43,627 research outputs found
Electrostatic Storage Ring
In the trial \cite{BNL} of measuring the proton electric moment, storage
rings with electrostatic lattice have been considered. Here an overview is
given about the main parameters regarding such a kind of focusing. Beyond
confirming all the issues regarding this subject, a non-null element
is introduced in all the matrices which deal with the vector
and its role is discussed.Comment: 7 page
An Investigation on the Basic Conceptual Foundations of Quantum Mechanics by Using the Clifford Algebra
We review our approach to quantum mechanics adding also some new interesting
results. We start by giving proof of two important theorems on the existence of
the and Clifford algebras. This last algebra gives proof of the von Neumann
basic postulates on the quantum measurement explaining thus in an algebraic
manner the wave function collapse postulated in standard quantum theory. In
this manner we reach the objective to expose a self-consistent version of
quantum mechanics. We give proof of the quantum like Heisenberg uncertainty
relations, the phenomenon of quantum Mach Zender interference as well as
quantum collapse in some cases of physical interest We also discuss the problem
of time evolution of quantum systems as well as the changes in space location.
We also give demonstration of the Kocken-Specher theorem, and also we give an
algebraic formulation and explanation of the EPR . By using the same approach
we also derive Bell inequalities. Our formulation is strongly based on the use
of idempotents that are contained in Clifford algebra. Their counterpart in
quantum mechanics is represented by the projection operators that are
interpreted as logical statements, following the basic von Neumann results.
Using the Clifford algebra we are able to invert such result. According to the
results previously obtained by Orlov in 1994, we are able to give proof that
quantum mechanics derives from logic. We show that indeterminism and quantum
interference have their origin in the logic.Comment: forthcoming papers; http://www.m-hikari.com/astp/forth/index.htm
Analytic solitary waves of nonintegrable equations
Even if it is nonintegrable, a differential equation may nevertheless admit
particular solutions which are globally analytic. On the example of the
dynamical system of Kuramoto and Sivashinsky, which is generically chaotic and
presents a high physical interest, we review various methods, all based on the
structure of singularities, allowing us to characterize the analytic solution
which depends on the largest possible number of constants of integration.Comment: LaTex 2e. To appear, Physica
Integration of partially integrable equations
Most evolution equations %or wave equations are partially integrable and, in
order to explicitly integrate all possible cases, there exist several methods
of complex analysis, but none is optimal. The theory of Nevanlinna and
Wiman-Valiron on the growth of the meromorphic solutions gives predictions and
bounds, but it is not constructive and restricted to meromorphic solutions. The
Painleve' approach via the a priori singularities of the solutions gives no
bounds but it is often (not always) constructive. It seems that an adequate
combination of the two methods could yield much more output in terms of
explicit (i.e. closed form) analytic solutions. We review this question, mainly
taking as an example the chaotic equation of Kuramoto and Sivashinsky nu u''' +
b u'' + mu u' + u^2/2 +A=0, nu nonzero, with nu,b,mu,A constants.Comment: 12 p, WASCOM XIII (Acireale, 19-25 June 2005
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