1,729 research outputs found
Stochastic Master Equations in Thermal Environment
We derive the stochastic master equations which describe the evolution of
open quantum systems in contact with a heat bath and undergoing indirect
measurements. These equations are obtained as a limit of a quantum repeated
measurement model where we consider a small system in contact with an infinite
chain at positive temperature. At zero temperature it is well-known that one
obtains stochastic differential equations of jump-diffusion type. At strictly
positive temperature, we show that only pure diffusion type equations are
relevant
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
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
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
Non Markovian Quantum Repeated Interactions and Measurements
A non-Markovian model of quantum repeated interactions between a small
quantum system and an infinite chain of quantum systems is presented. By
adapting and applying usual pro jection operator techniques in this context,
discrete versions of the integro-differential and time-convolutioness Master
equations for the reduced system are derived. Next, an intuitive and rigorous
description of the indirect quantum measurement principle is developed and a
discrete non Markovian stochastic Master equation for the open system is
obtained. Finally, the question of unravelling in a particular model of
non-Markovian quantum interactions is discussed.Comment: 22 page
Integrable theories and loop spaces: fundamentals, applications and new developments
We review our proposal to generalize the standard two-dimensional flatness
construction of Lax-Zakharov-Shabat to relativistic field theories in d+1
dimensions. The fundamentals from the theory of connections on loop spaces are
presented and clarified. These ideas are exposed using mathematical tools
familiar to physicists. We exhibit recent and new results that relate the
locality of the loop space curvature to the diffeomorphism invariance of the
loop space holonomy. These result are used to show that the holonomy is abelian
if the holonomy is diffeomorphism invariant.
These results justify in part and set the limitations of the local
implementations of the approach which has been worked out in the last decade.
We highlight very interesting applications like the construction and the
solution of an integrable four dimensional field theory with Hopf solitons, and
new integrability conditions which generalize BPS equations to systems such as
Skyrme theories. Applications of these ideas leading to new constructions are
implemented in theories that admit volume preserving diffeomorphisms of the
target space as symmetries. Applications to physically relevant systems like
Yang Mills theories are summarized. We also discuss other possibilities that
have not yet been explored.Comment: 64 pages, 8 figure
Testing fluvial erosion models using the transient response of bedrock rivers to tectonic forcing in the Apennines, Italy
The transient response of bedrock rivers to a drop in base level can be used to
discriminate between competing fluvial erosion models. However, some recent studies of
bedrock erosion conclude that transient river long profiles can be approximately
characterized by a transportâlimited erosion model, while other authors suggest that a
detachmentâlimited model best explains their field data. The difference is thought to be
due to the relative volume of sediment being fluxed through the fluvial system. Using a
pragmatic approach, we address this debate by testing the ability of endâmember fluvial
erosion models to reproduce the wellâdocumented evolution of three catchments in the
central Apennines (Italy) which have been perturbed to various extents by an
independently constrained increase in relative uplift rate. The transportâlimited model is
unable to account for the catchmentsâresponse to the increase in uplift rate, consistent with
the observed low rates of sediment supply to the channels. Instead, a detachmentâlimited
model with a threshold corresponding to the fieldâderived median grain size of the
sediment plus a slopeâdependent channel width satisfactorily reproduces the overall
convex long profiles along the studied rivers. Importantly, we find that the prefactor in the
hydraulic scaling relationship is uplift dependent, leading to landscapes responding faster
the higher the uplift rate, consistent with field observations. We conclude that a slopeâ
dependent channel width and an entrainment/erosion threshold are necessary ingredients
when modeling landscape evolution or mapping the distribution of fluvial erosion rates in
areas where the rate of sediment supply to channels is low
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