5,781 research outputs found
Finite-dimensional representations of twisted hyper loop algebras
We investigate the category of finite-dimensional representations of twisted
hyper loop algebras, i.e., the hyperalgebras associated to twisted loop
algebras over finite-dimensional simple Lie algebras. The main results are the
classification of the irreducible modules, the definition of the universal
highest-weight modules, called the Weyl modules, and, under a certain mild
restriction on the characteristic of the ground field, a proof that the simple
modules and the Weyl modules for the twisted hyper loop algebras are isomorphic
to appropriate simple and Weyl modules for the non-twisted hyper loop algebras,
respectively, via restriction of the action
The Hilbert space operator formalism within dynamical reduction models
Unlike standard quantum mechanics, dynamical reduction models assign no
particular a priori status to `measurement processes', `apparata', and
`observables', nor self-adjoint operators and positive operator valued measures
enter the postulates defining these models. In this paper, we show why and how
the Hilbert-space operator formalism, which standard quantum mechanics
postulates, can be derived from the fundamental evolution equation of dynamical
reduction models. Far from having any special ontological meaning, we show that
within the dynamical reduction context the operator formalism is just a compact
and convenient way to express the statistical properties of the outcomes of
experiments.Comment: 25 pages, RevTeX. Changes made and two figures adde
Dynamical Reduction Models: present status and future developments
We review the major achievements of the dynamical reduction program, showing
why and how it provides a unified, consistent description of physical
phenomena, from the microscopic quantum domain to the macroscopic classical
one. We discuss the difficulties in generalizing the existing models in order
to comprise also relativistic quantum field theories. We point out possible
future lines of research, ranging from mathematical physics to phenomenology.Comment: 12 pages. Contribution to the Proceedings of the "Third International
Workshop DICE2006", Castello di Piombino (Tuscany), September 11-15, 2006.
Minor changes mad
Determination of the magnetization profile of Co/Mg periodic multilayers by magneto-optic Kerr effect and X-ray magnetic resonant reflectivity
The resonant magnetic reflectivity of Co/Mg multilayers around the Co L2,3
absorption edge is simulated then measured on a specifically designed sample.
The dichroic signal is obtained when making the difference between the two
reflectivities measured with the magnetic field applied in two opposite
directions parallel to the sample surface. The simulations show that the
existence of magnetic dead layers at the interfaces between the Co and Mg
layers leads to an important increase of the dichroic signal measured in the
vicinity of the third Bragg peak that otherwise should be negligible. The
measurements are in agreement with the model introducing 0.25 nm thick dead
layers. This is attributed to the Co atoms in contact with the Mg layers and
thus we conclude that the Co-Mg interfaces are abrupt from the magnetic point
of view.Comment: 8 page
Non-clasical Nucleation in Supercooled Nickel
The dynamics of homogeneous nucleation and growth of crystalline nickel from
the super-cooled melt is examined during rapid quenching using molecular
dynamics and a modified embedded atom method potential. The character of the
critical nuclei of the crystallization transition is examined using common
neighbor analysis and visualization. At nucleation the saddle point droplet
consists of randomly stacked planar structures with an in plane triangular
order. These results are consistent with previous theoretical results that
predict that the nucleation process in some metals is non-classical due to the
presence of long-range forces and a spinodal.Comment: 4 pages, 5 figure
Collapse models with non-white noises II: particle-density coupled noises
We continue the analysis of models of spontaneous wave function collapse with
stochastic dynamics driven by non-white Gaussian noise. We specialize to a
model in which a classical "noise" field, with specified autocorrelator, is
coupled to a local nonrelativistic particle density. We derive general results
in this model for the rates of density matrix diagonalization and of state
vector reduction, and show that (in the absence of decoherence) both processes
are governed by essentially the same rate parameters. As an alternative route
to our reduction results, we also derive the Fokker-Planck equations that
correspond to the initial stochastic Schr\"odinger equation. For specific
models of the noise autocorrelator, including ones motivated by the structure
of thermal Green's functions, we discuss the qualitative and qantitative
dependence on model parameters, with particular emphasis on possible
cosmological sources of the noise field.Comment: Latex, 43 pages; versions 2&3 have minor editorial revision
Noise gates for decoherent quantum circuits
A major problem in exploiting microscopic systems for developing a new
technology based on the principles of Quantum Information is the influence of
noise which tends to work against the quantum features of such systems. It
becomes then crucial to understand how noise affects the evolution of quantum
circuits: several techniques have been proposed among which stochastic
differential equations (SDEs) can represent a very convenient tool. We show how
SDEs naturally map any Markovian noise into a linear operator, which we will
call a noise gate, acting on the wave function describing the state of the
circuit, and we will discuss some examples. We shall see that these gates can
be manipulated like any standard quantum gate, thus simplifying in certain
circumstances the task of computing the overall effect of the noise at each
stage of the protocol. This approach yields equivalent results to those derived
from the Lindblad equation; yet, as we show, it represents a handy and fast
tool for performing computations, and moreover, it allows for fast numerical
simulations and generalizations to non Markovian noise. In detail we review the
depolarizing channel and the generalized amplitude damping channel in terms of
this noise gate formalism and show how these techniques can be applied to any
quantum circuit.Comment: 10 pages, 4 figures: journal reference added + some typos correcte
Discounting in Games across Time Scales
We introduce two-level discounted games played by two players on a
perfect-information stochastic game graph. The upper level game is a discounted
game and the lower level game is an undiscounted reachability game. Two-level
games model hierarchical and sequential decision making under uncertainty
across different time scales. We show the existence of pure memoryless optimal
strategies for both players and an ordered field property for such games. We
show that if there is only one player (Markov decision processes), then the
values can be computed in polynomial time. It follows that whether the value of
a player is equal to a given rational constant in two-level discounted games
can be decided in NP intersected coNP. We also give an alternate strategy
improvement algorithm to compute the value
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