2,220 research outputs found
Neumark Operators and Sharp Reconstructions, the finite dimensional case
A commutative POV measure with real spectrum is characterized by the
existence of a PV measure (the sharp reconstruction of ) with real
spectrum such that can be interpreted as a randomization of . This paper
focuses on the relationships between this characterization of commutative POV
measures and Neumark's extension theorem. In particular, we show that in the
finite dimensional case there exists a relation between the Neumark operator
corresponding to the extension of and the sharp reconstruction of . The
relevance of this result to the theory of non-ideal quantum measurement and to
the definition of unsharpness is analyzed.Comment: 37 page
On the nature of continuous physical quantities in classical and quantum mechanics
Within the traditional Hilbert space formalism of quantum mechanics, it is
not possible to describe a particle as possessing, simultaneously, a sharp
position value and a sharp momentum value. Is it possible, though, to describe
a particle as possessing just a sharp position value (or just a sharp momentum
value)? Some, such as Teller (Journal of Philosophy, 1979), have thought that
the answer to this question is No -- that the status of individual continuous
quantities is very different in quantum mechanics than in classical mechanics.
On the contrary, I shall show that the same subtle issues arise with respect to
continuous quantities in classical and quantum mechanics; and that it is, after
all, possible to describe a particle as possessing a sharp position value
without altering the standard formalism of quantum mechanics.Comment: 26 pages, LaTe
Born-Oppenheimer Approximation near Level Crossing
We consider the Born-Oppenheimer problem near conical intersection in two
dimensions. For energies close to the crossing energy we describe the wave
function near an isotropic crossing and show that it is related to generalized
hypergeometric functions 0F3. This function is to a conical intersection what
the Airy function is to a classical turning point. As an application we
calculate the anomalous Zeeman shift of vibrational levels near a crossing.Comment: 8 pages, 1 figure, Lette
On Quantum State Observability and Measurement
We consider the problem of determining the state of a quantum system given
one or more readings of the expectation value of an observable. The system is
assumed to be a finite dimensional quantum control system for which we can
influence the dynamics by generating all the unitary evolutions in a Lie group.
We investigate to what extent, by an appropriate sequence of evolutions and
measurements, we can obtain information on the initial state of the system. We
present a system theoretic viewpoint of this problem in that we study the {\it
observability} of the system. In this context, we characterize the equivalence
classes of indistinguishable states and propose algorithms for state
identification
Quantum Cryptography
Quantum cryptography is a new method for secret communications offering the
ultimate security assurance of the inviolability of a Law of Nature. In this
paper we shall describe the theory of quantum cryptography, its potential
relevance and the development of a prototype system at Los Alamos, which
utilises the phenomenon of single-photon interference to perform quantum
cryptography over an optical fiber communications link.Comment: 36 pages in compressed PostScript format, 10 PostScript figures
compressed tar fil
Characterizing Multiple Solutions to the Time-Energy Canonical Commutation Relation via Quantum Dynamics
We address the multiplicity of solutions to the time-energy canonical
commutation relation for a given Hamiltonian. Specifically, we consider a
particle spatially confined in a potential free interval, where it is known
that two distinct self-adjoint and compact time operators conjugate to the
system Hamiltonian exist. The dynamics of the eigenvectors of these operators
indicate that different time operators posses distinguishing properties that
can unambiguously associate them to specific aspects of the quantum time
problem
A Precision Measurement of pp Elastic Scattering Cross Sections at Intermediate Energies
We have measured differential cross sections for \pp elastic scattering with
internal fiber targets in the recirculating beam of the proton synchrotron
COSY. Measurements were made continuously during acceleration for projectile
kinetic energies between 0.23 and 2.59 GeV in the angular range deg. Details of the apparatus and the data analysis are
given and the resulting excitation functions and angular distributions
presented. The precision of each data point is typically better than 4%, and a
relative normalization uncertainty of only 2.5% within an excitation function
has been reached. The impact on phase shift analysis as well as upper bounds on
possible resonant contributions in lower partial waves are discussed.Comment: 23 pages 29 figure
Measurement of Spin Correlation Parameters A, A, and A_ at 2.1 GeV in Proton-Proton Elastic Scattering
At the Cooler Synchrotron COSY/J\"ulich spin correlation parameters in
elastic proton-proton (pp) scattering have been measured with a 2.11 GeV
polarized proton beam and a polarized hydrogen atomic beam target. We report
results for A, A, and A_ for c.m. scattering angles between
30 and 90. Our data on A -- the first measurement of this
observable above 800 MeV -- clearly disagrees with predictions of available of
pp scattering phase shift solutions while A and A_ are reproduced
reasonably well. We show that in the direct reconstruction of the scattering
amplitudes from the body of available pp elastic scattering data at 2.1 GeV the
number of possible solutions is considerably reduced.Comment: 4 pages, 4 figure
A general T-matrix approach applied to two-body and three-body problems in cold atomic gases
We propose a systematic T-matrix approach to solve few-body problems with
s-wave contact interactions in ultracold atomic gases. The problem is generally
reduced to a matrix equation expanded by a set of orthogonal molecular states,
describing external center-of-mass motions of pairs of interacting particles;
while each matrix element is guaranteed to be finite by a proper
renormalization for internal relative motions. This approach is able to
incorporate various scattering problems and the calculations of related
physical quantities in a single framework, and also provides a physically
transparent way to understand the mechanism of resonance scattering. For
applications, we study two-body effective scattering in 2D-3D mixed dimensions,
where the resonance position and width are determined with high precision from
only a few number of matrix elements. We also study three fermions in a
(rotating) harmonic trap, where exotic scattering properties in terms of mass
ratios and angular momenta are uniquely identified in the framework of
T-matrix.Comment: 14 pages, 4 figure
Toy Model for a Relational Formulation of Quantum Theory
In the absence of an external frame of reference physical degrees of freedom
must describe relations between systems. Using a simple model, we investigate
how such a relational quantum theory naturally arises by promoting reference
systems to the status of dynamical entities. Our goal is to demonstrate using
elementary quantum theory how any quantum mechanical experiment admits a purely
relational description at a fundamental level, from which the original
"non-relational" theory emerges in a semi-classical limit. According to this
thesis, the non-relational theory is therefore an approximation of the
fundamental relational theory. We propose four simple rules that can be used to
translate an "orthodox" quantum mechanical description into a relational
description, independent of an external spacial reference frame or clock. The
techniques used to construct these relational theories are motivated by a
Bayesian approach to quantum mechanics, and rely on the noiseless subsystem
method of quantum information science used to protect quantum states against
undesired noise. The relational theory naturally predicts a fundamental
decoherence mechanism, so an arrow of time emerges from a time-symmetric
theory. Moreover, there is no need for a "collapse of the wave packet" in our
model: the probability interpretation is only applied to diagonal density
operators. Finally, the physical states of the relational theory can be
described in terms of "spin networks" introduced by Penrose as a combinatorial
description of geometry, and widely studied in the loop formulation of quantum
gravity. Thus, our simple bottom-up approach (starting from the semi-classical
limit to derive the fully relational quantum theory) may offer interesting
insights on the low energy limit of quantum gravity.Comment: References added, extended discussio
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