614 research outputs found
Wigner function and Schroedinger equation in phase space representation
We discuss a family of quasi-distributions (s-ordered Wigner functions of
Agarwal and Wolf) and its connection to the so called phase space
representation of the Schroedinger equation. It turns out that although Wigner
functions satisfy the Schroedinger equation in phase space they have completely
different interpretation.Comment: 6 page
Quantum versus classical phase-locking transition in a driven-chirped oscillator
Classical and quantum-mechanical phase locking transition in a nonlinear
oscillator driven by a chirped frequency perturbation is discussed. Different
limits are analyzed in terms of the dimensionless parameters and
( and being the driving amplitude,
the frequency chirp rate, the nonlinearity parameter and the linear frequency
of the oscillator). It is shown that for , the passage
through the linear resonance for above a threshold yields classical
autoresonance (AR) in the system, even when starting in a quantum ground state.
In contrast, for , the transition involves
quantum-mechanical energy ladder climbing (LC). The threshold for the
phase-locking transition and its width in in both AR and LC limits are
calculated. The theoretical results are tested by solving the Schrodinger
equation in the energy basis and illustrated via the Wigner function in phase
space
Optical second harmonic generation near a black hole horizon as possible source of experimental information on quantum gravitational effects
Optical second harmonic generation near a black hole horizon is suggested as
a source of experimental information on quantum gravitational effects. While
absent in the framework of general relativity, second harmonic generation
appears in the toy models of sonic and electromagnetic black holes, where
spatial dispersion at high frequencies for waves boosted towards the horizon is
introduced. Localization effects in the light scattering from random
fluctuations of matter fields and space-time metric near the black hole horizon
produce a pronounced peak in the angular distribution of second harmonics of
light in the direction normal to the horizon. Such second harmonic light has
the best chances to escape the vicinity of the black hole. This phenomenon is
similar to the well-known strong enhancement of diffuse second harmonic
emission from a randomly rough metal surface in the direction normal to the
surface.Comment: 4 pages, 1 figur
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