7,689 research outputs found
A Relativistic Version of the Two-Level Atom in the Rest-Frame Instant Form of Dynamics
We define a relativistic version of the two-level atom, in which an extended
atom is replaced by a point particle carrying suitable Grassmann variables for
the description of the two-level structure and of the electric dipole. After
studying the isolated system "atom plus the electro-magnetic field" in the
electric-dipole representation as a parametrized Minkowski theory, we give its
restriction to the inertial rest frame and the explicit form of the Poincar\'e
generators. After quantization we get a two-level atom with a spin 1/2 electric
dipole and the relativistic generalization of the Hamiltonians of the Rabi and
Jaynes-Cummings models.Comment: 23 page
New Directions in Non-Relativistic and Relativistic Rotational and Multipole Kinematics for N-Body and Continuous Systems
In non-relativistic mechanics the center of mass of an isolated system is
easily separated out from the relative variables. For a N-body system these
latter are usually described by a set of Jacobi normal coordinates, based on
the clustering of the centers of mass of sub-clusters. The Jacobi variables are
then the starting point for separating {\it orientational} variables, connected
with the angular momentum constants of motion, from {\it shape} (or {\it
vibrational}) variables. Jacobi variables, however, cannot be extended to
special relativity. We show by group-theoretical methods that two new sets of
relative variables can be defined in terms of a {\it clustering of the angular
momenta of sub-clusters} and directly related to the so-called {\it dynamical
body frames} and {\it canonical spin bases}. The underlying group-theoretical
structure allows a direct extension of such notions from a non-relativistic to
a special- relativistic context if one exploits the {\it rest-frame instant
form of dynamics}. The various known definitions of relativistic center of mass
are recovered. The separation of suitable relative variables from the so-called
{\it canonical internal} center of mass leads to the correct kinematical
framework for the relativistic theory of the orbits for a N-body system with
action -at-a-distance interactions. The rest-frame instant form is also shown
to be the correct kinematical framework for introducing the Dixon multi-poles
for closed and open N-body systems, as well as for continuous systems,
exemplified here by the configurations of the Klein-Gordon field that are
compatible with the previous notions of center of mass.Comment: Latex, p.75, Invited contribution for the book {\it Atomic and
Molecular Clusters: New Research} (Nova Science
Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: I. Admissible 3+1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames
By using the 3+1 point of view and parametrized Minkowski theories we develop
the theory of {\it non-inertial} frames in Minkowski space-time. The transition
from a non-inertial frame to another one is a gauge transformation connecting
the respective notions of instantaneous 3-space (clock synchronization
convention) and of the 3-coordinates inside them. As a particular case we get
the extension of the inertial rest-frame instant form of dynamics to the
non-inertial rest-frame one. We show that every isolated system can be
described as an external decoupled non-covariant canonical center of mass
(described by frozen Jacobi data) carrying a pole-dipole structure: the
invariant mass and an effective spin. Moreover we identify the constraints
eliminating the internal 3-center of mass inside the instantaneous 3-spaces. In
the case of the isolated system of positive-energy scalar particles with
Grassmann-valued electric charges plus the electro-magnetic field we obtain
both Maxwell equations and their Hamiltonian description in non-inertial
frames. Then by means of a non-covariant decomposition we define the
non-inertial radiation gauge and we find the form of the non-covariant Coulomb
potential. We identify the coordinate-dependent relativistic inertial
potentials and we show that they have the correct Newtonian limit. In the
second paper we will study properties of Maxwell equations in non-inertial
frames like the wrap-up effect and the Faraday rotation in astrophysics. Also
the 3+1 description without coordinate-singularities of the rotating disk and
the Sagnac effect will be given, with added comments on pulsar magnetosphere
and on a relativistic extension of the Earth-fixed coordinate system.Comment: This paper and the second one are an adaptation of arXiv 0812.3057
for publication on Int.J.Geom. Methods in Modern Phys. 77
Mean Reversion of Real Exchange Rates and Purchasing Power Parity in Turkey
The important concept of purchasing power parity (PPP) has a number of practical implications. Our central objective is to examine the stationarity of Turkeyâs real exchange rates to test for the empirical validity of PPP. Our results from conventional univariate unit root tests fail to support PPP. However, when we use the empirical methodology developed by Caner and Hansen (2001), which allows us to jointly consider non-stationarity and non-linearity, we find evidence of non-linear mean reversion in Turkeyâs real exchange rates. This implies that PPP holds in one threshold regime but not in another.Turkey, purchasing power parity, real exchange rate, unit root, non-linearity
Generating Interpretable Fuzzy Controllers using Particle Swarm Optimization and Genetic Programming
Autonomously training interpretable control strategies, called policies,
using pre-existing plant trajectory data is of great interest in industrial
applications. Fuzzy controllers have been used in industry for decades as
interpretable and efficient system controllers. In this study, we introduce a
fuzzy genetic programming (GP) approach called fuzzy GP reinforcement learning
(FGPRL) that can select the relevant state features, determine the size of the
required fuzzy rule set, and automatically adjust all the controller parameters
simultaneously. Each GP individual's fitness is computed using model-based
batch reinforcement learning (RL), which first trains a model using available
system samples and subsequently performs Monte Carlo rollouts to predict each
policy candidate's performance. We compare FGPRL to an extended version of a
related method called fuzzy particle swarm reinforcement learning (FPSRL),
which uses swarm intelligence to tune the fuzzy policy parameters. Experiments
using an industrial benchmark show that FGPRL is able to autonomously learn
interpretable fuzzy policies with high control performance.Comment: Accepted at Genetic and Evolutionary Computation Conference 2018
(GECCO '18
Disentangling density and temperature effects in the viscous slowing down of glassforming liquids
We present a consistent picture of the respective role of density and
temperature in the viscous slowing down of glassforming liquids and polymers.
