7,858 research outputs found
Non-hermitian approach to decaying ultracold bosonic systems
A paradigm model of modern atom optics is studied, strongly interacting
ultracold bosons in an optical lattice. This many-body system can be
artificially opened in a controlled manner by modern experimental techniques.
We present results based on a non-hermitian effective Hamiltonian whose quantum
spectrum is analyzed. The direct access to the spectrum of the metastable
many-body system allows us to easily identify relatively stable quantum states,
corresponding to previously predicted solitonic many-body structures
Inflation Dynamicsâ Micro Foundations: How Important is Imperfect Competition Really?
This paper analyzes price formation and dynamics according to the industry structure. It divides manufacturing industries of Mexico into two groups: perfectly and imperfectly competitive. The results show that imperfectly competitive industries predominate. Then this classification is used to build consumer price sub indexes for the goods of both sectors. These sub indexesâ inflation dynamics indicate that the exchange rate pass-through in the perfectly competitive sector is significantly higher than in the imperfectly competitive sector, while wage pass-through only affects the imperfectly competitive sector. Also, that inflation inertia is lower in the former than in the latter; adding up in more volatility of the perfectly competitive inflation rate. For policy makers an interesting feature of the perfectly competitive price index is that the evidence suggests that its variations precede those of the imperfectly competitive price index. For economic theorists these features validate recent macroeconomic models with heterogeneous price setting behaviorPanzar-Rosse, Industry Structure, Inflation, Price Dynamics, Price Indexes
Exact numerical methods for a many-body Wannier Stark system
We present exact methods for the numerical integration of the Wannier-Stark
system in a many-body scenario including two Bloch bands. Our ab initio
approaches allow for the treatment of a few-body problem with bosonic
statistics and strong interparticle interaction. The numerical implementation
is based on the Lanczos algorithm for the diagonalization of large, but sparse
symmetric Floquet matrices. We analyze the scheme efficiency in terms of the
computational time, which is shown to scale polynomially with the size of the
system. The numerically computed eigensystem is applied to the analysis of the
Floquet Hamiltonian describing our problem. We show that this allows, for
instance, for the efficient detection and characterization of avoided crossings
and their statistical analysis. We finally compare the efficiency of our
Lanczos diagonalization for computing the temporal evolution of our many-body
system with an explicit fourth order Runge-Kutta integration. Both
implementations heavily exploit efficient matrix-vector multiplication schemes.
Our results should permit an extrapolation of the applicability of exact
methods to increasing sizes of generic many-body quantum problems with bosonic
statistics
Supercritical super-Brownian motion with a general branching mechanism and travelling waves
We consider the classical problem of existence, uniqueness and asymptotics of
monotone solutions to the travelling wave equation associated to the parabolic
semi-group equation of a super-Brownian motion with a general branching
mechanism. Whilst we are strongly guided by the probabilistic reasoning of
Kyprianou (2004) for branching Brownian motion, the current paper offers a
number of new insights. Our analysis incorporates the role of Seneta-Heyde
norming which, in the current setting, draws on classical work of Grey (1974).
We give a pathwise explanation of Evans' immortal particle picture (the spine
decomposition) which uses the Dynkin-Kuznetsov N-measure as a key ingredient.
Moreover, in the spirit of Neveu's stopping lines we make repeated use of
Dynkin's exit measures. Additional complications arise from the general nature
of the branching mechanism. As a consequence of the analysis we also offer an
exact X(log X)^2 moment dichotomy for the almost sure convergence of the
so-called derivative martingale at its critical parameter to a non-trivial
limit. This differs to the case of branching Brownian motion and branching
random walk where a moment `gap' appears in the necessary and sufficient
conditions.Comment: 34 page
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