1,357,294 research outputs found
Nondemolition Principle of Quantum Measurement Theory
We give an explicit axiomatic formulation of the quantum measurement theory
which is free of the projection postulate. It is based on the generalized
nondemolition principle applicable also to the unsharp, continuous-spectrum and
continuous-in-time observations. The "collapsed state-vector" after the
"objectification" is simply treated as a random vector of the a posteriori
state given by the quantum filtering, i.e., the conditioning of the a priori
induced state on the corresponding reduced algebra. The nonlinear
phenomenological equation of "continuous spontaneous localization" has been
derived from the Schroedinger equation as a case of the quantum filtering
equation for the diffusive nondemolition measurement. The quantum theory of
measurement and filtering suggests also another type of the stochastic equation
for the dynamical theory of continuous reduction, corresponding to the counting
nondemolition measurement, which is more relevant for the quantum experiments.Comment: 23 pages. See also related papers at
http://www.maths.nott.ac.uk/personal/vpb/research/mes_fou.html and
http://www.maths.nott.ac.uk/personal/vpb/research/cau_idy.htm
Multiple-electron losses of highly charged ions colliding with neutral atoms
We present calculations of the total and m-fold electron-loss cross sections
using the DEPOSIT code for highly charged U(q+) ions (q=10,31,33) colliding
with Ne and Ar targets at projectile energies E=1.4 and 3.5 MeV/u. Typical
examples of the deposited energy T(b) and m-fold ionization probabilities Pm(b)
used for the cross-section calculations as a function of the impact parameter b
are given. Calculated m-fold electron-loss cross sections are in a good
agreement with available experimental data. Although the projectile charge is
rather high, a contribution of multiple-electron loss cross sections to the
total electron-loss cross sections is high: about 65% for the cases mentioned.Comment: 6 pages, 4 figure
Quantization of the N=2 Supersymmetric KdV Hierarchy
We continue the study of the quantization of supersymmetric integrable KdV
hierarchies. We consider the N=2 KdV model based on the affine
algebra but with a new algebraic construction for the L-operator, different
from the standard Drinfeld-Sokolov reduction. We construct the quantum
monodromy matrix satisfying a special version of the reflection equation and
show that in the classical limit, this object gives the monodromy matrix of N=2
supersymmetric KdV system. We also show that at both the classical and the
quantum levels, the trace of the monodromy matrix (transfer matrix) is
invariant under two supersymmetry transformations and the zero mode of the
associated U(1) current.Comment: LaTeX2e, 12 page
On the superfluidity of classical liquid in nanotubes
In 2001, the author proposed the ultra second quantization method. The ultra
second quantization of the Schr\"odinger equation, as well as its ordinary
second quantization, is a representation of the N-particle Schr\"odinger
equation, and this means that basically the ultra second quantization of the
equation is the same as the original N-particle equation: they coincide in
3N-dimensional space.
We consider a short action pairwise potential V(x_i -x_j). This means that as
the number of particles tends to infinity, , interaction is
possible for only a finite number of particles. Therefore, the potential
depends on N in the following way: . If V(y) is finite
with support , then as the support engulfs a finite
number of particles, and this number does not depend on N.
As a result, it turns out that the superfluidity occurs for velocities less
than , where
is the critical Landau velocity and R is the radius of
the nanotube.Comment: Latex, 20p. The text is presented for the International Workshop
"Idempotent and tropical mathematics and problems of mathematical physics",
Independent University of Moscow, Moscow, August 25--30, 2007 and to be
published in the Russian Journal of Mathematical Physics, 2007, vol. 15, #
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