27,442 research outputs found
Exactly solvable one-qubit driving fields generated via non-linear equations
Using the Hubbard representation for we write the time-evolution
operator of a two-level system in the disentangled form. This allows us to map
the corresponding dynamical law into a set of non-linear coupled equations. In
order to find exact solutions, we use an inverse approach and find families of
time-dependent Hamiltonians whose off-diagonal elements are connected with the
Ermakov equation. The physical meaning of the so-obtained Hamiltonians is
discussed in the context of the nuclear magnetic resonance phenomeno
Leaky modes of waveguides as a classical optics analogy of quantum resonances
A classical optics waveguide structure is proposed to simulate resonances of
short range one-dimensional potentials in quantum mechanics. The analogy is
based on the well known resemblance between the guided and radiation modes of a
waveguide with the bound and scattering states of a quantum well. As resonances
are scattering states that spend some time in the zone of influence of the
scatterer, we associate them with the leaky modes of a waveguide, the latter
characterized by suffering attenuation in the direction of propagation but
increasing exponentially in the transverse directions. The resemblance is
complete since resonances (leaky modes) can be interpreted as bound states
(guided modes) with definite lifetime (longitudinal shift). As an immediate
application we calculate the leaky modes (resonances) associated with a
dielectric homogeneous slab (square well potential) and show that these modes
are attenuated as they propagate.Comment: The title has been modified to describe better the contents of the
article. Some paragraphs have been added to clarify the result
Superpositions of bright and dark solitons supporting the creation of balanced gain and loss optical potentials
Bright and dark solitons of the cubic nonlinear Schrodinger equation are used
to construct complex-valued potentials with all-real spectrum. The real part of
these potentials is equal to the intensity of a bright soliton while their
imaginary part is defined by the product of such soliton with its concomitant,
a dark soliton. Considering light propagation in Kerr media, the real part of
the potential refers to the self-focusing of the signal and the imaginary one
provides the system with balanced gain-and-loss rates.Comment: 6 figures, 17 pages, LaTeX file. The manuscript has been re-organized
(abstract, introduction and conclusions rewritten), and it now includes an
appendix with detailed calculations of some relevant results reported in the
paper. New references were adde
Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass
We analyze the dynamical equations obeyed by a classical system with
position-dependent mass. It is shown that there is a non-conservative force
quadratic in the velocity associated to the variable mass. We construct the
Lagrangian and the Hamiltonian for this system and find the modifications
required in the Euler-Lagrange and Hamilton's equations to reproduce the
appropriate Newton's dynamical law. Since the Hamiltonian is not time
invariant, we get a constant of motion suited to write the dynamical equations
in the form of the Hamilton's ones. The time-dependent first integrals of
motion are then obtained from the factorization of such a constant. A canonical
transformation is found to map the variable mass equations to those of a
constant mass. As particular cases, we recover some recent results for which
the dependence of the mass on the position was already unnoticed, and find new
solvable potentials of the P\"oschl-Teller form which seem to be new. The
latter are associated to either the su(1,1) or the su(2) Lie algebras depending
on the sign of the Hamiltonian
Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras
The purposes of this work are (1) to show that the appropriate
generalizations of the oscillator algebra permit the construction of a wide set
of nonlinear coherent states in unified form; and (2) to clarify the likely
contradiction between the nonclassical properties of such nonlinear coherent
states and the possibility of finding a classical analog for them since they
are P-represented by a delta function. In (1) we prove that a class of
nonlinear coherent states can be constructed to satisfy a closure relation that
is expressed uniquely in terms of the Meijer G-function. This property
automatically defines the delta distribution as the P-representation of such
states. Then, in principle, there must be a classical analog for them. Among
other examples, we construct a family of nonlinear coherent states for a
representation of the su(1,1) Lie algebra that is realized as a deformation of
the oscillator algebra. In (2), we use a beam splitter to show that the
nonlinear coherent states exhibit properties like anti-bunching that prohibit a
classical description for them. We also show that these states lack second
order coherence. That is, although the P-representation of the nonlinear
coherent states is a delta function, they are not full coherent. Therefore, the
systems associated with the generalized oscillator algebras cannot be
considered `classical' in the context of the quantum theory of optical
coherence.Comment: 26 pages, 10 figures, minor changes, misprints correcte
Spherical harmonic expansions of the Earth's gravitational potential to degree 360 using 30' mean anomalies
Two potential coefficient fields that are complete to degree and order 360 have been computed. One field (OSU86E) excludes geophysically predicted anomalies while the other (OSU86F) includes such anomalies. These fields were computed using a set of 30' mean gravity anomalies derived from satellite altimetry in the ocean areas and from land measurements in North America, Europe, Australia, Japan and a few other areas. Where no 30' data existed, 1 deg x 1 deg mean anomaly estimates were used if available. No rigorous combination of satellite and terrestrial data was carried out. Instead advantage was taken of the adjusted anomalies and potential coefficients from a rigorous combination of the GEML2' potential coefficient set and 1 deg x 1 deg mean gravity anomalies. The two new fields were computed using a quadrature procedure with de-smoothing factors. The spectra of the new fields agree well with the spectra of the fields with 1 deg x 1 deg data out to degree 180. Above degree 180 the new fields have more power. The fields have been tested through comparison of Doppler station geoid undulations with undulations from various geopotential models. The agreement between the two types of undulations is approximately + or - 1.6 m. The use of a 360 field over a 180 field does not significantly improve the comparison. Instead it allows the comparison to be done at some stations where high frequency effects are important. In addition maps made in areas of high frequency information (such as trench areas) clearly reveal the signal in the new fields from degree 181 to 360
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