525 research outputs found
Non-linearity and related features of Makyoh (magic-mirror) imaging
Non-linearity in Makyoh (magic-mirror) imaging is analyzed using a geometrical optical approach. The sources of non-linearity are identified as (1) a topological mapping of the imaged surface due to surface gradients, (2) the hyperbolic-like dependence of the image intensity on the local curvatures, and (3) the quadratic dependence of the intensity due to local Gaussian surface curvatures. Criteria for an approximate linear imaging are given and the relevance to Makyoh-topography image evaluation is discussed
Infinite matrices may violate the associative law
The momentum operator for a particle in a box is represented by an infinite
order Hermitian matrix . Its square is well defined (and diagonal),
but its cube is ill defined, because . Truncating these
matrices to a finite order restores the associative law, but leads to other
curious results.Comment: final version in J. Phys. A28 (1995) 1765-177
A Quantum Yield Map for Synthetic Eumelanin
The quantum yield of synthetic eumelanin is known to be extremely low and it
has recently been reported to be dependent on excitation wavelength. In this
paper, we present quantum yield as a function of excitation wavelength between
250 and 500 nm, showing it to be a factor of 4 higher at 250 nm than at 500 nm.
In addition, we present a definitive map of the steady-state fluorescence as a
function of excitation and emission wavelengths, and significantly, a
three-dimensional map of the specific quantum yield: the fraction of photons
absorbed at each wavelength that are subsequently radiated at each emission
wavelength. This map contains clear features, which we attribute to certain
structural models, and shows that radiative emission and specific quantum yield
are negligible at emission wavelengths outside the range of 585 and 385 nm (2.2
and 3.2 eV), regardless of excitation wavelength. This information is important
in the context of understanding melanin biofunctionality, and the quantum
molecular biophysics therein.Comment: 10 pages, 6 figure
A Simple Proof of the Fundamental Theorem about Arveson Systems
With every Eo-semigroup (acting on the algebra of of bounded operators on a
separable infinite-dimensional Hilbert space) there is an associated Arveson
system. One of the most important results about Arveson systems is that every
Arveson system is the one associated with an Eo-semigroup. In these notes we
give a new proof of this result that is considerably simpler than the existing
ones and allows for a generalization to product systems of Hilbert module (to
be published elsewhere).Comment: Publication data added, acknowledgements and a note after acceptance
added, corrects a number of inconveniences that have been produced in the
published version during the publication proces
Quantum Degenerate Systems
Degenerate dynamical systems are characterized by symplectic structures whose
rank is not constant throughout phase space. Their phase spaces are divided
into causally disconnected, nonoverlapping regions such that there are no
classical orbits connecting two different regions. Here the question of whether
this classical disconnectedness survives quantization is addressed. Our
conclusion is that in irreducible degenerate systems --in which the degeneracy
cannot be eliminated by redefining variables in the action--, the
disconnectedness is maintained in the quantum theory: there is no quantum
tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces
are boundaries separating distinct physical systems, not only classically, but
in the quantum realm as well. The relevance of this feature for gravitation and
Chern-Simons theories in higher dimensions cannot be overstated.Comment: 18 pages, no figure
Positivity and conservation of superenergy tensors
Two essential properties of energy-momentum tensors T_{\mu\nu} are their
positivity and conservation. This is mathematically formalized by,
respectively, an energy condition, as the dominant energy condition, and the
vanishing of their divergence \nabla^\mu T_{\mu\nu}=0. The classical Bel and
Bel-Robinson superenergy tensors, generated from the Riemann and Weyl tensors,
respectively, are rank-4 tensors. But they share these two properties with
energy momentum tensors: the Dominant Property (DP) and the divergence-free
property in the absence of sources (vacuum). Senovilla defined a universal
algebraic construction which generates a basic superenergy tensor T{A} from any
arbitrary tensor A. In this construction the seed tensor A is structured as an
r-fold multivector, which can always be done. The most important feature of the
basic superenergy tensors is that they satisfy automatically the DP,
independently of the generating tensor A. In a previous paper we presented a
more compact definition of T{A} using the r-fold Clifford algebra. This form
for the superenergy tensors allowed to obtain an easy proof of the DP valid for
any dimension. In this paper we include this proof. We explain which new
elements appear when we consider the tensor T{A} generated by a
non-degree-defined r-fold multivector A and how orthogonal Lorentz
transformations and bilinear observables of spinor fields are included as
particular cases of superenergy tensors. We find some sufficient conditions for
the seed tensor A, which guarantee that the generated tensor T{A} is
divergence-free. These sufficient conditions are satisfied by some physical
fields, which are presented as examples.Comment: 19 pages, no figures. Language and minor changes. Published versio
The optimized Rayleigh-Ritz scheme for determining the quantum-mechanical spectrum
The convergence of the Rayleigh-Ritz method with nonlinear parameters
optimized through minimization of the trace of the truncated matrix is
demonstrated by a comparison with analytically known eigenstates of various
quasi-solvable systems. We show that the basis of the harmonic oscillator
eigenfunctions with optimized frequency ? enables determination of boundstate
energies of one-dimensional oscillators to an arbitrary accuracy, even in the
case of highly anharmonic multi-well potentials. The same is true in the
spherically symmetric case of V (r) = {\omega}2r2 2 + {\lambda}rk, if k > 0.
For spiked oscillators with k < -1, the basis of the pseudoharmonic oscillator
eigenfunctions with two parameters ? and {\gamma} is more suitable, and
optimization of the latter appears crucial for a precise determination of the
spectrum.Comment: 22 pages,8 figure
Classical 5D fields generated by a uniformly accelerated point source
Gauge fields associated with the manifestly covariant dynamics of particles
in spacetime are five-dimensional. In this paper we explore the old
problem of fields generated by a source undergoing hyperbolic motion in this
framework. The 5D fields are computed numerically using absolute time
-retarded Green-functions, and qualitatively compared with Maxwell fields
generated by the same motion. We find that although the zero mode of all fields
coincides with the corresponding Maxwell problem, the non-zero mode should
affect, through the Lorentz force, the observed motion of test particles.Comment: 36 pages, 8 figure
A dilemma in representing observables in quantum mechanics
There are self-adjoint operators which determine both spectral and
semispectral measures. These measures have very different commutativity and
covariance properties. This fact poses a serious question on the physical
meaning of such a self-adjoint operator and its associated operator measures.Comment: 10 page
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