773 research outputs found
Typicality vs. probability in trajectory-based formulations of quantum mechanics
Bohmian mechanics represents the universe as a set of paths with a
probability measure defined on it. The way in which a mathematical model of
this kind can explain the observed phenomena of the universe is examined in
general. It is shown that the explanation does not make use of the full
probability measure, but rather of a suitable set function deriving from it,
which defines relative typicality between single-time cylinder sets. Such a set
function can also be derived directly from the standard quantum formalism,
without the need of an underlying probability measure. The key concept for this
derivation is the {\it quantum typicality rule}, which can be considered as a
generalization of the Born rule. The result is a new formulation of quantum
mechanics, in which particles follow definite trajectories, but which is only
based on the standard formalism of quantum mechanics.Comment: 24 pages, no figures. To appear in Foundation of Physic
Evaluation of Automated Fermi GBM Localizations of Gamma-Ray Bursts
The capability of the Fermi Gamma-ray Burst Monitor (GBM) to localize gamma-ray bursts (GRBs) is evaluated for two different automate algorithms: the GBM Team's RoboBA algorithm and the independentl developed BALROG algorithm. Through a systematic study utilizing ove 500 GRBs with known locations from instruments like Swift and the Ferm LAT, we directly compare the effectiveness of, and accurately estimat the systematic uncertainty for, both algorithms. We show simpl adjustments to the GBM Team's RoboBA, in operation since early 2016 yields significant improvement in the systematic uncertainty, removin the long tail identified in the systematic, and improves the overal accuracy. The systematic uncertainty for the updated RoboB localizations is 1.8^\\circ for 52% of GRBs and 4.1^\\circ for th remaining 48%. Both from public reporting by BALROG and our systemati study, we find the systematic uncertainty of 1-2^\\circ quoted in GC circulars for bright GRBs localized by BALROG is an underestimate of th true magnitude of the systematic, which we find to be 2.7^\\circ fo 74% of GRBs and 33^\\circ for the remaining 26%. We show that, once th systematic uncertainty is considered, the RoboBA 90% localizatio confidence regions can be more than an order of magnitude smaller i area than those produced by BALROG
Quantum models of classical mechanics: maximum entropy packets
In a previous paper, a project of constructing quantum models of classical
properties has been started. The present paper concludes the project by turning
to classical mechanics. The quantum states that maximize entropy for given
averages and variances of coordinates and momenta are called ME packets. They
generalize the Gaussian wave packets. A non-trivial extension of the
partition-function method of probability calculus to quantum mechanics is
given. Non-commutativity of quantum variables limits its usefulness. Still, the
general form of the state operators of ME packets is obtained with its help.
The diagonal representation of the operators is found. A general way of
calculating averages that can replace the partition function method is
described. Classical mechanics is reinterpreted as a statistical theory.
Classical trajectories are replaced by classical ME packets. Quantum states
approximate classical ones if the product of the coordinate and momentum
variances is much larger than Planck constant. Thus, ME packets with large
variances follow their classical counterparts better than Gaussian wave
packets.Comment: 26 pages, no figure. Introduction and the section on classical limit
are extended, new references added. Definitive version accepted by Found.
Phy
The generalized non-conservative model of a 1-planet system - revisited
We study the long-term dynamics of a planetary system composed of a star and
a planet. Both bodies are considered as extended, non-spherical, rotating
objects. There are no assumptions made on the relative angles between the
orbital angular momentum and the spin vectors of the bodies. Thus, we analyze
full, spatial model of the planetary system. Both objects are assumed to be
deformed due to their own rotations, as well as due to the mutual tidal
interactions. The general relativity corrections are considered in terms of the
post-Newtonian approximation. Besides the conservative contributions to the
perturbing forces, there are also taken into account non-conservative effects,
i.e., the dissipation of the mechanical energy. This dissipation is a result of
the tidal perturbation on the velocity field in the internal zones with
non-zero turbulent viscosity (convective zones). Our main goal is to derive the
equations of the orbital motion as well as the equations governing
time-evolution of the spin vectors (angular velocities). We derive the
Lagrangian equations of the second kind for systems which do not conserve the
mechanical energy. Next, the equations of motion are averaged out over all fast
angles with respect to time-scales characteristic for conservative
perturbations. The final equations of motion are then used to study the
dynamics of the non-conservative model over time scales of the order of the age
of the star. We analyze the final state of the system as a function of the
initial conditions. Equilibria states of the averaged system are finally
discussed.Comment: 37 pages, 13 figures, accepted to Celestial Mechanics and Dynamical
Astronom
Trajectory versus probability density entropy
We study the problem of entropy increase of the Bernoulli-shift map without
recourse to the concept of trajectory and we discuss whether, and under which
conditions if it does, the distribution density entropy coincides with the
Kolmogorov-Sinai entropy, namely, with the trajectory entropy.Comment: 24 page
On Thermalization in de Sitter Space
We discuss thermalization in de Sitter space and argue, from two different
points of view, that the typical time needed for thermalization is of order
, where is the radius of the de Sitter space in question.
