4,206 research outputs found
The high energy limit of the trajectory representation of quantum mechanics
The trajectory representation in the high energy limit (Bohr correspondence
principle) manifests a residual indeterminacy. This indeterminacy is compared
to the indeterminacy found in the classical limit (Planck's constant to 0)
[Int. J. Mod. Phys. A 15, 1363 (2000)] for particles in the classically allowed
region, the classically forbiden region, and near the WKB turning point. The
differences between Bohr's and Planck's principles for the trajectory
representation are compared with the differences between these correspondence
principles for the wave representation. The trajectory representation in the
high energy limit is shown to go to neither classical nor statistical
mechanics. The residual indeterminacy is contrasted to Heisenberg uncertainty.
The relationship between indeterminacy and 't Hooft's information loss and
equivalence classes is investigated.Comment: 12 pages of LaTeX. No figures. Incorporated into the "Proceedings of
the Seventh International Wigner Symposium" (ed. M. E. Noz), 24-29 August
2001, U. of Maryland. Proceedings available at
http://www.physics.umd.edu/robo
Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment
The double slit problem is idealized by simplifying each slit by a point
source. A composite reduced action for the two correlated point sources is
developed. Contours of the reduced action, trajectories and loci of transit
times are developed in the region near the two point sources. The trajectory
through any point in Euclidian 3-space also passes simultaneously through both
point sources.Comment: 12 pages LaTeX2e, 9 figures. Typos corrected. Author's final
submission. A companion paper to "Interference, reduced action, and
trajectories", quant-ph/0605120. Keywords: interference, Young's experiment,
entanglement, nonlocality, trajectory representation, determinis
Interference, reduced action, and trajectories
Instead of investigating the interference between two stationary, rectilinear
wave functions in a trajectory representation by examining the two rectilinear
wave functions individually, we examine a dichromatic wave function that is
synthesized from the two interfering wave functions. The physics of
interference is contained in the reduced action for the dichromatic wave
function. As this reduced action is a generator of the motion for the
dichromatic wave function, it determines the dichromatic wave function's
trajectory. The quantum effective mass renders insight into the behavior of the
trajectory. The trajectory in turn renders insight into quantum nonlocality.Comment: 12 pages text, 5 figures. Typos corrected. Author's final submission.
A companion paper to "Welcher Weg? A trajectory representation of a quantum
Young's diffraction experiment", quant-ph/0605121. Keywords: interference,
nonlocality, trajectory representation, entanglement, dwell time, determinis
The Equivalence Postulate of Quantum Mechanics
The Equivalence Principle (EP), stating that all physical systems are
connected by a coordinate transformation to the free one with vanishing energy,
univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories
depend on the Planck length through hidden variables which arise as initial
conditions. The formulation has manifest p-q duality, a consequence of the
involutive nature of the Legendre transform and of its recently observed
relation with second-order linear differential equations. This reflects in an
intrinsic psi^D-psi duality between linearly independent solutions of the
Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even
for bound states. No use of any axiomatic interpretation of the wave-function
is made. Tunnelling is a direct consequence of the quantum potential which
differs from the usual one and plays the role of particle's self-energy. The
QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of
the extended real line. This is an important feature as the L^2 condition,
which in the usual formulation is a consequence of the axiomatic interpretation
of the wave-function, directly follows as a basic theorem which only uses the
geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP.
As a result, the EP itself implies a dynamical equation that does not require
any further assumption and reproduces both tunnelling and energy quantization.
Several features of the formulation show how the Copenhagen interpretation
hides the underlying nature of QM. Finally, the non-stationary higher
dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the
action of SL(2,R) subgroups acting on the reduced action explicitly reveals
that the wave-function describes only equivalence classes of Planck length
deterministic physics. New derivation of the Schwarzian derivative from the
cocycle condition. "Legendre brackets" introduced to further make "Legendre
duality" manifest. Introduction now contains examples and provides a short
pedagogical review. Clarifications, conclusions, ackn. and references adde
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‘Jugglers’, ‘copers’ and ‘strugglers’: academics’ perceptions of being a head of department in a post-1992 UK university and how it influences their future careers
This study investigates the experiences of academics who became department heads in a post-1992 UK university and explores the influence that being in the position has on their planned future academic career. Drawing on life history interviews undertaken with 17 male and female heads of department, the paper constitutes an in-depth study of their careers in the same university. The findings suggest that academics who become department heads not only need the capacity to assume a range of personal and professional identities, but need flexibility to regularly adopt and switch between them. Whether individuals can successfully balance and manage such multiple identities, or whether they experience major conflicts within or between them, greatly affects their experiences of being a head of department and seems to influence their subsequent career decisions. The paper concludes by proposing a conceptual framework and typology to interpret the career trajectories of academics that became department heads in the case university
Advanced tracking systems design and analysis
The results of an assessment of several types of high-accuracy tracking systems proposed to track the spacecraft in the National Aeronautics and Space Administration (NASA) Advanced Tracking and Data Relay Satellite System (ATDRSS) are summarized. Tracking systems based on the use of interferometry and ranging are investigated. For each system, the top-level system design and operations concept are provided. A comparative system assessment is presented in terms of orbit determination performance, ATDRSS impacts, life-cycle cost, and technological risk
The Cost of Stability in Coalitional Games
A key question in cooperative game theory is that of coalitional stability,
usually captured by the notion of the \emph{core}--the set of outcomes such
that no subgroup of players has an incentive to deviate. However, some
coalitional games have empty cores, and any outcome in such a game is unstable.
In this paper, we investigate the possibility of stabilizing a coalitional
game by using external payments. We consider a scenario where an external
party, which is interested in having the players work together, offers a
supplemental payment to the grand coalition (or, more generally, a particular
coalition structure). This payment is conditional on players not deviating from
their coalition(s). The sum of this payment plus the actual gains of the
coalition(s) may then be divided among the agents so as to promote stability.
We define the \emph{cost of stability (CoS)} as the minimal external payment
that stabilizes the game.
We provide general bounds on the cost of stability in several classes of
games, and explore its algorithmic properties. To develop a better intuition
for the concepts we introduce, we provide a detailed algorithmic study of the
cost of stability in weighted voting games, a simple but expressive class of
games which can model decision-making in political bodies, and cooperation in
multiagent settings. Finally, we extend our model and results to games with
coalition structures.Comment: 20 pages; will be presented at SAGT'0
Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof
In recent work, we formalized the theory of optimal-size sorting networks
with the goal of extracting a verified checker for the large-scale
computer-generated proof that 25 comparisons are optimal when sorting 9 inputs,
which required more than a decade of CPU time and produced 27 GB of proof
witnesses. The checker uses an untrusted oracle based on these witnesses and is
able to verify the smaller case of 8 inputs within a couple of days, but it did
not scale to the full proof for 9 inputs. In this paper, we describe several
non-trivial optimizations of the algorithm in the checker, obtained by
appropriately changing the formalization and capitalizing on the symbiosis with
an adequate implementation of the oracle. We provide experimental evidence of
orders of magnitude improvements to both runtime and memory footprint for 8
inputs, and actually manage to check the full proof for 9 inputs.Comment: IMADA-preprint-c
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