abstract

New methodology of classification of quantum systems with respect to their integrability basing on the analytical properties of statistical measures is proposed. Advantages of this methodology are discussed. Examples of possible applications of this approach are presented. Model of a paramagnetic atom moving in external magnetic field is discussed in detail. Predictions of different types of both quantum integrability and quantum chaos are given.

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The paper presents new method for calculating the low-temperature asymptotics of free energy of the \(3D\) Ising model in external magnetic field \((H\neq 0)\). For this purpose the method of transfer-matrix, and generalized Jordan–Wigner transformations are used. The results obtained are valid in the wide range of temperature and magnetic field values.

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Recently Herzlich proved a Penrose-like inequality with a coefficient being a kind of a Sobolev constant. We show that this constant tends to zero for charged black holes approaching maximal Reissner–Nordström solutions. The method proposed by Herzlich is not appropriate for charged matter with nonzero global charge.

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We outline a method of deriving boost invariant dynamics for effective particles in quantum field theory. The method is based on the similarity renormalization group transformation for Hamiltonians in the canonical light-front quantization scheme. The Hamiltonians are defined and calculated using creation and annihilation operators. The renormalization group equations are written for a sequence of unitary transformations which gradually transform the bare canonical creation and annihilation operators of a local theory to the creation and annihilation operators of effective particles in an effective theory with the same dynamical content but a finite range of energy transfers due to form factors in the interaction vertices. The form factors result from the similarity renormalization group flow of effective Hamiltonians. The regularized initial Hamiltonian and the renormalized effective Hamiltonians possess seven kinematical Poincaré symmetries specific to the light-front quantization scheme. Thus, the effective interactions can be used to describe the constituent dynamics in relativistically moving systems including the rest and the infinite momentum frame. Solutions to the general equations for the effective Hamiltonians are illustrated in perturbation theory by second-order calculations of self-energy and two-particle interaction terms in Yukawa theory, QED and QCD. In Yukawa theory, one obtains the generalized Yukawa potential including its full off-energy-shell extension and form factors in the vertices. In QED, the effective Hamiltonian eigenvalue problem converges for small coupling constants to the Schrödinger equation but the typical relativistic ultraviolet singularities at short distances between constituents are regularized by the similarity form factors. In the second-order QCD effective Hamiltonian one obtains a boost invariant logarithmically confining quark-anti-quark potential which may remain uncanceled in the non-abelian dynamics of effective quarks and gluons.

abstract

The advent of \(B\)-factories, rich sources of pure \(B-\overline {B}\) pairs, increased an interest in the rare \(B\) decays. The \(B\) decay channels involving the \(\tau \) lepton are very interesting both as a stringent test of the Standard Model and as a possible window for a new physics. These decays are difficult experimentally because of the presence of two neutrinos. We have performed extensive simulations of exclusive decays \(\overline {B^{0}}\rightarrow D^{+}\tau ^{-}\overline {\nu _{\tau }}\) and \(\overline {B^{0}}\rightarrow D^{*+}\tau ^{-}\overline {\nu _{\tau }}\) with a subsequent \(\tau ^{-}\rightarrow \pi ^{+}\pi ^{-}\pi ^{-}\nu _{\tau }\) decay in the BELLE detector at the KEK \(B\)-factory. It is possible to reconstruct kinematics of these decays provided we measure momentum of \(\overline {B^{0}}\) and the \(\tau ^{-}\) decay vertex. Thus obtained \(\tau ^{-}\) energy and direction are not far from the generated values. The main problem is the background from the inclusive \(\overline {B^{0}}\) decays. For \(10^{8}~B-\overline {B}\) pairs (one year of full-luminosity KEK-B running) we expect about \(35\) reconstructed \(\overline {B^{0}}\rightarrow D^{+}\tau ^{-}\overline {\nu _{\tau }}\) events and the same number of \(\overline {B^{0}}\rightarrow D^{*+}\tau ^{-}\overline {\nu _{\tau }}\)  decays. The corresponding numbers of the background events from inclusive \(B\) decays are \(35\) and \(15\).

