10,206 research outputs found
Quantization of classical integrable systems. Part IV: systems of resonant oscillators
By applying methods already discussed in a previous series of papers by the
same authors, we construct here classes of integrable quantum systems which
correspond to n fully resonant oscillators with nonlinear couplings. The same
methods are also applied to a series of nontrivial integral sets of functions,
which can be constructed when additional symmetries are present due to the
equality of some of the frequencies. Besides, for n=3 and resonance 1:1:2, an
exceptional integrable system is obtained, in which integrability is not
explicitly connected with this type of symmetry. In this exceptional case,
quantum integrability can be realized by means of a modification of the
symmetrization procedure.Comment: 23 page
Modern mechanisms make manless Martian mission mobile: Spin-off spells stairclimbing self-sufficiency for earthbound handicapped
Concepts were developed for three wheel chairs from progressively improving designs of a proposed unmanned roving vehicle for the surface exploration of Mars; as a spin-off, a concept for a stair-climbing wheel chair was generated. The mechanisms employed in these are described. The Mars mission is envisioned using the booster rockets and aeroshell of the Viking missions
Phase transitions and edge scaling of number variance in Gaussian random matrices
We consider Gaussian random matrices, whose average density of
eigenvalues has the Wigner semi-circle form over . For
such matrices, using a Coulomb gas technique, we compute the large behavior
of the probability that
eigenvalues lie within the box . This probability scales as
, where is the Dyson index of the ensemble
and is a -independent rate function that we compute
exactly. We identify three regimes as is varied: (i) (bulk), (ii) on a scale of
(edge) and (iii) (tail). We find a
dramatic non-monotonic behavior of the number variance as a function
of : after a logarithmic growth in the bulk (when ), decreases abruptly as approaches the edge of
the semi-circle before it decays as a stretched exponential for .
This "drop-off" of at the edge is described by a scaling function
which smoothly interpolates between the bulk (i) and the
tail (iii). For we compute explicitly in terms of the
Airy kernel. These analytical results, verified by numerical simulations,
directly provide for the full statistics of particle-number
fluctuations at zero temperature of 1d spinless fermions in a harmonic trap.Comment: 5 pag., 3 fig, published versio
Acoustic black holes in a two-dimensional "photon-fluid"
Optical field fluctuations in self-defocusing media can be described in terms
of sound waves in a 2D photon-fluid. It is shown that, while the background
fluid couples with the usual flat metric, sound-like waves experience an
effective curved spacetime determined by the physical properties of the flow.
In an optical cavity configuration, the background spacetime can be suitably
controlled by the driving beam allowing the formation of acoustic ergoregions
and event horizons. An experiment simulating the main features of the rotating
black hole geometry is proposed.Comment: revised versio
Quantized Skyrmion Fields in 2+1 Dimensions
A fully quantized field theory is developped for the skyrmion topological
excitations of the O(3) symmetric CP-Nonlinear Sigma Model in 2+1D. The
method allows for the obtainment of arbitrary correlation functions of quantum
skyrmion fields. The two-point function is evaluated in three different
situations: a) the pure theory; b) the case when it is coupled to fermions
which are otherwise non-interacting and c) the case when an electromagnetic
interaction among the fermions is introduced. The quantum skyrmion mass is
explicitly obtained in each case from the large distance behavior of the
two-point function and the skyrmion statistics is inferred from an analysis of
the phase of this function. The ratio between the quantum and classical
skyrmion masses is obtained, confirming the tendency, observed in semiclassical
calculations, that quantum effects will decrease the skyrmion mass. A brief
discussion of asymptotic skyrmion states, based on the short distance behavior
of the two-point function, is also presented.Comment: Accepted for Physical Review
Inverter-converter automatic paralleling and protection
Electric control and protection circuits for parallel operation of inverter-converte
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