2,203 research outputs found
Complex Obtuse Random Walks and their Continuous-Time Limits
We study a particular class of complex-valued random variables and their
associated random walks: the complex obtuse random variables. They are the
generalization to the complex case of the real-valued obtuse random variables
which were introduced in \cite{A-E} in order to understand the structure of
normal martingales in \RR^n.The extension to the complex case is mainly
motivated by considerations from Quantum Statistical Mechanics, in particular
for the seek of a characterization of those quantum baths acting as classical
noises. The extension of obtuse random variables to the complex case is far
from obvious and hides very interesting algebraical structures. We show that
complex obtuse random variables are characterized by a 3-tensor which admits
certain symmetries which we show to be the exact 3-tensor analogue of the
normal character for 2-tensors (i.e. matrices), that is, a necessary and
sufficient condition for being diagonalizable in some orthonormal basis. We
discuss the passage to the continuous-time limit for these random walks and
show that they converge in distribution to normal martingales in \CC^N. We
show that the 3-tensor associated to these normal martingales encodes their
behavior, in particular the diagonalization directions of the 3-tensor indicate
the directions of the space where the martingale behaves like a diffusion and
those where it behaves like a Poisson process. We finally prove the
convergence, in the continuous-time limit, of the corresponding multiplication
operators on the canonical Fock space, with an explicit expression in terms of
the associated 3-tensor again
Entanglement of Bipartite Quantum Systems driven by Repeated Interactions
We consider a non-interacting bipartite quantum system undergoing repeated quantum interactions with an
environment modeled by a chain of independant quantum systems interacting one
after the other with the bipartite system. The interactions are made so that
the pieces of environment interact first with and then with
. Even though the bipartite systems are not interacting, the
interactions with the environment create an entanglement. We show that, in the
limit of short interaction times, the environment creates an effective
interaction Hamiltonian between the two systems. This interaction Hamiltonian
is explicitly computed and we show that it keeps track of the order of the
successive interactions with and . Particular
physical models are studied, where the evolution of the entanglement can be
explicitly computed. We also show the property of return of equilibrium and
thermalization for a family of examples
Dynamical Semigroups for Unbounded Repeated Perturbation of Open System
We consider dynamical semigroups with unbounded Kossakowski-Lindblad-Davies
generators which are related to evolution of an open system with a tuned
repeated harmonic perturbation. Our main result is the proof of existence of
uniquely determined minimal trace-preserving strongly continuous dynamical
semigroups on the space of density matrices. The corresponding dual W
*-dynamical system is shown to be unital quasi-free and completely positive
automorphisms of the CCR-algebra. We also comment on the action of dynamical
semigroups on quasi-free states
Conservation laws in Skyrme-type models
The zero curvature representation of Zakharov and Shabat has been generalized
recently to higher dimensions and has been used to construct non-linear field
theories which either are integrable or contain integrable submodels. The
Skyrme model, for instance, contains an integrable subsector with infinitely
many conserved currents, and the simplest Skyrmion with baryon number one
belongs to this subsector. Here we use a related method, based on the geometry
of target space, to construct a whole class of theories which are either
integrable or contain integrable subsectors (where integrability means the
existence of infinitely many conservation laws). These models have
three-dimensional target space, like the Skyrme model, and their infinitely
many conserved currents turn out to be Noether currents of the
volume-preserving diffeomorphisms on target space. Specifically for the Skyrme
model, we find both a weak and a strong integrability condition, where the
conserved currents form a subset of the algebra of volume-preserving
diffeomorphisms in both cases, but this subset is a subalgebra only for the
weak integrable submodel.Comment: Latex file, 22 pages. Two (insignificant) errors in Eqs. 104-106
correcte
Steady state fluctuations of the dissipated heat for a quantum stochastic model
We introduce a quantum stochastic dynamics for heat conduction. A multi-level
subsystem is coupled to reservoirs at different temperatures. Energy quanta are
detected in the reservoirs allowing the study of steady state fluctuations of
the entropy dissipation. Our main result states a symmetry in its large
deviation rate function.Comment: 41 pages, minor changes, published versio