Specifically, based in part upon a new analysis of simulation and experimental
data on liquid ortho-terphenyl, we conclude that a zeroth-order description of
the approach to the glass transition should be formulated in terms of a
temperature-driven super-Arrhenius activated behavior rather than a
density-driven congestion or jamming phenomenon. The density plays a role at a
quantitative level, but its effect on the viscosity and the structural
relaxation time can be simply described via a single parameter, an effective
interaction energy that is characteristic of the high temperature liquid
regime; as a result, density does not affect the ``fragility'' of the
glassforming system.Comment: RevTeX4, 8 pages, 8 eps figure
The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics
A modern re-visitation of the consequences of the lack of an intrinsic notion
of instantaneous 3-space in relativistic theories leads to a reformulation of
their kinematical basis emphasizing the role of non-inertial frames centered on
an arbitrary accelerated observer. In special relativity the exigence of
predictability implies the adoption of the 3+1 point of view, which leads to a
well posed initial value problem for field equations in a framework where the
change of the convention of synchronization of distant clocks is realized by
means of a gauge transformation. This point of view is also at the heart of the
canonical approach to metric and tetrad gravity in globally hyperbolic
asymptotically flat space-times, where the use of Shanmugadhasan canonical
transformations allows the separation of the physical degrees of freedom of the
gravitational field (the tidal effects) from the arbitrary gauge variables.
Since a global vision of the equivalence principle implies that only global
non-inertial frames can exist in general relativity, the gauge variables are
naturally interpreted as generalized relativistic inertial effects, which have
to be fixed to get a deterministic evolution in a given non-inertial frame. As
a consequence, in each Einstein's space-time in this class the whole
chrono-geometrical structure, including also the clock synchronization
convention, is dynamically determined and a new approach to the Hole Argument
leads to the conclusion that "gravitational field" and "space-time" are two
faces of the same entity. This view allows to get a classical scenario for the
unification of the four interactions in a scheme suited to the description of
the solar system or our galaxy with a deperametrization to special relativity
and the subsequent possibility to take the non-relativistic limit.Comment: 33 pages, Lectures given at the 42nd Karpacz Winter School of
Theoretical Physics, "Current Mathematical Topics in Gravitation and
Cosmology", Ladek, Poland, 6-11 February 200
Foreign Output Shocks and Monetary Policy Regimes in Small Open Economies: A DSGE Evaluation of East Asia
East Asiaâs small open economies were hit in varying degrees by the sharp drop in the output of major industrial countries during the global financial and economic crisis of 2008-2009. This highlights the role of monetary policy regimes in cushioning small open economies from adverse external output shocks. To assess the welfare impact of external shocks on key macroeconomic variables under different monetary policy regimes, we numerically solve and calculate the welfare loss function of a dynamic stochastic general equilibrium (DSGE) model. We find that CPI inflation targeting minimizes welfare losses for import-to-GDP ratios from 0.3 to 0.9. However, welfare under the pegged exchange rate regime is almost equivalent to CPI inflation targeting when the import-to-GDP ratio is one while the Taylor-type rule minimizes welfare when the import-to-GDP ratio is 0.1. We calibrate the model and derive welfare implications for eight East Asian small open economies.Trade channel, Import-to-GDP ratio, small open economies, welfare, exchange rate regimes, inflation targeting, Taylor rule, foreign output shock
Foreign Output Shocks and Monetary Policy Regimes in Small Open Economies: A DSGE Evaluation of East Asia
East Asiaâs small open economies were hit in varying degrees by the sharp drop in the output of major industrial countries during the global financial and economic crisis of 2008-2009. This highlights the role of monetary policy regimes in cushioning small open economies from adverse external output shocks. To assess the welfare impact of external shocks on key macroeconomic variables under different monetary policy regimes, we numerically solve and calculate the welfare loss function of a dynamic stochastic general equilibrium (DSGE) model. We find that CPI inflation targeting minimizes welfare losses for import-to-GDP ratios from 0.3 to 0.9. However, welfare under the pegged exchange rate regime is almost equivalent to CPI inflation targeting when the import-to-GDP ratio is one while the Taylor-type rule minimizes welfare when the import-to-GDP ratio is 0.1. We calibrate the model and derive welfare implications for eight East Asian small open economies.
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