We present a semiclassical analysis of the instability of an electron shuttle composed of three quantum dots: two are fixed and coupled via leads to electron resevoirs at µ L,R with µ L ≫ µ R , while the central dot is mounted on a classical harmonic oscillator. The semiclassical analysis, which is valid if the central dot oscillation amplitude is larger than the quantum mechanical zero point m...

A recent general model of entanglement, [5], that goes much beyond the usual one based on tensor products of vector spaces is further developed here. It is shown that the usual Cartesian product can be seen as two extreme particular instances of non-entanglement. Also the recent approach to entanglement in [8] is incorporated in the general model in [5]. The idea pursued is that entanglement is...

I obtain an exact, axially symmetric, stationary solution of Einstein's equations for two massless spinning particles. The term representing the spin-spin interaction agrees with recently published approximate work. The spin-spin force appears to be proportional to the inverse fourth power of the coordinate distance between the particles.

For every regular cardinal κ there exists a simple complete Boolean algebra with κ generators.

We construct spectral triples associated to Schottky–Mumford curves, in such a way that the local Euler factor can be recovered from the zeta functions of such spectral triples. We propose a way of extending this construction to the case where the curve is not k-split degenerate.

The current acceleration of the universe leads us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical view point without the need of introducing dark energy by hand. We argue that the terms containing higher dimensional metric coefficients produce an extra negative pressure that apparently drives an acceleration of the 3D space, tempting us...

We present an up-to-date survey of theoretical concepts and results in the field of one-dimensional magnetism and of their relevance to experiments and real materials. Main emphasis of the chapter is on quantum phenomena in models of localized spins with isotropic exchange and additional interactions from anisotropy and external magnetic fields. Three sections deal with the main classes of mode...

Using the Boltzmann weights of classical Statistical Mechanics vertex models we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems, characterized by a strong anisotropy, which gives rise to stripe like structures. In the case of the six vertex model we compute exactly, in the thermodynamic limit, the norm of the ansatz and other observables. Employing this ansatz we stu...

The electronic properties of type II quasicrystals (QCs) in one dimension, namely ternary QCs which are generated by the cut-and-projection method, are analyzed. In particular, we present in detail the existence of a special kind of critical states called marginal critical states in these QCs. By the use of the exact real-space renormalization-group method, it is shown that the scaling properti...