1,319 research outputs found
Symplectic Cuts and Projection Quantization
The recently proposed projection quantization, which is a method to quantize
particular subspaces of systems with known quantum theory, is shown to yield a
genuine quantization in several cases. This may be inferred from exact results
established within symplectic cutting.Comment: 12 pages, v2: additional examples and a new reference to related wor
Existence of Spinorial States in Pure Loop Quantum Gravity
We demonstrate the existence of spinorial states in a theory of canonical
quantum gravity without matter. This should be regarded as evidence towards the
conjecture that bound states with particle properties appear in association
with spatial regions of non-trivial topology. In asymptotically trivial general
relativity the momentum constraint generates only a subgroup of the spatial
diffeomorphisms. The remaining diffeomorphisms give rise to the mapping class
group, which acts as a symmetry group on the phase space. This action induces a
unitary representation on the loop state space of the Ashtekar formalism.
Certain elements of the diffeomorphism group can be regarded as asymptotic
rotations of space relative to its surroundings. We construct states that
transform non-trivially under a -rotation: gravitational quantum states
with fractional spin.Comment: 26 pages, 6 figures. Changes made to section 2 and Lemma
Group averaging in the (p,q) oscillator representation of SL(2,R)
We investigate refined algebraic quantisation with group averaging in a
finite-dimensional constrained Hamiltonian system that provides a simplified
model of general relativity. The classical theory has gauge group SL(2,R) and a
distinguished o(p,q) observable algebra. The gauge group of the quantum theory
is the double cover of SL(2,R), and its representation on the auxiliary Hilbert
space is isomorphic to the (p,q) oscillator representation. When p>1, q>1 and
p+q == 0 (mod 2), we obtain a physical Hilbert space with a nontrivial
representation of the o(p,q) quantum observable algebra. For p=q=1, the system
provides the first example known to us where group averaging converges to an
indefinite sesquilinear form.Comment: 34 pages. LaTeX with amsfonts, amsmath, amssymb. (References added;
minor typos corrected.
Effect of phase noise on useful quantum correlations in Bose Josephson junctions
In a two-mode Bose Josephson junction the dynamics induced by a sudden quench
of the tunnel amplitude leads to the periodic formation of entangled states.
For instance, squeezed states are formed at short times and macroscopic
superpositions of phase states at later times. The two modes of the junction
can be viewed as the two arms of an interferometer; use of entangled states
allows to perform atom interferometry beyond the classical limit. Decoherence
due to the presence of noise degrades the quantum correlations between the
atoms, thus reducing phase sensitivity of the interferometer. We consider the
noise induced by stochastic fluctuations of the energies of the two modes of
the junction. We analyze its effect on squeezed states and macroscopic
superpositions and study quantitatively the amount of quantum correlations
which can be used to enhance the phase sensitivity with respect to the
classical limit. To this aim we compute the squeezing parameter and the quantum
Fisher information during the quenched dynamics. For moderate noise intensities
we show that these useful quantum correlations increase on time scales beyond
the squeezing regime. This suggests multicomponent superpositions as
interesting candidates for high-precision atom interferometry
A Uniqueness Theorem for Constraint Quantization
This work addresses certain ambiguities in the Dirac approach to constrained
systems. Specifically, we investigate the space of so-called ``rigging maps''
associated with Refined Algebraic Quantization, a particular realization of the
Dirac scheme. Our main result is to provide a condition under which the rigging
map is unique, in which case we also show that it is given by group averaging
techniques. Our results comprise all cases where the gauge group is a
finite-dimensional Lie group.Comment: 23 pages, RevTeX, further comments and references added (May 26. '99
Noise in Bose Josephson junctions: Decoherence and phase relaxation
Squeezed states and macroscopic superpositions of coherent states have been
predicted to be generated dynamically in Bose Josephson junctions. We solve
exactly the quantum dynamics of such a junction in the presence of a classical
noise coupled to the population-imbalance number operator (phase noise),
accounting for, for example, the experimentally relevant fluctuations of the
magnetic field. We calculate the correction to the decay of the visibility
induced by the noise in the non-Markovian regime. Furthermore, we predict that
such a noise induces an anomalous rate of decoherence among the components of
the macroscopic superpositions, which is independent of the total number of
atoms, leading to potential interferometric applications.Comment: Fig 2 added; version accepted for publicatio
Subdynamics as a mechanism for objective description
The relationship between microsystems and macrosystems is considered in the
context of quantum field formulation of statistical mechanics: it is argued
that problems on foundations of quantum mechanics can be solved relying on this
relationship. This discussion requires some improvement of non-equilibrium
statistical mechanics that is briefly presented.Comment: latex, 15 pages. Paper submitted to Proc. Conference "Mysteries,
Puzzles And Paradoxes In Quantum Mechanics, Workshop on Entanglement And
Decoherence, Palazzo Feltrinelli, Gargnano, Garda Lake, Italy, 20-25
September, 199
Mass Superselection, Canonical Gauge Transformations, and Asymptotically Flat Variational Principles
The phase space reduction of Schwarzschild black holes by Thiemann and
Kastrup and by Kucha\v{r} is reexamined from a different perspective on gauge
freedom. This perspective introduces additional gauge transformations which
correspond to asymptotically nontrivial diffeomorphisms. Various subtleties
concerning variational principles for asymptotically flat systems are addressed
which allow us to avoid the usual conclusion that treating such transformations
as gauge implies the vanishing of corresponding total charges. Instead,
superselection rules are found for the (nonvanishing) ADM mass at the
asymptotic boundaries. The addition of phenomenological clocks at each
asymptotic boundary is also studied and compared with the `parametrization
clocks' of Kucha\v{r}.Comment: 15 pages, ReVTeX, Minor changes made in response to referee's
commment
The structure of the quantum mechanical state space and induced superselection rules
The role of superselection rules for the derivation of classical probability
within quantum mechanics is investigated and examples of superselection rules
induced by the environment are discussed.Comment: 11 pages, Standard Latex 2.0
Generalized quantum measurements. Part I: Information properties of soft quantum measurements
A special class of soft quantum measurements as a physical model of the fuzzy
measurements widely used in physics is introduced and its information
properties are studied in detail.Comment: 25 pages, 3 figures, 25 ref
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