821 research outputs found
The exponential map for the unitary group SU(2,2)
In this article we extend our previous results for the orthogonal group,
, to its homomorphic group . Here we present a closed, finite
formula for the exponential of a traceless matrix, which can be
viewed as the generator (Lie algebra elements) of the group. We apply
this result to the group, which Lie algebra can be represented by the
Dirac matrices, and discuss how the exponential map for can be
written by means of the Dirac matrices.Comment: 10 page
Operator Transformations Between Exactly Solvable Potentials and Their Lie Group Generators
One may obtain, using operator transformations, algebraic relations between
the Fourier transforms of the causal propagators of different exactly solvable
potentials. These relations are derived for the shape invariant potentials.
Also, potentials related by real transformation functions are shown to have the
same spectrum generating algebra with Hermitian generators related by this
operator transformation.Comment: 13 pages with one Postscript figure, uses LaTeX2e with revte
Critical sets of the total variance of state detect all SLOCC entanglement classes
We present a general algorithm for finding all classes of pure multiparticle
states equivalent under Stochastic Local Operations and Classsical
Communication (SLOCC). We parametrize all SLOCC classes by the critical sets of
the total variance function. Our method works for arbitrary systems of
distinguishable and indistinguishable particles. We also discuss the Morse
indices of critical points which have the interpretation of the number of
independent non-local perturbations increasing the variance and hence
entanglement of a state. We illustrate our method by two examples.Comment: 4 page
Detecting Neutrino Magnetic Moments with Conducting Loops
It is well established that neutrinos have mass, yet it is very difficult to
measure those masses directly. Within the standard model of particle physics,
neutrinos will have an intrinsic magnetic moment proportional to their mass. We
examine the possibility of detecting the magnetic moment using a conducting
loop. According to Faraday's Law of Induction, a magnetic dipole passing
through a conducting loop induces an electromotive force, or EMF, in the loop.
We compute this EMF for neutrinos in several cases, based on a fully covariant
formulation of the problem. We discuss prospects for a real experiment, as well
as the possibility to test the relativistic formulation of intrinsic magnetic
moments.Comment: 6 pages, 4 b/w figures, uses RevTe
Self-accelerated Universe
It is widely believed that the large redshifts for distant supernovae are
explained by the vacuum energy dominance, or, in other words, by the
cosmological constant in Einstein's equations, which is responsible for the
anti-gravitation effect. A tacit assumption is that particles move along a
geodesic for the background metric. This is in the same spirit as the consensus
regarding the uniform Galilean motion of a free electron. However, there is a
runaway solution to the Lorentz--Dirac equation governing the behavior of a
radiating electron, in addition to the Galilean solution. Likewise, a runaway
solution to the entire system of equations, both gravitation and matter
equations of motion including, may provide an alternative explanation for the
accelerated expansion of the Universe, without recourse to the hypothetic
cosmological constant.Comment: 11 pages; Talk at the 9th Adriatic Meeting, Dubrovnic, Croatia, 4-14
September, 2003, Minor improvement, references added; to appear in ``Progress
in General Relativity and Quantum Cosmology Research'', Nova Science
Publisher
Generation of single-mode SU(1,1) intelligent states and an analytic approach to their quantum statistical properties
We discuss a scheme for generation of single-mode photon states associated
with the two-photon realization of the SU(1,1) algebra. This scheme is based on
the process of non-degenerate down-conversion with the signal prepared
initially in the squeezed vacuum state and with a measurement of the photon
number in one of the output modes. We focus on the generation and properties of
single-mode SU(1,1) intelligent states which minimize the uncertainty relations
for Hermitian generators of the group. Properties of the intelligent states are
studied by using a ``weak'' extension of the analytic representation in the
unit disk. Then we are able to obtain exact analytical expressions for
expectation values describing quantum statistical properties of the SU(1,1)
intelligent states. Attention is mainly devoted to the study of photon
statistics and linear and quadratic squeezing.Comment: to appear in Quantum Semiclass. Opt., LaTeX, epsf style, 21 pages
including 5 Postscript figures. More information on
http://www.technion.ac.il/~brif/science.htm
Merajut Kembali Relasionallitas Masyarakat dan Pemerintah: Relevansi Politik Berasaskan Rekonsiliasi dan Kebenaran
The center of the study of this paper is to explore and understand Armada Riyantoâs ideas about reconciliation and truth. The ongoing political and security dynamics generate new and rich awareness and meaning in the pursuit of peace. The methodology used in this paper is âphenomenologyâ, that is, everyday phenomena become the main source of philosophy. By looking at the political reality from marginal notes, from phenomenological experience, this research comes to the finding that the political concept based on reconciliation and truth is a relevant political program to seek peace. Reconciliation cannot be carried out without revealing the truth and a truth will have a deep meaning in the act of reconciliation. The government and society have a responsibility to cultivate the virtue of peace. The synergy between the government and the community determines the progress of the life of the nation and state
Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians,
we analyze three sets of complex potentials with real spectra, recently derived
by a potential algebraic approach based upon the complex Lie algebra sl(2, C).
This extends to the complex domain the well-known relationship between SUSYQM
and potential algebras for Hermitian Hamiltonians, resulting from their common
link with the factorization method and Darboux transformations. In the same
framework, we also generate for the first time a pair of elliptic partner
potentials of Weierstrass type, one of them being real and the other
imaginary and PT symmetric. The latter turns out to be quasiexactly solvable
with one known eigenvalue corresponding to a bound state. When the Weierstrass
function degenerates to a hyperbolic one, the imaginary potential becomes PT
non-symmetric and its known eigenvalue corresponds to an unbound state.Comment: 20 pages, Latex 2e + amssym + graphics, 2 figures, accepted in Int.
J. Mod. Phys.
Alternative Solution of the Path Integral for the Radial Coulomb Problem
In this Letter I present an alternative solution of the path integral for the
radial Coulomb problem which is based on a two-dimensional singular version of
the Levi-Civita transformation.Comment: 7 pages, Late
Identification and Establishment of Fisheries Refugia: Experience in the Philippines
The process of identifying and establishing fisheries refugia is discussed in this paper, where 'fisheries refugia' is an approach that integrates fisheries and habitat management to improve fisheries management in terms of space and time for sustainable use of fish stocks and protection of habitats. Also presented in this paper are site specific studies that showed the source and sink of fish eggs and larvae used in identifying the spawning and nursery refugia. Success of fisheries refugia depends on the actions at the local level where the level of community support depends on the involvement of local stakeholders in actions. Harnessing local knowledge is critical for good site selection and establishment of management measures. Science based management measure is most acceptable while education, information and communication is very helpful in terms of community acceptance of the fisheries refugia approaches. Other resource enhancement and management described in the paper are the closed fishing season for sardines in Zamboanga Peninsula, and closed fishing season for small pelagic fishes in the Visayan Sea and Davao Gulf. The effects of these management measures are seen in increased number of fish species as well as fish production
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