11,818 research outputs found
On the parametric dependences of a class of non-linear singular maps
We discuss a two-parameter family of maps that generalize piecewise linear,
expanding maps of the circle. One parameter measures the effect of a
non-linearity which bends the branches of the linear map. The second parameter
rotates points by a fixed angle. For small values of the nonlinearity
parameter, we compute the invariant measure and show that it has a singular
density to first order in the nonlinearity parameter. Its Fourier modes have
forms similar to the Weierstrass function. We discuss the consequences of this
singularity on the Lyapunov exponents and on the transport properties of the
corresponding multibaker map. For larger non-linearities, the map becomes
non-hyperbolic and exhibits a series of period-adding bifurcations.Comment: 17 pages, 13 figures, to appear in Discrete and Continuous Dynamical
Systems, series B Higher resolution versions of Figures 5 downloadable at
http://www.glue.umd.edu/~jrd
Multidimensional spectroscopy with entangled light; loop vs ladder delay scanning protocols
Multidimensional optical signals are commonly recorded by varying the delays
between time ordered pulses. These control the evolution of the density matrix
and are described by ladder diagrams. We propose a new non-time-ordered
protocol based on following the time evolution of the wavefunction and
described by loop diagrams. The time variables in this protocol allow to
observe different types of resonances and reveal information about intraband
dephasing not readily available by time ordered techniques. The time variables
involved in this protocol become coupled when using entangled light, which
provides high selectivity and background free measurement of the various
resonances. Entangled light can resolve certain states even when strong
background due to fast dephasing suppresses the resonant features when probed
by classical light
Chaotic Scattering Theory of Transport and Reaction-Rate Coefficients
The chaotic scattering theory is here extended to obtain escape-rate
expressions for the transport coefficients appropriate for a simple classical
fluid, or for a chemically reacting system. This theory allows various
transport coefficients such as the coefficients of viscosity, thermal
conductivity, etc., to be expressed in terms of the positive Lyapunov exponents
and Kolmogorov-Sinai entropy of a set of phase space trajectories that take
place on an appropriate fractal repeller. This work generalizes the previous
results of Gaspard and Nicolis for the coefficient of diffusion of a particle
moving in a fixed array of scatterers.Comment: 27 pages LaTeX, no figure
Nonlinear fluctuations and dissipation in matter revealed by quantum light
Quantum optical fields offer numerous control knobs which are not available
with classical light and may be used for monitoring the properties of matter by
novel types of spectroscopy. It has been recently argued that such quantum
spectroscopy signals can be obtained by a simple averaging of their classical
spectroscopy counterparts over the Glauber-Sudarshan quasiprobability
distribution of the quantum field; the quantum light thus merely provides a
novel gating window for the classical response functions. We show that this
argument only applies to the linear response and breaks down in the nonlinear
regime. The quantum response carries additional valuable information about
response and spontaneous fluctuations of matter that may not be retrieved from
the classical response by simple data processing. This is connected to the lack
of a nonlinear fluctuation-dissipation relation
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