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Stochastic Dynamics of Quantum Physical Systems  [PDF]
Malkhaz Mumladze
Open Access Library Journal (OALib Journal) , 2016, DOI: 10.4236/oalib.1103004
Abstract:
In this article we define and build the one method of description of stochastic evolution of a physical quantum system. For each quantum state wEU we construct the probability measure uw in the space (PU, S), where PU is the space of the pure states of the quantum system, S the Borel σ-algebra in PU. Farther, for any Hermit's positive element with norm ‖u‖=1, in the C*-algebra of observables U, we define the probability measure uu on the set of states EU. If strongly continuous group {αt}of * automorphisms on U describes the evolution of structure of observables, according to this, we have a picture of evolution of distribution of states of quantum system relatively to each observable u.
Quantum Physical Systems and Their Evolution  [PDF]
Malkhaz Mumladze
Open Access Library Journal (OALib Journal) , 2018, DOI: 10.4236/oalib.1104244
Abstract:
In this article, we proposed a method for describing the evolution of quantum physical systems. We define the action integral on the functional space and the entropy of distribution of observable values on the set of quantum states. Dynamic of quantum system in this article is described as dynamical system represented by one parametric semi group which is extremal of this action integral. Evolution is a chain of change of distribution of observable values. In the closed system, it must increase entropy. Based on the notion of entropy of distribution energy, on the principle of maximum entropy production, we get a picture of evolution of closed quantum systems.
Mod 2 Morava K-theory for Frobenius complements of exponent dividing 2^n 9
Malkhaz Bakuradze
Mathematics , 2011,
Abstract: We determine the cohomology rings K(s)*(BG) at 2 for all finite Frobenius complements G of exponent dividing 2n 9.
Computing the Krichever genus
Malkhaz Bakuradze
Mathematics , 2013, DOI: 10.1007/s40062-013-0049-0
Abstract: Let $\psi$ denote the genus that corresponds to the formal group law having invariant differential $\omega(t)$ equal to $\sqrt{1+p_1t+p_2t^2+p_3t^3+p_4t^4}$ and let $\kappa$ classify the formal group law strictly isomorphic to the universal formal group law under strict isomorphism $x\CP(x)$. We prove that on the rational complex bordism ring the Krichever-H\"ohn genus $\phi_{KH}$ is the composition $\psi\circ \kappa^{-1}$. We construct certain elements $A_{ij}$ in the Lazard ring and give an alternative definition of the universal Krichever formal group law. We conclude that the coefficient ring of the universal Krichever formal group law is the quotient of the Lazard ring by the ideal generated by all $A_{ij}$, $i,j\geq 3$.
Calculating mod $p$ Honda formal group law
Malkhaz Bakuradze
Mathematics , 2015,
Abstract: This note provides the calculation of the formal group law $F(x,y)$ in modulo $p$ Morava $K$-theory at prime $p$ and $s>1$ as an element in $K(s)^*[x][[y]]$ and one application to relevant examples.
Morava k(s)^* -rings of the extensions of C_p by the products of good groups under diagonal action
Malkhaz Bakuradze
Mathematics , 2014,
Abstract: This note provides a theorem on good groups in the sense of Hopkins-Kuhn-Ravenel and some relevant examples.
Transfer and complex oriented cohomology rings
Malkhaz Bakuradze,Stewart Priddy
Mathematics , 2003, DOI: 10.2140/agt.2003.3.473
Abstract: For finite coverings we elucidate the interaction between transferred Chern classes and Chern classes of transferred bundles. This involves computing the ring structure for the complex oriented cohomology of various homotopy orbit spaces. In turn these results provide universal examples for computing the stable Euler classes (i.e. Tr^*(1)) and transferred Chern classes for p-fold covers. Applications to the classifying spaces of p-groups are given.
Some explicit expressions concerning formal group laws
Malkhaz Bakuradze,Mamuka Jibladze
Mathematics , 2013,
Abstract: This paper provides some explicit expressions concerning the formal group laws of the Brown-Peterson cohomology, the cohomology theory obtained from Brown-Peterson theory by killing all but one Witt symbol, the Morava $K$-theory and the Abel cohomology.
Morava K-theory rings of the extensions of C_2 by the products of cyclic 2-groups
Malkhaz Bakuradze,Natia Gachechiladze
Mathematics , 2014,
Abstract: We determine the ring structure of the Morava K-theory of classifying spaces of groups of order 32, with Hall-Senior numbers 34,35,36,37.
K^*(BG) rings for groups $G=G_{38},...,G_{41}$ of order 32
Malkhaz Bakuradze,Mamuka Jibladze
Mathematics , 2011,
Abstract: B. Schuster \cite{SCH1} proved that the $mod$ 2 Morava $K$-theory $K(s)^*(BG)$ is evenly generated for all groups $G$ of order 32. For the four groups $G$ with the numbers 38, 39, 40 and 41 in the Hall-Senior list \cite{H}, the ring $K(2)^*(BG)$ has been shown to be generated as a $K(2)^*$-module by transferred Euler classes. In this paper, we show this for arbitrary $s$ and compute the ring structure of $K(s)^*(BG)$. Namely, we show that $K(s)^*(BG)$ is the quotient of a polynomial ring in 6 variables over $K(s)^*(pt)$ by an ideal for which we list explicit generators.
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