply warped product spacetimes, inequalities are given relating the Gaussian curvature of spacelike two-surfaces in these spacetimes with some principal sectional curvatures of the embedding space. Extremal and geodesic surfaces are respectively characterized if equality holds in an appropriate inequality.

abstract

We consider the successive measurement of position and momentum of a single particle. Let \(\cal P\) be the conditional probability to measure the momentum \(k\) with precision \(\Delta k\), given a previously successful position measurement \(q\) with precision \(\Delta q\). Several upper bounds for the probability \(\cal P\) are derived. For arbitrary, but given precisions \(\Delta q\) and \(\Delta k\), these bounds refer to the variation of \(q\), \(k\), and the state vector \(\psi \) of the particle. The first bound is given by the inequality \({\cal P}\leq \Delta k\Delta q/h\), where \(h\) is Planck’s quantum of action. It is nontrivial for all measurements with \(\Delta k\Delta q\lt h\). A sharper bound is obtained by applying the Hilbert–Schmidt norm. As our main result, the least upper bound of \(\cal P\) is determined. All bounds are independent of the order with which the measuring of the position and momentum is made.

abstract

In this article we study the possibility to bound effects of new interactions between neutrinos and the nucleons of the Earth using a recently introduced angular observable, \(\alpha \). This observable, which is to be registered in km\(^3\) neutrino telescopes such as IceCube, is only weakly dependent on the initial diffuse flux uncertainties. We investigate the capability of the observable to bound new interactions by fitting a set of values obtained for \(\alpha \) using the Standard Model cross-section and statistical errors distributed according a Poisson distribution for the surviving neutrino flux.

abstract

The chirally-odd twist-3 parton distribution function \(e^a(x)\) of the nucleon is studied in the large-\(N_c\) limit in the framework of the chiral quark-soliton model. It is demonstrated that in spite of properties not shared by other distribution functions, namely the appearance of a \(\delta (x)\)-singularity and quadratic divergences in \(e^a(x)\), an equally reliable calculation is possible. Among the most remarkable results obtained in this work is the fact that the coefficient of the \(\delta (x)\)-singularity can be computed exactly in this model, avoiding involved numerics. Our results complete existing studies in literature.

abstract

A two-source model is used in this paper to describe the reaction process of Em(\(^8\)B, \(p^7\)Be)Em at 1.2\(A\) GeV. The distribution of azimuthal angle between \(^7\)Be and \(p\), the transverse momentum distribution of \(p\), and the total transverse momentum distribution of \(^7\)Be and \(p\) produced in the reactions are analyzed. It is found that the modelling results describe approximately the fluctuation and mean trend of the experimental data of Stanoeva et al.

abstract

Gamow–Teller (GT) transitions play an important and consequential role in many astrophysical phenomena. These include, but are not limited to, electron and positron capture rates which determine the fate of massive stars and play an intricate role in the dynamics of core collapse. These GT\(_{\pm }\) transitions rates are the significant inputs in the description of supernova explosions. GT\(_{\pm }\) strength function values are sensitive to the \(^{56}\)Ni core excitation in the middle pf-shell region and to the size of the model space as well. We used the \(pn\)-QRPA theory for extracting the GT strength for ground and excited states of \(^{56}\)Ni. We then used these GT strength distributions to calculate the electron and positron capture rates which show differences with the earlier calculations. One curious finding of this paper is our enhanced electron capture rates on \(^{56}\)Ni at presupernova temperatures. These differences need to be taken into account for the modeling of the early stages of Type II supernova evolution.

abstract

Total cross-sections of the halo nuclei in both the zero- and the finite-ranges are calculated at energy range of 25–800 MeV/\(n\), by using the carbon nuclei as a probe. The calculations are based on the Optical Limit Approximation (OLA) of the Glauber theory and are done for Li, Be and B isotopes using the finite and the zero range interactions. We found that the total cross-sections depend slightly on the nuclear density. On the other hand, there is a discrepancy between the calculated results of both ranges in the surface region of the reaction probability. The theoretical results for the zero- and the finite-range are compared with experimental data. We found that the zero-range predictions are consistent with experimental data more than the finite-range.

