20,425 research outputs found
Beyond the Shannon-Khinchin Formulation: The Composability Axiom and the Universal Group Entropy
The notion of entropy is ubiquitous both in natural and social sciences. In
the last two decades, a considerable effort has been devoted to the study of
new entropic forms, which generalize the standard Boltzmann-Gibbs (BG) entropy
and are widely applicable in thermodynamics, quantum mechanics and information
theory. In [23], by extending previous ideas of Shannon [38], [39], Khinchin
proposed an axiomatic definition of the BG entropy, based on four requirements,
nowadays known as the Shannon-Khinchin (SK) axioms.
The purpose of this paper is twofold. First, we show that there exists an
intrinsic group-theoretical structure behind the notion of entropy. It comes
from the requirement of composability of an entropy with respect to the union
of two statistically independent subsystems, that we propose in an axiomatic
formulation. Second, we show that there exists a simple universal class of
admissible entropies. This class contains many well known examples of entropies
and infinitely many new ones, a priori multi-parametric. Due to its specific
relation with the universal formal group, the new family of entropies
introduced in this work will be called the universal-group entropy. A new
example of multi-parametric entropy is explicitly constructed.Comment: Extended version; 25 page
New Perturbation Theory for Nonstationary Anharmonic Oscillator
The new perturbation theory for the problem of nonstationary anharmonic
oscillator with polynomial nonstationary perturbation is proposed. As a zero
order approximation the exact wave function of harmonic oscillator with
variable frequency in external field is used. Based on some intrinsic
properties of unperturbed wave function the variational-iterational method is
proposed, that make it possible to correct both the amplitude and the phase of
wave function. As an application the first order correction are proposed both
for wave function and S-matrix elements for asymmetric perturbation potential
of type The transition amplitude
''ground state - ground state'' is analyzed in detail
depending on perturbation parameter (including strong coupling
region ) and one-dimensional refraction coefficient .Comment: LaTeX, 13 page
Direct measurement of optical quasidistribution functions: multimode theory and homodyne tests of Bell's inequalities
We develop a multimode theory of direct homodyne measurements of quantum
optical quasidistribution functions. We demonstrate that unbalanced homodyning
with appropriately shaped auxiliary coherent fields allows one to sample
point-by-point different phase space representations of the electromagnetic
field. Our analysis includes practical factors that are likely to affect the
outcome of a realistic experiment, such as non-unit detection efficiency,
imperfect mode matching, and dark counts. We apply the developed theory to
discuss feasibility of observing a loophole-free violation of Bell's
inequalities by measuring joint two-mode quasidistribution functions under
locality conditions by photon counting. We determine the range of parameters of
the experimental setup that enable violation of Bell's inequalities for two
states exhibiting entanglement in the Fock basis: a one-photon Fock state
divided by a 50:50 beam splitter, and a two-mode squeezed vacuum state produced
in the process of non-degenerate parametric down-conversion.Comment: 18 pages, 7 figure
Dynamical instability in kicked Bose-Einstein condensates: Bogoliubov resonances
Bose-Einstein condensates subject to short pulses (`kicks') from standing
waves of light represent a nonlinear analogue of the well-known chaos paradigm,
the quantum kicked rotor. Previous studies of the onset of dynamical
instability (ie exponential proliferation of non-condensate particles)
suggested that the transition to instability might be associated with a
transition to chaos. Here we conclude instead that instability is due to
resonant driving of Bogoliubov modes. We investigate the excitation of
Bogoliubov modes for both the quantum kicked rotor (QKR) and a variant, the
double kicked rotor (QKR-2). We present an analytical model, valid in the limit
of weak impulses which correctly gives the scaling properties of the resonances
and yields good agreement with mean-field numerics.Comment: 8 page
- …