Quantum Vacuum: The Structure of Empty Space-Time and Quintessence with Gauge Symmetry Group SU(2)⊗U(1)SU(2)\otimes U(1)

We consider the formation of structured and massless particles with spin 1, by using the Yang-Mills like stochastic equations system for the group symmetry $SU(2)\otimes U(1)$ without taking into account the nonlinear term characterizing self-action. We prove that, in the first phase of relaxation, as a result of multi-scale random fluctuations of quantum fields, massless particles with spin 1, further referred as \emph{hions}, are generated in the form of statistically stable quantized structures, which are localized on 2$D$ topological manifolds. We also study the wave state and the geometrical structure of the \emph{hion} when as a free particle and, accordingly, while it interacts with a random environment becoming a quasi-particle with a finite lifetime. In the second phase of relaxation, the vector boson makes spontaneous transitions to other massless and mass states. The problem of entanglement of two \emph{hions} with opposite projections of the spins $+1$ and $-1$ and the formation of a scalar zero-spin boson are also thoroughly studied. We analyze the properties of the scalar field and show that it corresponds to the Bose-Einstein (BE) condensate. The scalar boson decay problems, as well as a number of features characterizing the stability of BE condensate, are also discussed. Then, we report on the structure of empty space-time in the context of new properties of the quantum vacuum, implying on the existence of a natural quantum computer with complicated logic, which manifests in the form of dark energy. The possibilities of space-time engineering are also discussed.Comment: 40 pages, 4 figure

On the motion of classical three-body system with consideration of quantum fluctuations

We study the multichannel scattering in the classical three-body system and show that the problem can be formulated as a motion of the point mass on a curved hyper-surface of the energy of the body-system. It is proved that the local coordinate system on curved space produces additional symmetries which along with known integrals of motion allow to reduce the initial problem to the system of the sixth order. Assuming, that the metric of the curved space has a random component, we derive the system of \emph{stochastic differential equations} (SED) describing the classical motion of the three-body system taking into account the influence of random forces of various origin and in particular the quantum fluctuations. Using SDEs of motion, we obtain the partial differential equation of the second order describing the probability distribution of the point mass in the momentum representation. It is shown, that the equation for the probability distribution is solved jointly with the classical equations, which in turn are responsible for the topological peculiarities of tubes of quantum currents and transitions between asymptotic channels. The latter allows to solve the problem of the limiting transition from the quantum region to the region of classical chaotic motion (Poincar\'e region) without violating the analogue of Arnold's theorem on quantum mapping. The expression characterizing a measure of deviation of the quantum probabilistic currents and thus the appearance of quantum chaos in a dynamical system is determined

New Approach for Stochastic Quantum Processes, their Manipulation and Control

The dissipation and decoherence (for example, the effects of noise in quantum computations), interaction with thermostat or in general with physical vacuum, measurement and many other complicated problems of open quantum systems are a consequence of interaction of quantum system with the environment. These problems are described mathematically in terms of complex probabilistic process (CPP). Particularly, treating the environment as a Markovian process we derive an Langevin-Schroedinger type stochastic differential equation (SDE) for describing the quantum system interacting with environment. For the 1D randomly quantum harmonic oscillator (QHO) model L-Sh SDE is a solution in the form of orthogonal CPP. On the basis of orthogonal CPP the stochastic density matrix (SDM) method is developed and in its framework relaxation processes in the uncountable dimension closed system of "QHO+environment" is investigated. With the help of SDM method the thermodynamical potentials, like nonequilibrium entropy and the energy of ground state are exactly constructed. The dispersion for different operators are calculated. In particular, the expression for uncertain relations depending on parameter of interaction with environment is obtained. The Weyl transformation for stochastic operators is specified. Ground state Winger function is developed in detail.Comment: 13 page

Coherent production of the long-lived pionium nP states in relativistic nucleus-nucleus collisions

The coherent production of the nP states of the $\pi^+\pi^-$ atoms ($A_{2\pi}$) in relativistic nucleus-nucleus collisions is considered as a possible source of the $A_{2\pi}(nP)$ beam for the pionium Lamb-shift measurement. A general expression for estimation of the $A_{2\pi}(nP)$ yield is derived in the framework of the equivalent photon approximation.Comment: pdflatex, 4 pages, 1 figure: v2: typos are correcte

Lepton pair production in relativistic ion collisions to all orders in ZαZ\alpha with logarithmic accuracy

The problem of summation of the perturbation series for the process of lepton pair production in relativistic ion collisions is investigated. We show that the amplitude of this process can be obtained in the compact analytical form, if one confines to the terms growing as a powers of logarithm energy in the cross section, the approximation of which is completely justified for such colliders as RHIC and LHC. Using this result we calculate the Coulomb corrections to the cross section of the process under consideration.Comment: 11 pages, 3 figure

Photoproduction of ω\omega mesons off nuclei and impact of polarization on meson-nucleon interaction

We consider photoproduction of $\omega$ mesons off complex nuclei to study interactions of transversely and longitudinally polarized vector mesons with nucleons. Whereas the total cross section for interactions of the transversely polarized vector mesons with nucleons $\sigma_T=\sigma(V_TN)$ can be obtained from coherent photoproduction, measurements of vector meson photoproduction in the incoherent region provide a unique opportunity to extract the total cross section for longitudinally polarized mesons interacting with nucleons $\sigma_L=\sigma(V_LN)$, which has not yet been measured and strongly depends on theoretical approaches. This work is stimulated by the construction of the new experiment GlueX at Jefferson Lab, designed to study the photoproduction of mesons in a large beam energy range up to 12 GeV.Comment: 14 pages,3 figure

Random motion of quantum reactive harmonic oscillator. Thermodynamics of Vacuum of Asymptotic Subspace

The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the extended space. This wave functional obeys some stochastic differential equation (SDE). Based on the nonlinear Langevin type SDE of second order, introduced in the functional space R{W(t)}, the variables in original equation are separated. The general measure in the space R{W(t)} of the Fokker-Plank type is obtained and expression for total wave function (wave mixture) of random QRHO is constructed as functional expansion over the stochastic basis set. The pertinent transition matrix S_br is constructed. For Wiener type measure W(t) of functional space the exact representation for ''vacuum-vacuum'' transition probability is obtained. The thermodynamics of vacuum is described in detail for the asymptotic space R1_as. The exact values for Energy, shift and expansion of ground state of oscillator and its Entropy are calculated.Comment: LaTeX, 19 pages, 5 figures, title change

Three Body Multichannel Scattering as a Model of Irreversible Quantum Mechanics

The new formulation of the theory of multichannel scattering on the example of collinear model is proposed. It is shown, that in the closed three-body scattering system the principle of quantum determinism in general case breaks down and we have a micro- irreversible quantum mechanics.Comment: 4 pages, LaTeX, uses nolta.sty, accepted for presentation in the NOLTA'9

Exactly solvable models of quantum mechanics including fluctuations in the framework of representation of the wave function by random process

The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average transition probabilities are calculated. Stochastic density matrix method is developed, which is used for investigation of thermodinamical characteristics of the system, such as entropy and average energy.Comment: 29 pages, Late

The inelastic photon-electron collisions with polarized beams

We discussed the photoproduction of pair of charged particles $a\bar{a}\quad (a=e,\mu,\pi)$ as well as the double photon emission processes off an electron accounting for the polarization of colliding particles. In the kinematics when all the particles can be considered as a massless, we obtain the compact analytical expressions for the differential cross sections of these processes. As the application of obtained results the special cases of production by circular and linear polarized photons are considered.Comment: 6 page