4,389 research outputs found
Fundamental Limits on the Speed of Evolution of Quantum States
This paper reports on some new inequalities of
Margolus-Levitin-Mandelstam-Tamm-type involving the speed of quantum evolution
between two orthogonal pure states. The clear determinant of the qualitative
behavior of this time scale is the statistics of the energy spectrum. An
often-overlooked correspondence between the real-time behavior of a quantum
system and the statistical mechanics of a transformed (imaginary-time)
thermodynamic system appears promising as a source of qualitative insights into
the quantum dynamics.Comment: 6 pages, 1 eps figur
Complex Extension of Quantum Mechanics
It is shown that the standard formulation of quantum mechanics in terms of
Hermitian Hamiltonians is overly restrictive. A consistent physical theory of
quantum mechanics can be built on a complex Hamiltonian that is not Hermitian
but satisfies the less restrictive and more physical condition of space-time
reflection symmetry (PT symmetry). Thus, there are infinitely many new
Hamiltonians that one can construct to explain experimental data. One might
expect that a quantum theory based on a non-Hermitian Hamiltonian would violate
unitarity. However, if PT symmetry is not spontaneously broken, it is possible
to construct a previously unnoticed physical symmetry C of the Hamiltonian.
Using C, an inner product is constructed whose associated norm is positive
definite. This construction is completely general and works for any
PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is
governed by unitary time evolution. This work is not in conflict with
conventional quantum mechanics but is rather a complex generalisation of it.Comment: 4 Pages, Version to appear in PR
Automated System for Early Breast Cancer Detection in Mammograms
The increasing demand on mammographic screening for early breast cancer detection, and the subtlety of early breast cancer signs on mammograms, suggest an automated image processing system that can serve as a diagnostic aid in radiology clinics. We present a fully automated algorithm for detecting clusters of microcalcifications that are the most common signs of early, potentially curable breast cancer. By using the contour map of the mammogram, the algorithm circumvents some of the difficulties encountered with standard image processing methods. The clinical implementation of an automated instrument based on this algorithm is also discussed
On the dominance of J(P)=0(+) ground states in even-even nuclei from random two-body interactions
Recent calculations using random two-body interactions showed a preponderance
of J(P)=0(+) ground states, despite the fact that there is no strong pairing
character in the force. We carry out an analysis of a system of identical
particles occupying orbits with j=1/2, 3/2 and 5/2 and discuss some general
features of the spectra derived from random two-body interactions. We show that
for random two-body interactions that are not time-reversal invariant the
dominance of 0(+) states in this case is more pronounced, indicating that
time-reversal invariance cannot be the origin of the 0(+) dominance.Comment: 8 pages, 3 tables and 3 figures. Phys. Rev. C, in pres
The Information Geometry of the Ising Model on Planar Random Graphs
It has been suggested that an information geometric view of statistical
mechanics in which a metric is introduced onto the space of parameters provides
an interesting alternative characterisation of the phase structure,
particularly in the case where there are two such parameters -- such as the
Ising model with inverse temperature and external field .
In various two parameter calculable models the scalar curvature of
the information metric has been found to diverge at the phase transition point
and a plausible scaling relation postulated: . For spin models the necessity of calculating in
non-zero field has limited analytic consideration to 1D, mean-field and Bethe
lattice Ising models. In this letter we use the solution in field of the Ising
model on an ensemble of planar random graphs (where ) to evaluate the scaling behaviour of the scalar curvature, and find
. The apparent discrepancy is traced
back to the effect of a negative .Comment: Version accepted for publication in PRE, revtex
Non-Adaptive Data Structures For Predecessor Search
In this work, we continue the examination of the role non-adaptivity plays in maintaining dynamic data structures, initiated by Brody and Larsen. We consider non-adaptive data structures for predecessor search in the w-bit cell probe model. In this problem, the goal is to dynamically maintain a subset T of up to n elements from {1, ..., m}, while supporting insertions, deletions, and a predecessor query Pred(x), which returns the largest element in T that is less than or equal to x. Predecessor search is one of the most well-studied data structure problems. For this problem, using non-adaptivity comes at a steep price. We provide exponential cell probe complexity separations between (i) adaptive and non-adaptive data structures and (ii) non-adaptive and memoryless data structures for predecessor search. A classic data structure of van Emde Boas solves dynamic predecessor search in log(log(m)) probes; this data structure is adaptive. For dynamic data structures which make non-adaptive updates, we show the cell probe complexity is O(log(m)/log(w/log(m))). We also give a nearly-matching Omega(log(m)/log(w)) lower bound. We also give an m/w lower bound for memoryless data structures. Our lower bound technique is tailored to non-adaptive (as opposed to memoryless) updates and might be of independent interest
Wave Scattering through Classically Chaotic Cavities in the Presence of Absorption: An Information-Theoretic Model
We propose an information-theoretic model for the transport of waves through
a chaotic cavity in the presence of absorption. The entropy of the S-matrix
statistical distribution is maximized, with the constraint : n is the dimensionality of S, and meaning complete (no) absorption. For strong absorption our result
agrees with a number of analytical calculations already given in the
literature. In that limit, the distribution of the individual (angular)
transmission and reflection coefficients becomes exponential -Rayleigh
statistics- even for n=1. For Rayleigh statistics is attained even
with no absorption; here we extend the study to . The model is
compared with random-matrix-theory numerical simulations: it describes the
problem very well for strong absorption, but fails for moderate and weak
absorptions. Thus, in the latter regime, some important physical constraint is
missing in the construction of the model.Comment: 4 pages, latex, 3 ps figure
Research on nonlinear optical materials: an assessment. IV. Photorefractive and liquid crystal materials
This panel considered two separate subject areas: photorefractive materials used for nonlinear optics and liquid crystal materials used in light valves. Two related subjects were not considered due to lack of expertise on the panel: photorefractive materials used in light valves and liquid crystal materials used in nonlinear optics. Although the inclusion of a discussion of light valves by a panel on nonlinear optical materials at first seems odd, it is logical because light valves and photorefractive materials perform common functions
Canonical form of Hamiltonian matrices
On the basis of shell model simulations, it is conjectured that the Lanczos
construction at fixed quantum numbers defines---within fluctuations and
behaviour very near the origin---smooth canonical matrices whose forms depend
on the rank of the Hamiltonian, dimensionality of the vector space, and second
and third moments. A framework emerges that amounts to a general Anderson model
capable of dealing with ground state properties and strength functions. The
smooth forms imply binomial level densities. A simplified approach to canonical
thermodynamics is proposed.Comment: 4 pages 6 figure
1970 Problems in Legal Education
Five problems in legal education, much discussed recently, were posed by the Editors of this Review to a number of administrative figures in the law school world. These questions were and are frankly difficult and controversial, but their answers are important to our system of legal education and to our society. Capsule answers given by these concerned legal education administrators are believed to be interesting and significant. Each is a personal rather than a representative opinion. Brief answers such as these, of course, are not expected to be, nor do they pretend to be, complete or profound. Their purpose is to indicate succinctly the approach of some law school administrative opinion makers to difficult policy problems of legal education
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