Determinants of Block Tridiagonal Matrices

An identity is proven that evaluates the determinant of a block tridiagonal matrix with (or without) corners as the determinant of the associated transfer matrix (or a submatrix of it).Comment: 8 pages, final form. To appear on Linear Algebra and its Application

Identities and exponential bounds for transfer matrices

This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the transfer matrix describe localization of eigenstates and are linked to the spectrum of the block tridiagonal matrix by a determinantal identity, If the block tridiagonal matrix is invertible, it is shown that half of the singular values of the transfer matrix have a lower bound exponentially large in the length of the chain, and the other half have an upper bound that is exponentially small. This is a consequence of a theorem by Demko, Moss and Smith on the decay of matrix elements of inverse of banded matrices.Comment: To appear in J. Phys. A: Math. and Theor. (Special issue on Lyapunov Exponents, edited by F. Ginelli and M. Cencini). 16 page

Hedin's equations and enumeration of Feynman's diagrams

Hedin's equations are solved perturbatively in zero dimension to count Feynman graphs for self-energy, polarization, propagator, effective potential and vertex function in a many-body theory of fermions with two-body interaction. Counting numbers are also obtained in the GW approximation.Comment: Revised published version, 3 pages, no figure

RECENT DEVELOPMENTS IN LAND TENURE LAW IN ERITREA, HORN OF AFRICA

After a historical sketch of the evolution of land tenure systems in the Eritrean highlands, this paper describes the main features of the new Eritrean land law and its operative assumption that the legislation is meant to extend state control over land. The legal devices employed by the law are widely used in sub-Saharan Africa (and were largely inspired by colonial policies). The State of Eritrea frequently asserts that its recent independence gives it the opportunity to learn from other developing countries' mistakes and to avoid them. The basic patterns of the new land law, however, are common to the rest of Africa, notwithstanding the evident poor results. The central government wants its control to be widespread and pervasive. The fight against traditional social groups controlling land, at least in the highlands, is severe. Apart from a formal repeal of customary law, the state's acquisition of the power to modify village boundaries according to a scheme already completed at higher administrative levels and to introduce equal rights on land for women entails a disruption of the villages' social identity. Mandatory state control over landed property in Eritrea is, as usual, motivated by the necessity to address higher social needs. The ultimate intent, of course, is that the evolution from communal property to state property will eventually result in the widespread introduction of individual property once a sufficient level of economic development is achieved. This unfavorable attitude toward communal property is not supported by the evidence, which shows that, in fact, efficient land management can be obtained through renovation of traditional institutions.Land tenure -- Eritrea, Land tenure -- Government policy -- Eritrea, Land tenure -- Law and legislation -- Eritrea, Customary law -- Eritrea, Tenure types, Traditional -- Eritrea, Land reform -- Eritrea, Land Economics/Use,

Trihamiltonian extensions of separable systems in the plane

A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of the Euclidean plane, and some explicit examples are constructed. Finally a conjecture on possible generalizations to other classes of systems is discussed: in particular, the method can be easily adapted to the eleven orthogonal separable coordinate sets of the Euclidean three-space.Comment: 20 page

Optimal efficiency of quantum transport in a disordered trimer

Disordered quantum networks, as those describing light-harvesting complexes, are often characterized by the presence of peripheral ring-like structures, where the excitation is initialized, and inner reaction centers (RC), where the excitation is trapped. The peripheral rings display coherent features: their eigenstates can be separated in the two classes of superradiant and subradiant states. Both are important to optimize transfer efficiency. In the absence of disorder, superradiant states have an enhanced coupling strength to the RC, while the subradiant ones are basically decoupled from it. Static on-site disorder induces a coupling between subradiant and superradiant states, creating an indirect coupling to the RC. The problem of finding the optimal transfer conditions, as a function of both the RC energy and the disorder strength, is very complex even in the simplest network, namely a three-level system. In this paper we analyze such trimeric structure choosing as initial condition a subradiant state, rather than the more common choice of an excitation localized on a site. We show that, while the optimal disorder is of the order of the superradiant coupling, the optimal detuning between the initial state and the RC energy strongly depends on system parameters: when the superradiant coupling is much larger than the energy gap between the superradiant and the subradiant levels, optimal transfer occurs if the RC energy is at resonance with the subradiant initial state, whereas we find an optimal RC energy at resonance with a virtual dressed state when the superradiant coupling is smaller than or comparable with the gap. The presence of dynamical noise, which induces dephasing and decoherence, affects the resonance structure of energy transfer producing an additional 'incoherent' resonance peak, which corresponds to the RC energy being equal to the energy of the superradiant state.Comment: This article shares part of the introduction and most of Section II with arXiv:1508.01613, the remaining parts of the two articles treat different problem

Medical use of cannabis: italian and european legislation

This review illustrates some brief considerations of the medical use of cannabis recently issued in Italy. History and uses of cannabis throughout centuries and different countries are illustrated together with a description of botany and active phytocannabinoids. Then, medical use of cannabis anti-pain treatment for patients resistant to conventional therapies is described in case of chronic neuropathic pain, spasticity, for anticinetosic and antiemetic effect in nausea and vomiting caused by chemotherapy, for appetite stimulating effect in cachexia, anorexia, loss of appetite in cancer patients or patients with AIDS and in anorexia nervosa, hypotensive effect in glaucoma resistant to conventional therapies and for reduction of involuntary body and facial movements in Gilles de la Tourette syndrome. Italian most recent legislation on medical cannabis is detailed with some law proposals, also showing the inconsistent legislation within European Union. Some final considerations of future studies are also reported