23 research outputs found
Sub-Poissonian statistics in order-to-chaos transition
We study the phenomena at the overlap of quantum chaos and nonclassical
statistics for the time-dependent model of nonlinear oscillator. It is shown in
the framework of Mandel Q-parameter and Wigner function that the statistics of
oscillatory excitation number is drastically changed in order-to chaos
transition. The essential improvement of sub-Poissonian statistics in
comparison with an analogous one for the standard model of driven anharmonic
oscillator is observed for the regular operational regime. It is shown that in
the chaotic regime the system exhibits the range of sub- and super-Poissonian
statistics which alternate one to other depending on time intervals. Unusual
dependence of the variance of oscillatory number on the external noise level
for the chaotic dynamics is observed.Comment: 9 pages, RevTeX, 14 figure
Self-induced and induced transparencies of two-dimensional and three- dimensional superlattices
The phenomenon of transparency in two-dimensional and three-dimensional
superlattices is analyzed on the basis of the Boltzmann equation with a
collision term encompassing three distinct scattering mechanisms (elastic,
inelastic and electron-electron) in terms of three corresponding distinct
relaxation times. On this basis, we show that electron heating in the plane
perpendicular to the current direction drastically changes the conditions for
the occurrence of self-induced transparency in the superlattice. In particular,
it leads to an additional modulation of the current amplitudes excited by an
applied biharmonic electric field with harmonic components polarized in
orthogonal directions. Furthermore, we show that self-induced transparency and
dynamic localization are different phenomena with different physical origins,
displaced in time from each other, and, in general, they arise at different
electric fields.Comment: to appear in Physical Review
Soliton ratchets induced by ac forces with harmonic mixing
The ratchet dynamics of a kink (topological soliton) of a dissipative
sine-Gordon equation in the presence of ac forces with harmonic mixing (at
least bi-harmonic) of zero mean is studied. The dependence of the kink mean
velocity on system parameters is investigated numerically and the results are
compared with a perturbation analysis based on a point particle representation
of the soliton. We find that first order perturbative calculations lead to
incomplete descriptions, due to the important role played by the soliton-phonon
interaction in establishing the phenomenon. The role played by the temporal
symmetry of the system in establishing soliton ratchets is also emphasized. In
particular, we show the existence of an asymmetric internal mode on the kink
profile which couples to the kink translational mode through the damping in the
system. Effective soliton transport is achieved when the internal mode and the
external force get phase locked. We find that for kinks driven by bi-harmonic
drivers consisting of the superposition of a fundamental driver with its first
odd harmonic, the transport arises only due to this {\it internal mode}
mechanism, while for bi-harmonic drivers with even harmonic superposition, also
a point-particle contribution to the drift velocity is present. The phenomenon
is robust enough to survive the presence of thermal noise in the system and can
lead to several interesting physical applications.Comment: 9 pages, 13 figure
Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
Fuzzy spheres appear as classical solutions in a matrix model obtained via
dimensional reduction of 3-dimensional Yang-Mills theory with the Chern-Simons
term. Well-defined perturbative expansion around these solutions can be
formulated even for finite matrix size, and in the case of coincident fuzzy
spheres it gives rise to a regularized U() gauge theory on a noncommutative
geometry. Here we study the matrix model nonperturbatively by Monte Carlo
simulation. The system undergoes a first order phase transition as we change
the coefficient () of the Chern-Simons term. In the small
phase, the large properties of the system are qualitatively the same as in
the pure Yang-Mills model (), whereas in the large phase a
single fuzzy sphere emerges dynamically. Various `multi fuzzy spheres' are
observed as meta-stable states, and we argue in particular that the
coincident fuzzy spheres cannot be realized as the true vacuum in this model
even in the large limit. We also perform one-loop calculations of various
observables for arbitrary including . Comparison with our Monte Carlo
data suggests that higher order corrections are suppressed in the large
limit.Comment: Latex 37 pages, 13 figures, discussion on instabilities refined,
references added, typo corrected, the final version to appear in JHE
Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
We address a detailed non-perturbative numerical study of the scalar theory
on the fuzzy sphere. We use a novel algorithm which strongly reduces the
correlation problems in the matrix update process, and allows the investigation
of different regimes of the model in a precise and reliable way. We study the
modes associated to different momenta and the role they play in the ``striped
phase'', pointing out a consistent interpretation which is corroborated by our
data, and which sheds further light on the results obtained in some previous
works. Next, we test a quantitative, non-trivial theoretical prediction for
this model, which has been formulated in the literature: The existence of an
eigenvalue sector characterised by a precise probability density, and the
emergence of the phase transition associated with the opening of a gap around
the origin in the eigenvalue distribution. The theoretical predictions are
confirmed by our numerical results. Finally, we propose a possible method to
detect numerically the non-commutative anomaly predicted in a one-loop
perturbative analysis of the model, which is expected to induce a distortion of
the dispersion relation on the fuzzy sphere.Comment: 1+36 pages, 18 figures; v2: 1+55 pages, 38 figures: added the study
of the eigenvalue distribution, added figures, tables and references, typos
corrected; v3: 1+20 pages, 10 eps figures, new results, plots and references
added, technical details about the tests at small matrix size skipped,
version published in JHE