11,940 research outputs found
Information Geometry, Inference Methods and Chaotic Energy Levels Statistics
In this Letter, we propose a novel information-geometric characterization of
chaotic (integrable) energy level statistics of a quantum antiferromagnetic
Ising spin chain in a tilted (transverse) external magnetic field. Finally, we
conjecture our results might find some potential physical applications in
quantum energy level statistics.Comment: 9 pages, added correct journal referenc
Thermodynamic properties of compounds of biochemical interest in aqueous solution. A survey of thermodynamic properties of the compounds of the elements CHNOPS Progress report
Thermodynamic properties of compounds of biochemical interest in aqueous solutio
Graviton propagator from background-independent quantum gravity
We study the graviton propagator in euclidean loop quantum gravity, using the
spinfoam formalism. We use boundary-amplitude and group-field-theory
techniques, and compute one component of the propagator to first order, under a
number of approximations, obtaining the correct spacetime dependence. In the
large distance limit, the only term of the vertex amplitude that contributes is
the exponential of the Regge action: the other terms, that have raised doubts
on the physical viability of the model, are suppressed by the phase of the
vacuum state, which is determined by the extrinsic geometry of the boundary.Comment: 6 pages. Substantially revised second version. Improved boundary
state ansat
The complete LQG propagator: II. Asymptotic behavior of the vertex
In a previous article we have show that there are difficulties in obtaining
the correct graviton propagator from the loop-quantum-gravity dynamics defined
by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude
that depends nontrivially on the intertwiners can yield the correct propagator.
We give an explicit example of asymptotic behavior of a vertex amplitude that
gives the correct full graviton propagator in the large distance limit.Comment: 16 page
Optimal stochastic modelling with unitary quantum dynamics
Identifying and extracting the past information relevant to the future
behaviour of stochastic processes is a central task in the quantitative
sciences. Quantum models offer a promising approach to this, allowing for
accurate simulation of future trajectories whilst using less past information
than any classical counterpart. Here we introduce a class of phase-enhanced
quantum models, representing the most general means of causal simulation with a
unitary quantum circuit. We show that the resulting constructions can display
advantages over previous state-of-art methods - both in the amount of
information they need to store about the past, and in the minimal memory
dimension they require to store this information. Moreover, we find that these
two features are generally competing factors in optimisation - leading to an
ambiguity in what constitutes the optimal model - a phenomenon that does not
manifest classically. Our results thus simultaneously offer new quantum
advantages for stochastic simulation, and illustrate further qualitative
differences in behaviour between classical and quantum notions of complexity.Comment: 9 pages, 5 figure
Reconnection of superfluid vortex bundles
Using the vortex filament model and the Gross Pitaevskii nonlinear
Schroedinger equation, we show that bundles of quantised vortex lines in helium
II are structurally robust and can reconnect with each other maintaining their
identity. We discuss vortex stretching in superfluid turbulence and show that,
during the bundle reconnection process, Kelvin waves of large amplitude are
generated, in agreement with the finding that helicity is produced by nearly
singular vortex interactions in classical Euler flows.Comment: 10 pages, 7 figure
Multiple-event probability in general-relativistic quantum mechanics: a discrete model
We introduce a simple quantum mechanical model in which time and space are
discrete and periodic. These features avoid the complications related to
continuous-spectrum operators and infinite-norm states. The model provides a
tool for discussing the probabilistic interpretation of generally-covariant
quantum systems, without the confusion generated by spurious infinities. We use
the model to illustrate the formalism of general-relativistic quantum
mechanics, and to test the definition of multiple-event probability introduced
in a companion paper. We consider a version of the model with unitary
time-evolution and a version without unitary time-evolutio
A simple background-independent hamiltonian quantum model
We study formulation and probabilistic interpretation of a simple
general-relativistic hamiltonian quantum system. The system has no unitary
evolution in background time. The quantum theory yields transition
probabilities between measurable quantities (partial observables). These
converge to the classical predictions in the limit. Our main tool
is the kernel of the projector on the solutions of Wheeler-deWitt equation,
which we analyze in detail. It is a real quantity, which can be seen as a
propagator that propagates "forward" as well as "backward" in a local parameter
time. Individual quantum states, on the other hand, may contain only "forward
propagating" components. The analysis sheds some light on the interpretation of
background independent transition amplitudes in quantum gravity
Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
A Planck-scale minimal observable length appears in many approaches to
quantum gravity. It is sometimes argued that this minimal length might conflict
with Lorentz invariance, because a boosted observer could see the minimal
length further Lorentz contracted. We show that this is not the case within
loop quantum gravity. In loop quantum gravity the minimal length (more
precisely, minimal area) does not appear as a fixed property of geometry, but
rather as the minimal (nonzero) eigenvalue of a quantum observable. The boosted
observer can see the same observable spectrum, with the same minimal area. What
changes continuously in the boost transformation is not the value of the
minimal length: it is the probability distribution of seeing one or the other
of the discrete eigenvalues of the area. We discuss several difficulties
associated with boosts and area measurement in quantum gravity. We compute the
transformation of the area operator under a local boost, propose an explicit
expression for the generator of local boosts and give the conditions under
which its action is unitary.Comment: 12 pages, 3 figure
Multiple-event probability in general-relativistic quantum mechanics
We discuss the definition of quantum probability in the context of "timeless"
general--relativistic quantum mechanics. In particular, we study the
probability of sequences of events, or multi-event probability. In conventional
quantum mechanics this can be obtained by means of the ``wave function
collapse" algorithm. We first point out certain difficulties of some natural
definitions of multi-event probability, including the conditional probability
widely considered in the literature. We then observe that multi-event
probability can be reduced to single-event probability, by taking into account
the quantum nature of the measuring apparatus. In fact, by exploiting the
von-Neumann freedom of moving the quantum classical boundary, one can always
trade a sequence of non-commuting quantum measurements at different times, with
an ensemble of simultaneous commuting measurements on the joint
system+apparatus system. This observation permits a formulation of quantum
theory based only on single-event probability, where the results of the "wave
function collapse" algorithm can nevertheless be recovered. The discussion
bears also on the nature of the quantum collapse
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