2,285 research outputs found
Lamb shift of non-degenerate energy level systems placed between two infinite parallel conducting plates
The issue of the observability of the Lamb shift in systems with
non-degenerate energy levels is put to question. To this end, we compute the
Lamb shift of such systems in the electromagnetic environment provided by two
infinite parallel conducting plates, which is instrumental in demonstrating the
existence of the so-called Casimir effect. A formula giving the relative change
in the Lamb shift (as compared to the standard one in vacuum) is explicitly
obtained for spherical semiconductor Quantum Dots (QD). It is the result of a
careful mathematical treatment of divergences in the calculations involving
distribution theory, which also settles a controversy on two different
expressions in the existing literature. It suggests a possibility of QD
non-degenerate energy spectrum fine-tuning for experimental purposes as well as
a Gedankenexperiment to observe the Lamb shift in spherical semiconductor
quantum dots.Comment: submit/040994
The Lord Edward and the County of Chester: Lordship andcommunity, 1254-1272.
This thesis analyses the Lord Edward’s lordship of the county of Chester between 1254 and 1272 and the impact it had on local inhabitants.
The first chapter investigates the general administration of the county, including its financial structure, and the officials and men recruited by Edward to control his Cheshire estates. This chapter shows that Edward, in spite of his father’s influence, led an independent policy by relying primarily on the justiciar and on local tenants to govern the county.
The second chapter tackles the organisation of justice and the law administered in Cheshire. It demonstrates that the judicial machinery in Cheshire was preserved during Edward’s lordship with its distinctive characteristics inherited from the earls of Chester, and that Edward was far more involved in the administration of justice in the county, and in the rest of his apanage, than previously envisaged.
The third chapter considers the relationship Cheshire maintained with Wales in the thirteenth century, and more precisely, how Edward’s lordship of the county disrupted the stability that existed in the area. It shows that he was not directly responsible for the tensions that existed, but that his inability to address them eventually led to the outbreak of 1256. It also demonstrates that Edward failed to protect his estates despite multiple attempts, and how he progressively lost interest in his Welsh dominions.
The fourth chapter discusses Edward’s relationship, and the difficulties he had, with his Cheshire tenants, especially during the baronial movement of reform and rebellion (1258-67). It analyses how problems in the county mirrored those elsewhere in the realm, because of the financial pressure and of the desire of local communities to have their laws and customs preserved, and how Edward’s considered approach and political discernment were eventually successful in restoring order in the county
Quantum properties of spherical semiconductor quantum dots
Quantum effects at the nanometric level have been observed in many confined
structures, and particularly in semiconductor quantum dots (QDs). In this work,
we propose a theoretical improvement of the so-called effective mass
approximation with the introduction of an effective pseudo-potential. This
advantageously allows analytic calculations to a large extent, and leads to a
better agreement with experimental data. We have obtained, as a function of the
QD radius, in precise domains of validity, the QD ground state energy, its
Stark and Lamb shifts. An observable Lamb shift is notably predicted for
judiciously chosen semiconductor and radius. Despite the intrinsic
non-degeneracy of the QD energy spectrum, we propose a Gedankenexperiment based
on the use of the Casimir effect to test its observability. Finally, the effect
of an electromagnetic cavity on semiconductor QDs is also considered, and its
Purcell factor evaluated. This last result raises the possibility of having a
QD-LASER emitting in the range of visible light
Classification of Non-Affine Non-Hecke Dynamical R-Matrices
A complete classification of non-affine dynamical quantum -matrices
obeying the -Gervais-Neveu-Felder equation is
obtained without assuming either Hecke or weak Hecke conditions. More general
dynamical dependences are observed. It is shown that any solution is built upon
elementary blocks, which individually satisfy the weak Hecke condition. Each
solution is in particular characterized by an arbitrary partition of the set of indices into classes,
being the class of the index , and an arbitrary family of
signs
on this partition. The weak Hecke-type -matrices exhibit the analytical
behaviour , where is a
particular trigonometric or rational function, , and
denotes the family of dynamical coordinates
Principal bundle structure of matrix manifolds
In this paper, we introduce a new geometric description of the manifolds of
matrices of fixed rank. The starting point is a geometric description of the
Grassmann manifold of linear subspaces of
dimension in which avoids the use of equivalence classes.
The set is equipped with an atlas which provides
it with the structure of an analytic manifold modelled on
. Then we define an atlas for the set
of full rank matrices and prove that
the resulting manifold is an analytic principal bundle with base
and typical fibre , the general
linear group of invertible matrices in . Finally, we
define an atlas for the set of
non-full rank matrices and prove that the resulting manifold is an analytic
principal bundle with base and typical fibre . The atlas of
is indexed on the manifold itself,
which allows a natural definition of a neighbourhood for a given matrix, this
neighbourhood being proved to possess the structure of a Lie group. Moreover,
the set equipped with the topology
induced by the atlas is proven to be an embedded submanifold of the matrix
space equipped with the subspace topology. The
proposed geometric description then results in a description of the matrix
space , seen as the union of manifolds
, as an analytic manifold equipped with
a topology for which the matrix rank is a continuous map
New Theoretical Approach to Quantum Size Effects of Interactive Electron-hole in Spherical Semiconductor Quantum Dots
The issue of quantum size effects of interactive electron-hole systems in
spherical semiconductor quantum dots is put to question. A sharper theoretical
approach is suggested based on a new pseudo-potential method. In this new
setting, analytical computations can be performed in most intermediate steps
lending stronger support to the adopted physical assumptions. The resulting
numerical values for physical quantities are found to be much closer to the
experimental values than those existing so far in the literature
A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems
In this paper, we propose a method for the approximation of the solution of
high-dimensional weakly coercive problems formulated in tensor spaces using
low-rank approximation formats. The method can be seen as a perturbation of a
minimal residual method with residual norm corresponding to the error in a
specified solution norm. We introduce and analyze an iterative algorithm that
is able to provide a controlled approximation of the optimal approximation of
the solution in a given low-rank subset, without any a priori information on
this solution. We also introduce a weak greedy algorithm which uses this
perturbed minimal residual method for the computation of successive greedy
corrections in small tensor subsets. We prove its convergence under some
conditions on the parameters of the algorithm. The residual norm can be
designed such that the resulting low-rank approximations are quasi-optimal with
respect to particular norms of interest, thus yielding to goal-oriented order
reduction strategies for the approximation of high-dimensional problems. The
proposed numerical method is applied to the solution of a stochastic partial
differential equation which is discretized using standard Galerkin methods in
tensor product spaces
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