Theory of controlled quantum dynamics

We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general linear, and it amounts to introduce additional quadratic and linear time-dependent terms to the given potential. In this way one can construct for general systems either coherent packets moving with constant dispersion, or dynamically squeezed packets whose spreading remains bounded for all times. In the standard operatorial framework our scheme corresponds to a suitable generalization of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator.Comment: LaTeX, A4wide, 28 pages, no figures. To appear in J. Phys. A: Math. Gen., April 199

The solution space of metabolic networks: producibility, robustness and fluctuations

Flux analysis is a class of constraint-based approaches to the study of biochemical reaction networks: they are based on determining the reaction flux configurations compatible with given stoichiometric and thermodynamic constraints. One of its main areas of application is the study of cellular metabolic networks. We briefly and selectively review the main approaches to this problem and then, building on recent work, we provide a characterization of the productive capabilities of the metabolic network of the bacterium E.coli in a specified growth medium in terms of the producible biochemical species. While a robust and physiologically meaningful production profile clearly emerges (including biomass components, biomass products, waste etc.), the underlying constraints still allow for significant fluctuations even in key metabolites like ATP and, as a consequence, apparently lay the ground for very different growth scenarios.Comment: 10 pages, prepared for the Proceedings of the International Workshop on Statistical-Mechanical Informatics, March 7-10, 2010, Kyoto, Japa

Thermodynamics of rotating self-gravitating systems

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse ``transition'' is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters (``double stars''). We analyze the thermodynamics of the system and the stability of the different equilibrium configurations against rotational symmetry breaking, and provide the global phase diagram.Comment: 12 pages, 9 figure

Spin-resolved scattering through spin-orbit nanostructures in graphene

We address the problem of spin-resolved scattering through spin-orbit nanostructures in graphene, i.e., regions of inhomogeneous spin-orbit coupling on the nanometer scale. We discuss the phenomenon of spin-double refraction and its consequences on the spin polarization. Specifically, we study the transmission properties of a single and a double interface between a normal region and a region with finite spin-orbit coupling, and analyze the polarization properties of these systems. Moreover, for the case of a single interface, we determine the spectrum of edge states localized at the boundary between the two regions and study their properties

Quantitative constraint-based computational model of tumor-to-stroma coupling via lactate shuttle

Cancer cells utilize large amounts of ATP to sustain growth, relying primarily on non-oxidative, fermentative pathways for its production. In many types of cancers this leads, even in the presence of oxygen, to the secretion of carbon equivalents (usually in the form of lactate) in the cell's surroundings, a feature known as the Warburg effect. While the molecular basis of this phenomenon are still to be elucidated, it is clear that the spilling of energy resources contributes to creating a peculiar microenvironment for tumors, possibly characterized by a degree of toxicity. This suggests that mechanisms for recycling the fermentation products (e.g. a lactate shuttle) may be active, effectively inducing a mutually beneficial metabolic coupling between aberrant and non-aberrant cells. Here we analyze this scenario through a large-scale in silico metabolic model of interacting human cells. By going beyond the cell-autonomous description, we show that elementary physico-chemical constraints indeed favor the establishment of such a coupling under very broad conditions. The characterization we obtained by tuning the aberrant cell's demand for ATP, amino-acids and fatty acids and/or the imbalance in nutrient partitioning provides quantitative support to the idea that synergistic multi-cell effects play a central role in cancer sustainment

Rashba spin-orbit coupling and spin precession in carbon nanotubes

The Rashba spin-orbit coupling in carbon nanotubes and its effect on spin-dependent transport properties are analyzed theoretically. We focus on clean non-interacting nanotubes with tunable number of subbands $N$. The peculiar band structure is shown to allow in principle for Datta-Das oscillatory behavior in the tunneling magnetoresistance as a function of gate voltage, despite the presence of multiple bands. We discuss the conditions for observing Datta-Das oscillations in carbon nanotubes.Comment: 12 pages, published versio

Von Neumann's expanding model on random graphs

Within the framework of Von Neumann's expanding model, we study the maximum growth rate r achievable by an autocatalytic reaction network in which reactions involve a finite (fixed or fluctuating) number D of reagents. r is calculated numerically using a variant of the Minover algorithm, and analytically via the cavity method for disordered systems. As the ratio between the number of reactions and that of reagents increases the system passes from a contracting (r1). These results extend the scenario derived in the fully connected model (D\to\infinity), with the important difference that, generically, larger growth rates are achievable in the expanding phase for finite D and in more diluted networks. Moreover, the range of attainable values of r shrinks as the connectivity increases.Comment: 20 page