5,508 research outputs found
Magnetic Schr\"odinger Operators as the Quasi-Classical Limit of Pauli-Fierz-type Models
We study the quasi-classical limit of the Pauli-Fierz model: the system is
composed of finitely many non-relativistic charged particles interacting with a
bosonic radiation field. We trace out the degrees of freedom of the field, and
consider the classical limit of the latter. We prove that the partial trace of
the full Hamiltonian converges, in resolvent sense, to an effective
Schr\"odinger operator with magnetic field and a corrective electric potential
that depends on the field configuration. Furthermore, we prove the convergence
of the ground state energy of the microscopic system to the infimum over all
possible classical field configurations of the ground state energy of the
effective Schr\"odinger operator.Comment: 26 pages, pdfLatex. Final version to appear in J. Spectr. Theor
Renormalization-group at criticality and complete analyticity of constrained models: a numerical study
We study the majority rule transformation applied to the Gibbs measure for
the 2--D Ising model at the critical point. The aim is to show that the
renormalized hamiltonian is well defined in the sense that the renormalized
measure is Gibbsian. We analyze the validity of Dobrushin-Shlosman Uniqueness
(DSU) finite-size condition for the "constrained models" corresponding to
different configurations of the "image" system. It is known that DSU implies,
in our 2--D case, complete analyticity from which, as it has been recently
shown by Haller and Kennedy, Gibbsianness follows. We introduce a Monte Carlo
algorithm to compute an upper bound to Vasserstein distance (appearing in DSU)
between finite volume Gibbs measures with different boundary conditions. We get
strong numerical evidence that indeed DSU condition is verified for a large
enough volume for all constrained models.Comment: 39 pages, teX file, 4 Postscript figures, 1 TeX figur
Renormalization Group in the uniqueness region: weak Gibbsianity and convergence
We analyze the block averaging transformation applied to lattice gas models
with short range interaction in the uniqueness region below the critical
temperature. We prove weak Gibbsianity of the renormalized measure and
convergence of the renormalized potential in a weak sense. Since we are
arbitrarily close to the coexistence region we have a diverging characteristic
length of the system: the correlation length or the critical length for
metastability, or both. Thus, to perturbatively treat the problem we have to
use a scale-adapted expansion. Moreover, such a model below the critical
temperature resembles a disordered system in presence of Griffiths'
singularity. Then the cluster expansion that we use must be graded with its
minimal scale length diverging when the coexistence line is approached
A combinatorial proof of tree decay of semi-invariants
We consider finite range Gibbs fields and provide a purely combinatorial
proof of the exponential tree decay of semi--invariants, supposing that the
logarithm of the partition function can be expressed as a sum of suitable local
functions of the boundary conditions. This hypothesis holds for completely
analytical Gibbs fields; in this context the tree decay of semi--invariants has
been proven via analyticity arguments. However the combinatorial proof given
here can be applied also to the more complicated case of disordered systems in
the so called Griffiths' phase when analyticity arguments fail
Resource-driven Substructural Defeasible Logic
Linear Logic and Defeasible Logic have been adopted to formalise different
features relevant to agents: consumption of resources, and reasoning with
exceptions. We propose a framework to combine sub-structural features,
corresponding to the consumption of resources, with defeasibility aspects, and
we discuss the design choices for the framework
A novel topology for a HEMT negative current mirror
A new solution for the implementation of a HEMT negative current source is presented. The topology can be also profitably employed as a current mirror and as an active load in high-gain MMICs voltage amplifiers. A small-signal model of the proposed circuit is developed which allows to find accurate expressions for the required transfer functions (i.e., the output impedance of the current source, and the current gain of the circuit when operated as a current mirror). Design examples using Philips PML ED02AH GaAs PHEMT process are provided. Spice simulations show that a 10- kW output impedance for the current source and a 35dB voltage gain for a differential pair loaded with the proposed current mirror are easily achieved
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