283,015 research outputs found
Fractal von Neumann entropy
We consider the {\it fractal von Neumann entropy} associated with the {\it
fractal distribution function} and we obtain for some {\it universal classes h
of fractons} their entropies. We obtain also for each of these classes a {\it
fractal-deformed Heisenberg algebra}. This one takes into account the braid
group structure of these objects which live in two-dimensional multiply
connected space.Comment: latex, 9 pages, typos correcte
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
The Schnitzel Squad
Postcard from Cruz Morey, during the Linfield College Semester Abroad Program at the Austro-American Institute of Education in Vienna, Austri
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