Origin of the excitonic recombinations in hexagonal boron nitride by spatially resolved cathodoluminescence spectroscopy
The excitonic recombinations in hexagonal boron nitride (hBN) are
investigated with spatially resolved cathodoluminescence spectroscopy in the UV
range. Cathodoluminescence images of an individual hBN crystallite reveals that
the 215 nm free excitonic line is quite homogeneously emitted along the
crystallite whereas the 220 nm and 227 nm excitonic emissions are located in
specific regions of the crystallite. Transmission electron microscopy images
show that these regions contain a high density of crystalline defects. This
suggests that both the 220 nm and 227 nm emissions are produced by the
recombination of excitons bound to structural defects
Quantum Stochastic Processes: A Case Study
We present a detailed study of a simple quantum stochastic process, the
quantum phase space Brownian motion, which we obtain as the Markovian limit of
a simple model of open quantum system. We show that this physical description
of the process allows us to specify and to construct the dilation of the
quantum dynamical maps, including conditional quantum expectations. The quantum
phase space Brownian motion possesses many properties similar to that of the
classical Brownian motion, notably its increments are independent and
identically distributed. Possible applications to dissipative phenomena in the
quantum Hall effect are suggested.Comment: 35 pages, 1 figure
Assessment of Irradiation Damage on Stainless Steel by Acoustic Miroscopy
The plan to increase the life cycle of nuclear power stations opens up a new field of investigation for methods of characterizing materials. One of the main problems encountered by the operator is knowing how to evaluate the remaining useful life of components in its generating unit to prevent critical parts from suddenly breaking in service [1]. The aim is to end up with indicators of the degree of damage suffered by metal structures using nondestructive measurement tests whose effectiveness will have been proved in an industrial environment
Fluctuations of Quantum Currents and Unravelings of Master Equations
The very notion of a current fluctuation is problematic in the quantum
context. We study that problem in the context of nonequilibrium statistical
mechanics, both in a microscopic setup and in a Markovian model. Our answer is
based on a rigorous result that relates the weak coupling limit of fluctuations
of reservoir observables under a global unitary evolution with the statistics
of the so-called quantum trajectories. These quantum trajectories are
frequently considered in the context of quantum optics, but they remain useful
for more general nonequilibrium systems.
In contrast with the approaches found in the literature, we do not assume
that the system is continuously monitored. Instead, our starting point is a
relatively realistic unitary dynamics of the full system.Comment: 18 pages, v1-->v2, Replaced the former Appendix B by a (thematically)
different one. Mainly changes in the introductory Section 2+ added reference
Impact of recycling and lateral sediment input on grain size fining trends – implications for reconstructing tectonic and climate forcings in ancient sedimentary systems
Grain size trends in basin stratigraphy are thought to preserve a rich record of the climatic and tectonic controls on landscape evolution. Stratigraphic models assume that over geological timescales, the downstream profile of sediment deposition is in dynamic equilibrium with the spatial distribution of tectonic subsidence in the basin, sea level and the flux and calibre of sediment supplied from mountain catchments. Here, we demonstrate that this approach in modelling stratigraphic responses to environmental change is missing a key ingredient: the dynamic geomorphology of the sediment routing system. For three large alluvial fans in the Iglesia basin, Argentine Andes we measured the grain size of modern river sediment from fan apex to toe and characterise the spatial distribution of differential subsidence for each fan by constructing a 3D model of basin stratigraphy from seismic data. We find, using a self-similar grain size fining model, that the profile of grain size fining on all three fans cannot be reproduced given the subsidence profile measured and for any sediment supply scenario. However, by adapting the self-similar model, we demonstrate that the grain size trends on each fan can be effectively reproduced when sediment is not only sourced from a single catchment at the apex of the system, but also laterally, from tributary catchments and through fan surface recycling. Without constraint on the dynamic geomorphology of these large alluvial systems, signals of tectonic and climate forcing in grain size data are masked and would be indecipherable in the geological record. This has significant implications for our ability to make sensitive, quantitative reconstructions of external boundary conditions from the sedimentary record
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