292 research outputs found
Spatial Localization and Relativistic Transformation of Quantum Spins
The purity of a reduced state for spins that is pure in the rest frame will
most likely appear to degrade because spin and momentum become mixed when
viewed by a moving observer. We show that such a boost-induced decrease in spin
purity observed in a moving reference frame is intrinsically related to the
spatial localization properties of the wave package observed in the rest frame.
Furthermore, we prove that, for any localized pure state with separable spin
and momentum in the rest frame, its reduced density matrix for spins inevitably
appears to be mixed whenever viewed from a moving reference frame.Comment: 5 pages, 1 figur
Simultaneous Border-Collision and Period-Doubling Bifurcations
We unfold the codimension-two simultaneous occurrence of a border-collision
bifurcation and a period-doubling bifurcation for a general piecewise-smooth,
continuous map. We find that, with sufficient non-degeneracy conditions, a
locus of period-doubling bifurcations emanates non-tangentially from a locus of
border-collision bifurcations. The corresponding period-doubled solution
undergoes a border-collision bifurcation along a curve emanating from the
codimension-two point and tangent to the period-doubling locus here. In the
case that the map is one-dimensional local dynamics are completely classified;
in particular, we give conditions that ensure chaos.Comment: 22 pages; 5 figure
On the coexistence of position and momentum observables
We investigate the problem of coexistence of position and momentum
observables. We characterize those pairs of position and momentum observables
which have a joint observable
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
Barycentric decomposition of quantum measurements in finite dimensions
We analyze the convex structure of the set of positive operator valued
measures (POVMs) representing quantum measurements on a given finite
dimensional quantum system, with outcomes in a given locally compact Hausdorff
space. The extreme points of the convex set are operator valued measures
concentrated on a finite set of k \le d^2 points of the outcome space, d<
\infty being the dimension of the Hilbert space. We prove that for second
countable outcome spaces any POVM admits a Choquet representation as the
barycenter of the set of extreme points with respect to a suitable probability
measure. In the general case, Krein-Milman theorem is invoked to represent
POVMs as barycenters of a certain set of POVMs concentrated on k \le d^2 points
of the outcome space.Comment: !5 pages, no figure
Spreading of a Macroscopic Lattice Gas
We present a simple mechanical model for dynamic wetting phenomena. Metallic
balls spread along a periodically corrugated surface simulating molecules of
liquid advancing along a solid substrate. A vertical stack of balls mimics a
liquid droplet. Stochastic motion of the balls, driven by mechanical vibration
of the corrugated surface, induces diffusional motion. Simple theoretical
estimates are introduced and agree with the results of the analog experiments,
with numerical simulation, and with experimental data for microscopic spreading
dynamics.Comment: 19 pages, LaTeX, 9 Postscript figures, to be published in Phy. Rev. E
(September,1966
Master Stability Functions for Coupled Near-Identical Dynamical Systems
We derive a master stability function (MSF) for synchronization in networks
of coupled dynamical systems with small but arbitrary parametric variations.
Analogous to the MSF for identical systems, our generalized MSF simultaneously
solves the linear stability problem for near-synchronous states (NSS) for all
possible connectivity structures. We also derive a general sufficient condition
for stable near-synchronization and show that the synchronization error scales
linearly with the magnitude of parameter variations.Our analysis underlines
significant roles played by the Laplacian eigenvectors in the study of network
synchronization of near-identical systems.Comment: 11 pages, 2 figure
Bohrification of operator algebras and quantum logic
Following Birkhoff and von Neumann, quantum logic has traditionally been
based on the lattice of closed linear subspaces of some Hilbert space, or, more
generally, on the lattice of projections in a von Neumann algebra A.
Unfortunately, the logical interpretation of these lattices is impaired by
their nondistributivity and by various other problems. We show that a possible
resolution of these difficulties, suggested by the ideas of Bohr, emerges if
instead of single projections one considers elementary propositions to be
families of projections indexed by a partially ordered set C(A) of appropriate
commutative subalgebras of A. In fact, to achieve both maximal generality and
ease of use within topos theory, we assume that A is a so-called Rickart
C*-algebra and that C(A) consists of all unital commutative Rickart
C*-subalgebras of A. Such families of projections form a Heyting algebra in a
natural way, so that the associated propositional logic is intuitionistic:
distributivity is recovered at the expense of the law of the excluded middle.
Subsequently, generalizing an earlier computation for n-by-n matrices, we
prove that the Heyting algebra thus associated to A arises as a basis for the
internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the
"Bohrification" of A, which is a commutative Rickart C*-algebra in the topos of
functors from C(A) to the category of sets. We explain the relationship of this
construction to partial Boolean algebras and Bruns-Lakser completions. Finally,
we establish a connection between probability measure on the lattice of
projections on a Hilbert space H and probability valuations on the internal
Gelfand spectrum of A for A = B(H).Comment: 31 page
Epistemic and Ontic Quantum Realities
Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position
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