This time scale gives plenty of room for non-thermal deviations to survive
during long periods of inflation. We also speculate in more general terms on
the meaning of the time scale for finite quantum systems inside isolated boxes,
and comment on the relation to the Poincar\'{e} recurrence time.Comment: 14 pages, 2 figures, latex, references added. Improved discussion in
section 3 adde
On the spherical-axial transition in supernova remnants
A new law of motion for supernova remnant (SNR) which introduces the quantity
of swept matter in the thin layer approximation is introduced. This new law of
motion is tested on 10 years observations of SN1993J. The introduction of an
exponential gradient in the surrounding medium allows to model an aspherical
expansion. A weakly asymmetric SNR, SN1006, and a strongly asymmetric SNR,
SN1987a, are modeled. In the case of SN1987a the three observed rings are
simulated.Comment: 19 figures and 14 pages Accepted for publication in Astrophysics &
Space Science in the year 201
Roles of Fast-Cyclotron and Alfven-Cyclotron Waves for the Multi-Ion Solar Wind
Using linear Vlasov theory of plasma waves and quasi-linear theory of
resonant wave-particle interaction, the dispersion relations and the
electromagnetic field fluctuations of fast and Alfven waves are studied for a
low-beta multi-ion plasma in the inner corona. Their probable roles in heating
and accelerating the solar wind via Landau and cyclotron resonances are
quantified. We assume that (1) low-frequency Alfven and fast waves have the
same spectral shape and the same amplitude of power spectral density; (2) these
waves eventually reach ion cyclotron frequencies due to a turbulence cascade;
(3) kinetic wave-particle interaction powers the solar wind. The existence of
alpha particles in a dominant proton/electron plasma can trigger linear mode
conversion between oblique fast-whistler and hybrid alpha-proton cyclotron
waves. The fast-cyclotron waves undergo both alpha and proton cyclotron
resonances. The alpha cyclotron resonance in fast-cyclotron waves is much
stronger than that in Alfven-cyclotron waves. For alpha cyclotron resonance, an
oblique fast-cyclotron wave has a larger left-handed electric field
fluctuation, a smaller wave number, a larger local wave amplitude, and a
greater energization capability than a corresponding Alfven-cyclotron wave at
the same wave propagation angle \theta, particularly at < \theta <
. When Alfven-cyclotron or fast-cyclotron waves are present, alpha
particles are the chief energy recipient. The transition of preferential
energization from alpha particles to protons may be self-modulated by
differential speed and temperature anisotropy of alpha particles via the
self-consistently evolving wave-particle interaction. Therefore, fast-cyclotron
waves as a result of linear mode coupling is a potentially important mechanism
for preferential energization of minor ions in the main acceleration region of
the solar wind.Comment: 29 pages, 10 figures, 3 tables. Accepted for publication in Solar
Physic
The influence of individual cognitive style on performance in management education
This paper reports the outcomes of an empirical study undertaken to explore the possibility that cognitive style may be an important factor influencing performance on certain types of task in management education. Four hundred and twelve final-year undergraduate degree students studying management and business administration were tested using the Allinson-Hayes Cognitive Style Index. Their cognitive styles were then compared with assessment grades achieved for academic modules, the task categories of which were deemed to be consonant with either the wholist/intuitive or the analytic style of working. Overall ability defined by final degree grades was also tested against individuals’ cognitive styles. As expected, students whose dominant cognitive styles were analytic attained higher grades for long term solitary tasks involving careful planning and analysis of information. However, contrary to expectations, performance on tasks believed to be more suited to the wholist/intuitive style was also higher for analytic individuals, as was overall ability defined by final degree grades. The results were discussed in terms of the nature of the tasks and the need for methods of performance assessment that are independent of an orientation bias. Without this, it is argued, employment selection criteria may favour the wrong type of candidate in some circumstances
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