An exact evaluation of the Casimir energy in two planar models

The method of images is used to calculate the Casimir energy in Euclidean space with Dirichlet boundary conditions for two planar models, namely: i. the non-relativistic Landau problem for a charged particle of mass m for which - irrespective of the sign of the charge - the energy is negative, and ii. the model of a real, massive, noninteracting relativistic scalar field theory in 2 + 1 dimensions, for which the Casimir energy density is non-negative and is expressed in terms of the Lerch transcendent xxx and the polylogarithm xxx with 0 < xxx < 1 and n = 2, 3.Comment: 5 pages, 2 figures,IMFP2009 conference,to appear in forthcoming AIP Conf.Proc.1150 Request:There are three mathematical symbols denoted by xxx in the abstract below which are otherwise present in the abstract of the submission.Could you please include them so that the abstract below is complet

Formality of derived intersections

We study derived intersections of smooth analytic cycles, and provide in some cases necessary and sufficient conditions for this intersection be formal. In particular, if X is a complex submanifold of a complex manifold Y, we prove that X can be quantized if and only if the derived intersection of XxX and \Delta_Y is formal in D(XxX).Comment: A mistake has been corrected in Section

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Sardinian native diet: Traditional food habits and adaptation to its island terrains

openOne of the world's five mythical regions, or longevity blue zones (LBZ), is Sardinia. It has about 1.6 million people living on it, making it the second largest island in the Mediterranean Sea. Ogliastra and Barbagia are the greatest places of longevity all around the world, with the greatest number of centenarians leaving behind Okinawa, Japan. The world's first blue zone that was discovered was Ogliastra. But why is Sardinia's standard of living so drastically different from that of other people? How the Sardinian local eating routine and conventional food propensities make any distinction. We will be responding to this multitude of inquiries here in this paper. A Roman diet, according to some local Sardinians, is the key to longevity, and a well-balanced, nutritious diet can alter genes. The Sardinian people have proven that they are the direct descendants of their Neolithic-era Nuraghic ancestors. In Sardinia, the four things that work in symbiosis with each other—genetics, environment, food, and family—have been linked to gastronomy and longevity. Not only is the food that is grown in Sardinia nutritious, but the process of growing it also leads to less stress and longer lifespans.One of the world's five mythical regions, or longevity blue zones (LBZ), is Sardinia. It has about 1.6 million people living on it, making it the second largest island in the Mediterranean Sea. Ogliastra and Barbagia are the greatest places of longevity all around the world, with the greatest number of centenarians leaving behind Okinawa, Japan. The world's first blue zone that was discovered was Ogliastra. But why is Sardinia's standard of living so drastically different from that of other people? How the Sardinian local eating routine and conventional food propensities make any distinction. We will be responding to this multitude of inquiries here in this paper. A Roman diet, according to some local Sardinians, is the key to longevity, and a well-balanced, nutritious diet can alter genes. The Sardinian people have proven that they are the direct descendants of their Neolithic-era Nuraghic ancestors. In Sardinia, the four things that work in symbiosis with each other—genetics, environment, food, and family—have been linked to gastronomy and longevity. Not only is the food that is grown in Sardinia nutritious, but the process of growing it also leads to less stress and longer lifespans

Entanglement and symmetry effects in the transition to the Schroedinger cat regime

We study two-spin entanglement and order parameter fluctuations as a function of the system size in the XY model in a transverse field and in the isotropic XXX model. Both models are characterized by the occurrence of ground state degeneracy also when systems of finite size are considered. This is always true for the XXX model, but only at the factorizing field for the XY model. We study the size dependence of symmetric states, which, in the presence of degeneracy, can be expanded as a linear combination of broken symmetry states. We show that, while the XY model looses its quantum superposition content exponentially with the size $N$, a decrease of the order of 1/N is observed when the XXX model is considered. The emergence of two qualitatively different regimes is directly related to the difference in the symmetry of the models

From quantum affine groups to the exact dynamical correlation function of the Heisenberg model

The exact form factors of the Heisenberg models $XXX$ and $XXZ$ have been recently computed through the quantum affine symmetry of $XXZ$ model in the thermodynamic limit. We use them to derive an exact formula for the contribution of two spinons to the dynamical correlation function of $XXX$ model at zero temperature.Comment: 5 pages, Latex, Presented at the Symposium ``Exactly soluble models in statistical mechanics: historical perspectives and current status" March 30-31, 1996, Northeastern University, Bosto