33 research outputs found
Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process
The accuracy of the Arthurs-Kelly model of a simultaneous measurement of
position and momentum is analysed using concepts developed by Braginsky and
Khalili in the context of measurements of a single quantum observable. A
distinction is made between the errors of retrodiction and prediction. It is
shown that the distribution of measured values coincides with the initial state
Husimi function when the retrodictive accuracy is maximised, and that it is
related to the final state anti-Husimi function (the P representation of
quantum optics) when the predictive accuracy is maximised. The disturbance of
the system by the measurement is also discussed. A class of minimally
disturbing measurements is characterised. It is shown that the distribution of
measured values then coincides with one of the smoothed Wigner functions
described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final
published versio
A Short Range Force
Gravitomagnetic and gravitoelectric forces have been studied for sometime and
tests for detecting such forces arising from the earth, are under way. We apply
similar considerations at the level of elementary particles in a formulation
using General Relativity, and deduce the presence of short range forces. A
possible candidate could be the somewhat recently detected but otherwise
mysterious short range force, mediated by massive "photons".Comment: 4 pages, TeX, Based on the paper in the Fifth International
Symposium, Frontiers of Fundamental Physic
Degree of Complementarity Determines the Nonlocality in Quantum Mechanics
Complementarity principle is one of the central concepts in quantum mechanics
which restricts joint measurement for certain observables. Of course, later
development shows that joint measurement could be possible for such observables
with the introduction of a certain degree of unsharpness or fuzziness in the
measurement. In this paper, we show that the optimal degree of unsharpness,
which guarantees the joint measurement of all possible pairs of dichotomic
observables, determines the degree of nonlocality in quantum mechanics as well
as in more general no-signaling theories.Comment: Close to published versio
Fibre bundle formulation of nonrelativistic quantum mechanics. 0. Preliminary considerations: Quantum mechanics from a geometric-observer's viewpoint
We propose a version of the non-relativistic quantum mechanics in which the
pure states of a quantum system are described as sections of a Hilbert
(generally infinitely-dimensional) fibre bundle over the space-time. There
evolution is governed via (a kind of) a parallel transport in this bundle. Some
problems concerning observables are considered. There are derived the equations
of motion for the state sections and observables. We show that up to a constant
the matrix of the coefficients of the evolution operator (transport) coincides
with the matrix of the Hamiltonian of the investigated quantum system.Comment: 15 standard LaTeX 2e (11pt, A4) pages. The packages AMS-LaTeX and
amsfonts are require
Fibre bundle formulation of relativistic quantum mechanics. I. Time-dependent approach
We propose a new fibre bundle formulation of the mathematical base of
relativistic quantum mechanics. At the present stage the bundle form of the
theory is equivalent to its conventional one, but it admits new types of
generalizations in different directions.
In the present first part of our investigation we consider the time-dependent
or Hamiltonian approach to bundle description of relativistic quantum
mechanics. In it the wavefunctions are replaced by (state) liftings of paths or
sections along paths of a suitably chosen vector bundle over space-time whose
(standard) fibre is the space of the wavefunctions. Now the quantum evolution
is described as a linear transportation (by means of the evolution transport
along paths in the space-time) of the state liftings/sections in the (total)
bundle space. The equations of these transportations turn to be the bundle
versions of the corresponding relativistic wave equations.Comment: 16 standard LaTeX pages. The packages AMS-LaTeX and amsfonts are
required. The paper continuous the application of fibre bundle formalism to
quantum physics began in the series of works quant-ph/9803083,
quant-ph/9803084, quant-ph/9804062, quant-ph/9806046, quant-ph/9901039,
quant-ph/9902068, and quant-ph/0004041. For related papers, view
http://theo.inrne.bas.bg/~bozho
Husimi Transform of an Operator Product
It is shown that the series derived by Mizrahi, giving the Husimi transform
(or covariant symbol) of an operator product, is absolutely convergent for a
large class of operators. In particular, the generalized Liouville equation,
describing the time evolution of the Husimi function, is absolutely convergent
for a large class of Hamiltonians. By contrast, the series derived by
Groenewold, giving the Weyl transform of an operator product, is often only
asymptotic, or even undefined. The result is used to derive an alternative way
of expressing expectation values in terms of the Husimi function. The advantage
of this formula is that it applies in many of the cases where the anti-Husimi
transform (or contravariant symbol) is so highly singular that it fails to
exist as a tempered distribution.Comment: AMS-Latex, 13 page
Informationally complete measurements and groups representation
Informationally complete measurements on a quantum system allow to estimate
the expectation value of any arbitrary operator by just averaging functions of
the experimental outcomes. We show that such kind of measurements can be
achieved through positive-operator valued measures (POVM's) related to unitary
irreducible representations of a group on the Hilbert space of the system. With
the help of frame theory we provide a constructive way to evaluate the
data-processing function for arbitrary operators.Comment: 9 pages, no figures, IOP style. Some new references adde
Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport
We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. Its evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
The present first part of this investigation is devoted to the introduction
of basic concepts on which the fibre bundle approach to quantum mechanics
rests. We show that the evolution of pure quantum-mechanical states can be
described as a suitable linear transport along paths, called evolution
transport, of the state sections in the Hilbert fibre bundle of states of a
considered quantum system.Comment: 26 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and
amsfonts are required. Revised: new material, references, and comments are
added. Minor style chages. Continuation of quan-ph/9803083. For continuation
of the this series see http://www.inrne.bas.bg/mathmod/bozhome
General energy bounds for systems of bosons with soft cores
We study a bound system of N identical bosons interacting by model pair
potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a
variational trial function and the `equivalent 2-body method', we find explicit
upper and lower bound formulas for the N-particle ground-state energy in
arbitrary spatial dimensions d > 2 for the two cases p = 2 and p = -1. It is
demonstrated that the upper bound can be systematically improved with the aid
of a special large-N limit in collective field theory
Ages and Metallicities of Fornax Dwarf Ellipticals
Narrow band photometry is presented on 27 dwarf ellipticals in the Fornax
cluster. Calibrated with Galactic globular cluster data and spectrophotometric
population models, the colors indicated that dwarf ellipticals have a mean
[Fe/H] of -1.00+/-0.28 ranging from -1.6 to -0.4. The mean age of dwarf
ellipticals, also determined photometrically, is estimated at 10+/-1 Gyrs
compared to 13 Gyrs for bright Fornax ellipticals. Comparison of our
metallicity color and Mg_2 indices demonstrates that the [Mg/Fe] ratio is lower
in dwarf ellipticals than their more massive cousins, which is consistent with
a longer duration of initial star formation to explain their younger ages.
There is a increase in dwarf metallicity with distance from the Fornax cluster
center where core galaxies are, on average, 0.5 dex more metal-poor than halo
dwarfs. In addition, we find the halo dwarfs are younger in mean age compared
to core dwarfs. One possible explanation is that the intracluster medium ram
pressure strips the gas from dwarf ellipticals halting star formation (old age)
and stopping enrichment (low metallicity) as they enter the core.Comment: 40 pages AAS LaTeX, 14 figures, accepted for publication in A