1,732 research outputs found
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
Consistency of Semiclassical Gravity
We discuss some subtleties which arise in the semiclassical approximation to
quantum gravity. We show that integrability conditions prevent the existence of
Tomonaga-Schwinger time functions on the space of three-metrics but admit them
on superspace. The concept of semiclassical time is carefully examined. We
point out that central charges in the matter sector spoil the consistency of
the semiclassical approximation unless the full quantum theory of gravity and
matter is anomaly-free. We finally discuss consequences of these considerations
for quantum field theory in flat spacetime, but with arbitrary foliations.Comment: 12 pages, LATEX, Report Freiburg THEP-94/2
Double dot chain as a macroscopic quantum bit
We consider an array of N quantum dot pairs interacting via Coulomb
interaction between adjacent dots and hopping inside each pair. We show that at
the first order in the ratio of hopping and interaction amplitudes, the array
maps in an effective two level system with energy separation becoming
exponentially small in the macroscopic (large N) limit. Decoherence at zero
temperature is studied in the limit of weak coupling with phonons. In this case
the macroscopic limit is robust with respect to decoherence. Some possible
applications in quantum information processing are discussed.Comment: Phys. Rev. A (in press
Properties of 3-manifolds for relativists
In canonical quantum gravity certain topological properties of 3-manifolds
are of interest. This article gives an account of those properties which have
so far received sufficient attention, especially those concerning the
diffeomorphism groups of 3-manifolds. We give a summary of these properties and
list some old and new results concerning them. The appendix contains a
discussion of the group of large diffeomorphisms of the -handle 3-manifold.Comment: 20 pages. Plain-TeX, no figures, 1 Table (A4 format
Bell inequality for pairs of particle-number-superselection-rule restricted states
Proposals for Bell inequality tests on systems restricted by superselection
rules often require operations that are difficult to implement in practice. In
this paper, we derive a new Bell inequality, where pairs of states are used to
by-pass the superselection rule. In particular, we focus on mode entanglement
of an arbitrary number of massive particles and show that our Bell inequality
detects the entanglement in the pair when other inequalities fail. However, as
the number of particles in the system increases, the violation of our Bell
inequality decreases due to the restriction in the measurement space caused by
the superselection rule. This Bell test can be implemented using techniques
that are routinely used in current experiments.Comment: 9 pages, 6 figures; v2 is the published versio
Towards Quantum Superpositions of a Mirror: an Exact Open Systems Analysis
We analyze the recently proposed mirror superposition experiment of Marshall,
Simon, Penrose, and Bouwmeester, assuming that the mirror's dynamics contains a
non-unitary term of the Lindblad type proportional to -[q,[q,\rho]], with q the
position operator for the center of mass of the mirror, and \rho the
statistical operator. We derive an exact formula for the fringe visibility for
this system. We discuss the consequences of our result for tests of
environmental decoherence and of collapse models. In particular, we find that
with the conventional parameters for the CSL model of state vector collapse,
maintenance of coherence is expected to within an accuracy of at least 1 part
in 10^{8}. Increasing the apparatus coupling to environmental decoherence may
lead to observable modifications of the fringe visibility, with time dependence
given by our exact result.Comment: 4 pages, RevTeX. Substantial changes mad
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
Quantum rings with time dependent spin-orbit coupling: Rabi oscillations, spintronic Schrodinger-cat states, and conductance properties
The strength of the (Rashba-type) spin-orbit coupling in mesoscopic
semiconductor rings can be tuned with external gate voltages. Here we consider
the case of a periodically changing spin-orbit interaction strength as induced
by sinusoidal voltages. In a closed one dimensional quantum ring with weak
spin-orbit coupling, Rabi oscillations are shown to appear. We find that the
time evolution of initially localized wave packets exhibits a series of
collapse and revival phenomena. Partial revivals -- that are typical in
nonlinear systems -- are shown to correspond to superpositions of states
localized at different spatial positions along the ring. These "spintronic
Schrodinger-cat sates" appear periodically, and similarly to their counterparts
in other physical systems, they are found to be sensitive to environment
induced disturbances. The time dependent spin transport problem, when leads are
attached to the ring, is also solved. We show that the "sideband currents"
induced by the oscillating spin-orbit interaction strength can become the
dominant output channel, even in the presence of moderate thermal fluctuations
and random scattering events.Comment: 11 pages, 9 figures, submitted to PR
Reference frames, superselection rules, and quantum information
Recently, there has been much interest in a new kind of ``unspeakable''
quantum information that stands to regular quantum information in the same way
that a direction in space or a moment in time stands to a classical bit string:
the former can only be encoded using particular degrees of freedom while the
latter are indifferent to the physical nature of the information carriers. The
problem of correlating distant reference frames, of which aligning Cartesian
axes and synchronizing clocks are important instances, is an example of a task
that requires the exchange of unspeakable information and for which it is
interesting to determine the fundamental quantum limit of efficiency. There
have also been many investigations into the information theory that is
appropriate for parties that lack reference frames or that lack correlation
between their reference frames, restrictions that result in global and local
superselection rules. In the presence of these, quantum unspeakable information
becomes a new kind of resource that can be manipulated, depleted, quantified,
etcetera. Methods have also been developed to contend with these restrictions
using relational encodings, particularly in the context of computation,
cryptography, communication, and the manipulation of entanglement. This article
reviews the role of reference frames and superselection rules in the theory of
quantum information processing.Comment: 55 pages, published versio
The CWKB particle production and classical condensate in de Sitter spacetime
The complex time WKB approximation is an effective tool in studying particle
production in curved spacetime. We use it in this work to understand the
formation of classical condensate in expanding de Sitter spacetime. The CWKB
leads to the emergence of thermal spectrum that depends crucially on horizons
(as in de Sitter spacetime) or observer dependent horizons (as in Rindler
spacetime). A connection is sought between the horizon and the formation of
classical condensate. We concentrate on de Sitter spacetime and study the
cosmological perturbation of mode with various values of . We find
that for a minimally coupled free scalar field for , the one-mode
occupation number grows more than unity soon after the physical wavelength of
the mode crosses the Hubble radius and soon after diverges as , where . The results substantiates the previous works in this
direction. We also find the correct oscillation and behaviour of at
small from a single expression using CWKB approximation for various values
of . We also discuss decoherence in relation to the formation of
classical condensate. We also find that the squeezed state formalism and CWKB
method give identical results.Comment: 19 pages, revtex, 5 figure
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