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Noise assisted transport in the Wannier-Stark system
No full textSUMMARY We investigated how the presence of an additional lattice potential, driven
by a harmonic noise process, changes the transition rate from the ground band
to the first excited band in a Wannier-Stark system. Alongside numerical
simulations, we present two models that capture the essential features of the
dynamics. The first model uses a noise-driven Landau-Zener approximation and
describes the short time evolution of the full system very well. The second
model assumes that the noise process' correlation time is much larger than the
internal timescale of the system, yet it allows for good estimates of the
observed transition rates and gives a simple interpretation of the dynamics.
One of the central results is that we obtain a way to control the interband
transitions with the help of the second lattice. This could readily be realized
in state-of-the-art experiments using either Bose-Einstein condensates or
optical pulses in engineered potentials
Cohomologies of deformations of solvmanifolds and closedness of some properties
No full textWe provide further techniques to study the Dolbeault and Bott-Chern
cohomologies of deformations of solvmanifolds by means of finite-dimensional
complexes. By these techniques, we can compute the Dolbeault and Bott-Chern
cohomologies of some complex solvmanifolds, and we also get explicit examples,
showing in particular that either the -Lemma or the
property that the Hodge and Fr\"olicher spectral sequence degenerates at the
first level are not closed under deformations
Learning from Polyhedral Sets
No full textParameterized linear systems allow for modelling
and reasoning over classes of polyhedra. Collections
of squares, rectangles, polytopes, and so on,
can readily be defined by means of linear systems
with parameters. In this paper, we investigate the
problem of learning a parameterized linear system
whose class of polyhedra includes a given set of example
polyhedral sets and it is minimal
Approximated Perspective Relaxations: a Project&Lift Approach
No full textThe Perspective Reformulation (PR) of a Mixed-Integer NonLinear Program with semi-continuous variables is obtained by replacing each term in the (separable) objective function with its convex envelope. Solving the corresponding Perspective Relaxation requires appropriate techniques. Under some rather restrictive assumptions, the Projected PR can be defined where the integer variables are eliminated by projecting the solution set on the space of the continuous variables only. This approach produces a simple piecewise-convex problem with the same structure as the original one; however, this prevents the use of general-purpose solvers, in that some variables are then only implicitly represented in the formulation. We show how to construct an Approximated Projected PR whereby the projected formulation is "lifted" back to the original variable space, with the integer variables expressing one piece of the obtained piecewise-convex function; in some cases, this produces a reformulation of the original problem with exactly the same size and structure as the standard continuous relaxation but with a substantially improved bound. While the bound can be weaker than that of the PR, this approach can be applied in many more cases and allows direct use of off-the-shelf MIQP software; this is shown to be beneficial in different applications. In the process we also relax some of the other restrictive assumptions of the original development, such as the need for the objective function to be quadratic and the need for the left endpoint of the domain of the variables to be non-negative
A Compact Variant of the QCR Method for 0-1 Quadratically Constrained Quadratic Programs
No full textQuadratic Convex Reformulation (QCR) is a technique that was originally proposed for 0-1 quadratic programs, and then extended to various other problems. It is used to convert non-convex instances into convex ones, in such a way that the bound obtained by solving the continuous relaxation of the reformulated instance is as strong as possible.In this paper, we focus on the case of 0-1 quadratically constrained quadratic programs. The variant of QCR previously proposed for this case involves the addition of a quadratic number of auxiliary continuous variables. We show that, in fact, at most one additional variable is needed. Some computational results are also presented
Towards a Methodology for Parallel Data Stream Processing: application to Parallel Stream Join
No full textThis paper deals with high-performance Parallel Data Stream Processing methodologies and implementation techniques. Data Stream Processing (DaSP) is referred to in the most general and interesting sense: on-line (often real-time) applications working on multiple, nondeterministic streams, with unlimited or unknown length and highly variable arrival rate, whose elements must processed efficiently “on the fly”. Traditional high-performance solutions are not sufficient to meet the critical requirements of high throughput and low latency with acceptable memory size: typical DaSP applications require quite novel parallelism models, as well as related design and implementation techniques on the emerging highly parallel architectures. The aim of this paper is to give an original contribution to the design and implementation of parallel DaSP applications. The contribution is twofold: (1) the definition of an approach to a new general model for data-parallel DaSP computations according to a paradigm called Data Stream Parallelism, (2) the application of this approach to the parallel Stream Join problem, showing that the most interesting parallelizations in the literature are particular cases of our approach and that, compared to them, better throughput and latency are achieved by our implementation on multicore architectures
Symplectic Bott-Chern cohomology of solvmanifolds
No full textWe study the symplectic Bott-Chern cohomology by L.-S. Tseng and S.-T. Yau
for solvmanifolds endowed with left-invariant symplectic structures
On the phase diagram of Yang-Mills theories in the presence of a theta therm
No full textWe study the phase diagram of non-Abelian pure gauge theories in the presence
of a topological theta term. The dependence of the deconfinement temperature on
theta is determined on the lattice both by analytic continuation and by
reweighting, obtaining consistent results. The general structure of the diagram
is discussed on the basis of large-N considerations and of the possible
analogies and dualities existing with the phase diagram of QCD in presence of
an imaginary baryon chemical potential
Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
No full textWe investigate the general features of the renormalization-group flow at the
Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough
quantitative description of the asymptotc critical behavior, including the
multiplicative and subleading logarithmic corrections. For this purpose, we
consider the RG flow of the sine-Gordon model around the renormalizable point
which describes the BKT transition. We reduce the corresponding beta-functions
to a universal canonical form, valid to all perturbative orders. Then, we
determine the asymptotic solutions of the RG equations in various critical
regimes: the infinite-volume critical behavior in the disordered phase, the
finite-size scaling limit for homogeneous systems of finite size, and the
trap-size scaling limit occurring in 2D bosonic particle systems trapped by an
external space-dependent potential
Relevance of the axial anomaly at the finite-temperature chiral transition in QCD
No full textWe investigate the nature of the finite-temperature chiral transition in QCD
with two light flavors, in the case of an effective suppression of the the
U(1)_A symmetry breaking induced by the axial anomaly, which implies the
symmetry breaking U(2)_L X U(2)_R -> U(2)_V, instead of SU(2)_L X SU(2)_R ->
SU(2)_V. For this purpose, we perform a high-order field-theoretical
perturbative study of the renormalization-group (RG) flow of the corresponding
three-dimensional multiparameter Landau-Ginzburg-Wilson Phi4 theory with the
same symmetry-breaking pattern. We confirm the existence of a stable fixed
point (FP), and determine its attraction domain in the space of the bare
quartic parameters. Therefore, the chiral QCD transition might be continuous
also if the U(1)_A symmetry is effectively restored at Tc. However, the
corresponding universality class differs from the O(4) vector universality
class which would describe a continuous transition in the presence of a
substantial U(1)_A symmetry breaking at Tc. We estimate the critical exponents
of the U(2)_L X U(2)_R -> U(2)_V universality class by computing and analyzing
their high-order perturbative expansions. These results are important to
discriminate among the different scenarios for the scaling behavior of QCD with
two light flavors close to the chiral transition