abstract

The well-known formal analogy between time and absolute temperature, existing on the quantum level, is considered as a profound duality relationship requiring some modifications in the conventional quantum dynamics. They consist of tiny deviations from uniform time run in the physical spacetime, as well as of tiny deviations from unitary time evolution characteristic for the conventional quantum theory. The first deviations are conjectured to be produced by local changes of total average particle number. Then, they imply the second deviations exerting in turn influence upon this particle number. Two examples of the second deviations are described: hypothetic tiny violation of optical theorem for particle scattering, and hypothetic slow variation of the average number of probe particles contained in a sample situated in proximity of a big accelerator (producing abundantly particles on a target).

abstract

Forward differential cross-section for diffraction dissociation of vir- tual photons on nucleon target is calculated in the QCD dipole picture. The numerical estimates are presented and discussed.

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Classical arguments predict that the quark and the antiquark of a pair created during string fragmentation are both transversely polarized in the direction of \(\hat {\bf z}\times {\bf q}_\perp \), where \(\hat {\bf z}\) is the direction of the pull exerted by the string on the antiquark and \({\bf q}_\perp \) (\(-{\bf q}_\perp \)) is the transverse momentum of the quark (antiquark). The existence of this effect at the quantum-mechanical level is investigated by considering two analogous processes involving the tunnel effect in a strong field: (1) dissociation of the positronium atom (2) electron pair creation. In case (1) the positronium is taken in the \(^3\!P_0\) state to simulate the vacuum quantum numbers \(J^{\rm PC}=0^{++}\). Using the nonrelativistic WKB method, the final electron and positron are indeed found to be transversely polarized along \(\hat {\bf z}\times {\bf p}_\perp \). On the contrary, case (2), treated with the Dirac equation, shows no correlation between transverse polarization and transverse momentum both when the field is uniform and when it depends on \(z\) and \(t\). The pair is nevertheless produced in a triplet spin state. The difference between these two results and their relevance to transverse spin asymmetry in inclusive reactions is discussed.

abstract

High multiplicity nucleus-nucleus collisions are studied on an event-by-event basis. Different methods of analysis of individual collision events are presented and their ability to reveal anomalous features of the events is discussed. This study is based on full acceptance measurements of particle production in the interactions of 158 GeV/nucleon Pb with the heavy target nuclei in nuclear emulsion. No events are observed with global characteristics that differ significantly from expectations based on either Monte Carlo simulations, or the characteristics of the entire sample of events. On the other hand, it is shown that systematic analysis of particle density fluctuations in phase space domains of varying size, performed in terms of factorial moments, can be used as an effective triggering for events with large dynamical fluctuations.

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Pion spectra from (\(K^-,\pi ^+\)) reactions on \(^{16}\)O and \(^9\)Be targets in the region of \({\mit \Sigma }\) production are analyzed in impulse approximation for different strengths of the \({\mit \Sigma }\) single particle potential. It is concluded that this potential is repulsive. It is pointed out that among the Nijmegen models of the hyperon–nucleon interaction only model F is compatible with this conclusion.

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We have investigated the process of fragmentation of the Pb nucleus at 158 GeV/nucleon in Pb–Pb interactions recorded in lead-emulsion chambers of the EMU13 CERN experiment. The number of Pb–Pb interactions found was larger than that expected from the nuclear charge changing cross section which indicates an important role of electromagnetic dissociation processes in Pb–Pb interactions at this high energy. The emission angles of multiply charged projectile fragments as well as of spectator protons were measured using the semiautomated device with the CCD camera mounted on a microscope. Taking the advantage of the unconventional design of the emulsion chambers the charges of all multiply charged projectile fragments were measured. On the basis of these measurements, different modes of the Pb projectile break-up are discussed. The rates and properties of the fragmentation processes such as fission, multifragmentation and disintegration only into singly charged fragments are presented.

abstract

One of the basic problems of quantum cosmology is the problem of time. Various solutions have been proposed for this problem. One approach is to use the Bohmian time. Another approach is to use the probabilistic time which was recently introduced by Castagnino. We consider both of these definitions as generalizations of a semi-classical time and compare them for a mini-super space.