abstract

The muon catalyzed fusion cycle in mixtures of deuterium and tritium is of particular interest due to the observation of high fusion yields. In the D–T mixture, the most serious limitation to the efficiency of the fusion chain is the probability of muon sticking to the \(\alpha \)-particle produced in the nuclear reaction. An accurate kinetic treatment has been applied to the muonic helium atoms formed by a muon sticking to the \(\alpha \)-particles. In this work accurate rates for collisions of \(\alpha \mu ^{+}\) ions with hydrogen atoms have been used for calculation of muon stripping probability and the intensities of X-ray transitions by solving a set of coupled differential equations numerically. Our calculated results are in good agreement with experimental data available in literature.

abstract

The excited states in the \(^{149}\)Nd nucleus up to an excitation energy of about 2 MeV were investigated by (\(d,p\)) and (\(d,t\)) reactions with good energy resolution. The reaction products were analysed in a magnetic spectrograph and detected with photographic emulsion. Triton spectra from the \(^{150}\)Nd(\(d,t\))\(^{149}\)Nd reaction were measured at thirteen reaction angles from 5\(^{\circ }\) to 125\(^{\circ }\) and the \(^{148}\)Nd(\(d,p\))\(^{149}\)Nd reaction was studied at three angles, 60\(^{\circ }\), 90\(^{\circ }\) and 125\(^{\circ }\), using beams of 12.1 MeV deuterons. The (\(d,t\)) angular distributions and ratios of (\(d,t\)) and (\(d,p\)) cross sections at selected angles were used to determine \(l\) values for a number of transitions. The reaction products were analysed with standard DWBA calculations and spectroscopic factors were deduced. The measured triton angular distributions are well described by the DWBA calculations and on these bases it was possible to give unambiguous assignments for a numbers of levels.

abstract

A critical evaluation of all the data on the level structures of \(^{178}\)Hf, \(^{168}\)Er, \(^{162}\)Dy and \(^{164}\)Dy with special emphasis on the \((n,\gamma )\) studies with average resonance capture (ARC) indicates the presence of a total of 4 states which are anomalous and may be chaotic (1 in \(^{178}\)Hf below 1800 keV, 1 in \(^{162}\)Dy below 2000 keV, and 2 in \(^{164}\)Dy below 2000 keV) imbedded among the normal quadrupole deformed rotational states.

abstract

The hydrodynamic description of transversally thermalized matter, possibly formed at the early stages of ultra-relativistic heavy-ion collisions, is developed. The formalism is based on the thermodynamically consistent approach with all thermodynamic variables referring to two-dimensional objects, the so-called transverse clusters, which are identified with the particles having the same rapidity. The resulting hydrodynamic equations for a single cluster have the form of the two-dimensional hydrodynamic equations of the perfect fluid. Since the clusters do not perform any work in the longitudinal direction, their energy is completely transformed and used to generate strong radial and elliptic flows that turn out to be compatible with the experimental data.

abstract

We introduce the alternate social networks (ASN) model to study the epidemic threshold of SIS epidemic. The alternate social networks consist of a family network and a public network, mimicking the human contacts during some time (e.g. nighttime) and other time (e.g. daytime) respectively. Both the family network and the public network are constructed by a set of sub networks which can exhibit small-world properties, scale-free degree distribution or the household structure, representing various types of local interactions among social groups in modern society. Simulations show that the ASN has the essential characteristics of social networks, and the local fully connected structures (households) as well as the existence of local structures (publics) in the public network are two dominating ingredients for the epidemic threshold. Moreover, results show that the epidemic threshold in ASN is independent of the initial condition and the system size.