1,563 research outputs found
The Canonical Approach to Quantum Gravity: General Ideas and Geometrodynamics
We give an introduction to the canonical formalism of Einstein's theory of
general relativity. This then serves as the starting point for one approach to
quantum gravity called quantum geometrodynamics. The main features and
applications of this approach are briefly summarized.Comment: 21 pages, 6 figures. Contribution to E. Seiler and I.-O. Stamatescu
(editors): `Approaches To Fundamental Physics -- An Assessment Of Current
Theoretical Ideas' (Springer Verlag, to appear
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
Quantum computing with incoherent resources and quantum jumps
Spontaneous emission and the inelastic scattering of photons are two natural
processes usually associated with decoherence and the reduction in the capacity
to process quantum information. Here we show that when suitably detected, these
photons are sufficient to build all the fundamental blocks needed to perform
quantum computation in the emitting qubits while protecting them from
deleterious dissipative effects. We exemplify by showing how to teleport an
unknown quantum state and how to efficiently prepare graph states for the
implementation of measurement-based quantum computation.Comment: 5 pages, 5 figure
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.
Anomalies of weakened decoherence criteria for quantum histories
The theory of decoherent histories is checked for the requirement of
statistical independence of subsystems. Strikingly, this is satisfied only when
the decoherence functional is diagonal in both its real a n d imaginary parts.
In particular, the condition of consistency (or weak decoherence) required for
the assignment of probabilities appears to be ruled out. The same conclusion is
obtained independently, by claiming a plausible dynamical robustness of
decoherent histories.Comment: 3pp, submitted to Phys. Rev. Let
Refined Algebraic Quantization in the oscillator representation of SL(2,R)
We investigate Refined Algebraic Quantization (RAQ) with group averaging in a
constrained Hamiltonian system with unreduced phase space T^*R^4 and gauge
group SL(2,R). The reduced phase space M is connected and contains four
mutually disconnected `regular' sectors with topology R x S^1, but these
sectors are connected to each other through an exceptional set where M is not a
manifold and where M has non-Hausdorff topology. The RAQ physical Hilbert space
H_{phys} decomposes as H_{phys} = (direct sum of) H_i, where the four subspaces
H_i naturally correspond to the four regular sectors of M. The RAQ observable
algebra A_{obs}, represented on H_{phys}, contains natural subalgebras
represented on each H_i. The group averaging takes place in the oscillator
representation of SL(2,R) on L^2(R^{2,2}), and ensuring convergence requires a
subtle choice for the test state space: the classical analogue of this choice
is to excise from M the exceptional set while nevertheless retaining
information about the connections between the regular sectors. A quantum theory
with the Hilbert space H_{phys} and a finitely-generated observable subalgebra
of A_{obs} is recovered through both Ashtekar's Algebraic Quantization and
Isham's group theoretic quantization.Comment: 30 pages, REVTeX v3.1 with amsfonts. (v4: Published version.
Thermodynamic Limit and Decoherence: Rigorous Results
Time evolution operator in quantum mechanics can be changed into a
statistical operator by a Wick rotation. This strict relation between
statistical mechanics and quantum evolution can reveal deep results when the
thermodynamic limit is considered. These results translate in a set of theorems
proving that these effects can be effectively at work producing an emerging
classical world without recurring to any external entity that in some cases
cannot be properly defined. In a many-body system has been recently shown that
Gaussian decay of the coherence is the rule with a duration of recurrence more
and more small as the number of particles increases. This effect has been
observed experimentally. More generally, a theorem about coherence of bulk
matter can be proved. All this takes us to the conclusion that a well definite
boundary for the quantum to classical world does exist and that can be drawn by
the thermodynamic limit, extending in this way the deep link between
statistical mechanics and quantum evolution to a high degree.Comment: 5 pages, no figures. Contribution to proceedings of DICE 2006
(Piombino, Italy, September 11-15, 2006
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
Bowen-York Tensors
There is derived, for a conformally flat three-space, a family of linear
second-order partial differential operators which send vectors into tracefree,
symmetric two-tensors. These maps, which are parametrized by conformal Killing
vectors on the three-space, are such that the divergence of the resulting
tensor field depends only on the divergence of the original vector field. In
particular these maps send source-free electric fields into TT-tensors.
Moreover, if the original vector field is the Coulomb field on
, the resulting tensor fields on
are nothing but the family of
TT-tensors originally written down by Bowen and York.Comment: 12 pages, Contribution to CQG Special Issue "A Spacetime Safari:
Essays in Honour of Vincent Moncrief
Rate of decoherence for an electron weakly coupled to a phonon gas
We study the dynamics of an electron weakly coupled to a phonon gas. The
initial state of the electron is the superposition of two spatially localized
distant bumps moving towards each other, and the phonons are in a thermal
state. We investigate the dynamics of the system in the kinetic regime and show
that the time evolution makes the non-diagonal terms of the density matrix of
the electron decay, destroying the interference between the two bumps. We show
that such a damping effect is exponential in time, and the related decay rate
is proportional to the total scattering cross section of the electron-phonon
interaction.Comment: 27 pages, 2 figure
- …