Regular Series

Vol. 44 (2013), No. 10, pp. 1945 – 2073

Inequivalence of Canonical and Grand Canonical Ensembles for Bosonic Systems


For many-particle quantum systems, calculating thermodynamic quantities in the canonical ensemble is a very hard task, while this is tractable in the grand canonical ensemble. The second ensemble is then used. The results are supposed to be the same, at least in the thermodynamic limit. Is this actually the case? In this work, we consider a system of \(N\) non-interacting bosons distributed among few energy levels. We can calculate the canonical partition function in this case and deduce the canonical mean energy. We compare it to the mean energy deduced from the grand canonical ensemble for the same number of particles. We consider the case of a large number of particles.

New Method for Mapping of Exact Analytic S-wave Solutions for Regenerated Central Hyperbolic Potentials


We present a new method in the framework of non-relativistic quantum mechanics for mapping of exact analytic s-wave solutions for hyperbolic central potentials from the angular wave functions of already known quantum systems with exactly solvable ring-shaped potentials. The method is based on a coordinate redesignation and a coordinate transformation supplemented by a functional transformation. Invocation of plausible ansatz is indispensable to (re)generate hyperbolic central potentials, and the radial wave functions for the generated central potentials are shown to be normalizable elegantly.

Next-to-leading Order Perturbative Contributions in the QCD Sum Rules for Mesonic Two-point Correlation Functions with Unequal Quark Masses


In this article, we assume that two quarks have unequal masses and calculate the next-to-leading order contributions to the spectral densities of the mesonic two-point correlation functions of the vector, axialvector, scalar and pseudoscalar currents. We take dimensional regularization to regularize both the ultraviolet and infrared divergences, and use optical theorem to obtain the spectral densities directly, furthermore, we present some necessary technical details for readers convenience. The analytical expressions are applicable in many phenomenological analysis besides the QCD sum rules.

Three-body Forces from a Classical Nonlinear Field


Forces in the systems of two opposite sign and three identical charges coupled to the dynamical scalar field of the signum-Gordon model are investigated. Three-body force is present, and the exact formula for it is found. Flipping the sign of one of the two charges changes not only the sign but also the magnitude of the force. Both effects are due to nonlinearity of the field equation.

Mixture of Anisotropic Fluids


The recently introduced approach describing coupled quark and gluon anisotropic fluids is generalized to include explicitly the transitions between quarks and gluons. We study the effects of such processes on the thermalization rate of anisotropic systems. We find that the quark–gluon transitions may enhance the overall thermalization rate in the cases where the initial momentum anisotropies correspond to mixed oblate–prolate or prolate configurations. On the other hand, no effect on the thermalization rate is found in the case of oblate configurations. The observed regularities are connected with the late-time behavior of the analyzed systems which is described either by the exponential decay or the power law.

Feasibility Studies of Open Charm Measurements with the NA61/SHINE Experiment at CERN-SPS


The results of feasibility studies for the \(D^{0}\) meson (open charm) measurements by its decay into two daughter particles, pion and kaon, in central Pb–Pb collisions at SPS energies are presented. To generate the physical input we use AMPT (A Multi-Phase Transport model) event generator. We employ GEANT4 application to describe particle transport through the experimental setup. The study is done assuming NA61/SHINE detector system supplemented with a future Vertex Detector (VD), which allows for precise track reconstruction at the target proximity. This precision is needed to select pion and kaon pairs that originate from the \(D^{0}\) decays. The simulation results show that this measurement is feasible. This study also addresses the issue of vertex detector optimization with emphasis on the prospect of the development of a vertex detector based on CMOS technology.

Stock Returns Versus Trading Volume: Is the Correspondence More General?


This paper presents a quantitative analysis of the relationship between the stock market returns and corresponding trading volumes using high-frequency data from the Polish stock market. First, for stocks that were traded for sufficiently long period of time, we study the return and volume distributions and identify their consistency with the power-law functions. We find that, for majority of stocks, the scaling exponents of both distributions are systematically related by about a factor of 2 with the ones for the returns being larger. Second, we study the empirical price impact of trades of a given volume and find that this impact can be well described by a square-root dependence: \(r(V) \sim V^{1/2}\). We conclude that the properties of data from the Polish market resemble those reported in literature concerning certain mature markets.

Quantum Corrections to the Dynamics of the Expanding Universe


The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schrödinger equation, complemented by the equations of motion for the momentum operator and its time derivative in Heisenberg’s form reduce to the Einstein equations with an additional source of the gravitational field of quantum nature. The spatially closed universe with cosmological constant, originally filled with a uniform scalar field and radiation, is considered as quantum cosmological system. The perfect fluid in the form of radiation defines the material reference frame. The properties of the averaged scalar field acting like ordinary matter are investigated. After averaging over its quantum states, the free scalar field turns into the Weyssenhoff fluid characterized by the energy density, pressure, and spin of constituent particles. The cases when the contribution of the quantum effects into the gravitational interaction becomes significant on macroscopic scale are analyzed. It is demonstrated that, unless the whole, at least a part of such matter–energy constituents as dark matter and dark energy may have a quantum origin.


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