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Engineering of Landau-Zener tunneling
No full textSeveral ways are discussed how to control the Landau-Zener tunneling in the
Wannier-Stark system. We focus on a realization of this system with interacting
and noninteracting ultracold bosons. The tunneling from the ground band to the
continuum is shown to depend crucially on the initial condition and system
parameters and, more interestingly, on added timedependent disorder -- noise --
on the lattice beams
Photoionization spectroscopy of excited states of cold cesium dimers
No full textSUMMARY Photoionization spectroscopy of cold cesium dimers obtained by
photoassociation of cold atoms in a magneto-optical trap is reported here. In
particular, we report on the observation and on the spectroscopic analysis of
all the excited states that have actually been used for efficient detection of
cold molecules stabilized in the triplet a^3Sigma_u^+ ground state. They are:
the (1)^3Sigma_g^+ state connected to the 6s+6p asymptote, the (2)^3Sigma_g^+
and (2)^3Pi_g states connected to the 6s+5d asymptote and finally the
(3)^3Sigma_g^+ state connected to the 6s + 7s asymptote. The detection through
these states spans a wide range of laser energies, from 8000 to 16500 cm-1,
obtained with different laser dyes and techniques. Information on the initial
distribution of cold molecules among the different vibrational levels of the
a^3Sigma_u^+ ground state is also provided. This spectroscopic knowledge is
important when conceiving schemes for quantum manipulation, population transfer
and optical detection of cold cesium molecules
Detecting monopoles on the lattice
No full textWe address the issue why the number and the location of magnetic monopoles
detected on lattice configurations are gauge dependent, in contrast with the
physical expectation that monopoles have a gauge invariant status. By use of
the Non-Abelian Bianchi Identities we show that monopoles are gauge invariant,
but the efficiency of the technique usually adopted to detect them depends on
the choice of the gauge in a well understood way. In particular we have studied
a class of gauges which interpolates between the Maximal Abelian gauge, where
all monopoles are observed, and the Landau gauge, where all monopoles escape
detection
Trap-size scaling in confined particle systems at quantum transitions
No full textWe develop a trap-size scaling theory for trapped particle systems at quantum
transitions. As a theoretical laboratory, we consider a quantum XY chain in an
external transverse field acting as a trap for the spinless fermions of its
quadratic Hamiltonian representation. We discuss trap-size scaling at the Mott
insulator to superfluid transition in the Bose-Hubbard model. We present exact
and accurate numerical results for the XY chain and for the low-density Mott
transition in the hard-core limit of the one-dimensional Bose-Hubbard model.
Our results are relevant for systems of cold atomic gases in optical lattices
Experiments with robust asset allocation strategies: classical versus relaxed robustness
No full textAim of this paper is to compare alternative
forms of robustness in the context of portfolio asset allocation. Starting with
the concept of convex risk measures, a new family of models, called models, is firstly proposed where not only the values of the uncertainty
parameters, but also their degree of feasibility are specified. This relaxed
form of robustness is obtained by exploiting the link between convex risk
measures and classical robustness. Then, we
test some norm-portfolio models, as well as various robust strategies from the
literature, with real market data on three different data sets. The objective
of the computational study is to compare alternative forms of relaxed
robustness - the relaxed robustness characterizing the norm portfolio models,
the so-called soft robustness and the CVaR robustness. In addition, the models
above are compared to a more classical robust model from the literature, in
order to experiment similarities and dissimilarities between robust models
based on convex risk measures and more traditional
robust approaches. To the best of our knowledge, this is the first attempt at
comparing robust strategies of different kinds in the framework of portfolio asset allocation
Self-gravitating Brownian particles in two dimensions: the case of N=2 particles
No full textSUMMARY We study the motion of N=2 overdamped Brownian particles in gravitational
interaction in a space of dimension d=2. This is equivalent to the simplified
motion of two biological entities interacting via chemotaxis when time delay
and degradation of the chemical are ignored. This problem also bears some
similarities with the stochastic motion of two point vortices in viscous
hydrodynamics [Agullo & Verga, Phys. Rev. E, 63, 056304 (2001)]. We
analytically obtain the density probability of finding the particles at a
distance r from each other at time t. We also determine the probability that
the particles have coalesced and formed a Dirac peak at time t (i.e. the
probability that the reduced particle has reached r=0 at time t). Finally, we
investigate the variance of the distribution and discuss the proper form
of the virial theorem for this system. The reduced particle has a normal
diffusion behaviour for small times with a gravity-modified diffusion
coefficient =r_0^2+(4k_B/\xi\mu)(T-T_*)t, where k_BT_{*}=Gm_1m_2/2 is a
critical temperature, and an anomalous diffusion for large times
~t^(1-T_*/T). As a by-product, our solution also describes the growth of
the Dirac peak (condensate) that forms in the post-collapse regime of the
Smoluchowski-Poisson system (or Keller-Segel model) for T<T_c=GMm/(4k_B). We
find that the saturation of the mass of the condensate to the total mass is
algebraic in an infinite domain and exponential in a bounded domain
Spectral Optimization Problems
No full textSUMMARY In this survey paper we present a class of shape optimization problems where
the cost function involves the solution of a PDE of elliptic type in the
unknown domain. In particular, we consider cost functions which depend on the
spectrum of an elliptic operator and we focus on the existence of an optimal
domain. The known results are presented as well as a list of still open
problems. Related fields as optimal partition problems, evolution flows,
Cheeger-type problems, are also considered
Comment on "Influence of Noise on Force Measurement" [arXiv:1004.0874]
No full textSUMMARY In a recent Letter [arXiv:1004.0874], Volpe et al. describe experiments on a
colloidal particle near a wall in the presence of a gravitational field for
which they study the influence of noise on the measurement of force. Their
central result is a striking discrepancy between the forces derived from
experimental drift measurements via their Eq. (1), and from the equilibrium
distribution. From this discrepancy they infer the stochastic calculus realised
in the system.
We comment, however: (a) that Eq. (1) does not hold for space-dependent
diffusion, and corrections should be introduced; and (b) that the "force"
derived from the drift need not coincide with the "force" obtained from the
equilibrium distribution
On the analytic continuation of the critical line
No full textSUMMARY We perform a numerical study of the systematic effects involved in the
determination of the critical line at real baryon chemical potential by
analytic continuation from results obtained at imaginary chemical potentials.
We present results obtained in a theory free of the sign problem, three-color
QCD with finite isospin chemical potential, and comment on general features
which could be relevant also to the continuation of the critical line in real
QCD at finite baryon density
Low-energy U(1) x USp(2M) gauge theory from simple high-energy gauge group
No full textWe give an explicit example of the embedding of a near BPS low-energy (U(1) x
USp(2M))/Z_2 gauge theory into a high-energy theory with a simple gauge group
and adjoint matter content. This system possesses degenerate monopoles arising
from the high-energy symmetry breaking as well as non-Abelian vortices due to
the symmetry breaking at low energies. These solitons of different codimensions
are related by the exact homotopy sequences