Accelerated Bose-Einstein condensates in a double-well potential

Devices based on ultracold atoms moving in an accelerating optical lattice or double-well potential are a promising tool for precise measurements of fundamental physical constants as well as for the construction of sensors. Here, we carefully analyze the model of a couple of BECs separated by a barrier in an accelerated field and we show how the observable quantities, mainly the period of the beating motion or of the phase-shift, are related to the physical parameters of the model as well as to the energy of the initial state.Comment: 5 figure

Nonlinear Schrodinger equations with a multiple-well potential and a Stark-type perturbation

A Bose-Einstein condensate (BEC) confined in a one-dimensional lattice under the effect of an external homogeneous field is described by the Gross-Pitaevskii equation. Here we prove that such an equation can be reduced, in the semiclassical limit and in the case of a lattice with a finite number of wells, to a finite-dimensional discrete nonlinear Schrodinger equation. Then, by means of numerical experiments we show that the BEC's center of mass exhibits an oscillating behavior with modulated amplitude; in particular, we show that the oscillating period actually depends on the shape of the initial wavefunction of the condensate as well as on the strength of the nonlinear term. This fact opens a question concerning the validity of a method proposed for the determination of the gravitational constant by means of the measurement of the oscillating period.Comment: 24 pages, 8 figure

Exponential times in the one-dimensional Gross--Petaevskii equation with multiple well potential

We consider the Gross-Petaevskii equation in 1 space dimension with a $n$-well trapping potential. We prove, in the semiclassical limit, that the finite dimensional eigenspace associated to the lowest n eigenvalues of the linear operator is slightly deformed by the nonlinear term into an almost invariant manifold M. Precisely, one has that solutions starting on M, or close to it, will remain close to M for times exponentially long with the inverse of the size of the nonlinearity. As heuristically expected the effective equation on M is a perturbation of a discrete nonlinear Schroedinger equation. We deduce that when the size of the nonlinearity is large enough then tunneling among the wells essentially disappears: that is for almost all solutions starting close to M their restriction to each of the wells has norm approximatively constant over the considered time scale. In the particular case of a double well potential we give a more precise result showing persistence or destruction of the beating motions over exponentially long times. The proof is based on canonical perturbation theory; surprisingly enough, due to the Gauge invariance of the system, no non-resonance condition is required

Inclusive governance in non-profit organisations

The study of private non-profit enterprises that offer general interest services is only at the start. The understanding of existing organisations resists an inclusive, public interest view of governance. This contribution aims at providing a reflection on specific features that non-profit enterprises should have, and outlines four main justifications for including stakeholders in production governance: 1) access to knowledge and other resources, 2) trust creation, 3) internal efficiency, 4) external efficiency. Conclusions elaborate on Hansmann’s classic theory of the firm to suggest that governance solutions need to be assessed on the basis of total costs, considering also the lower level of social costs that is created when governance includes relevant stakeholders. Our model highlights that when social costs are high, even an enterprise with costly decisional processes, such as the multi-stakeholder, can be the most efficient solution amongst other possible alternatives

Neurotrophic factors and corneal nerve regeneration

The cornea has unique features that make it a useful model for regenerative medicine studies. It is an avascular, transparent, densely innervated tissue and any pathological changes can be easily detected by slit lamp examination. Corneal sensitivity is provided by the ophthalmic branch of the trigeminal nerve that elicits protective reflexes such as blinking and tearing and exerts trophic support by releasing neuromediators and growth factors. Corneal nerves are easily evaluated for both function and morphology using standard instruments such as corneal esthesiometer and in vivo confocal microscope. All local and systemic conditions that are associated with damage of the trigeminal nerve cause the development of neurotrophic keratitis, a rare degenerative disease. Neurotrophic keratitis is characterized by impairment of corneal sensitivity associated with development of persistent epithelial defects that may progress to corneal ulcer, melting and perforation. Current neurotrophic keratitis treatments aim at supporting corneal healing and preventing progression of corneal damage. Novel compounds able to stimulate corneal nerve recovery are in advanced development stage. Among them, nerve growth factor eye drops showed to be safe and effective in stimulating corneal healing and improving corneal sensitivity in patients with neurotrophic keratitis. Neurotrophic keratitis represents an useful model to evaluate in clinical practice novel neuro-regenerative drugs

Stability of spectral eigenspaces in nonlinear Schrodinger equations

We consider the time-dependent non linear Schrodinger equations with a double well potential in dimensions d =1 and d=2. We prove, in the semiclassical limit, that the finite dimensional eigenspace associated to the lowest two eigenvalues of the linear operator is almost invariant for any time

A needs theory of governance

New-institutional economics hypothesizes imperfect rationality, self-seeking preferences, monetary-related needs, and opportunism as fundamental features of human behavior. Consistently, new-institutionalist models of governance highlight the efficiency and transaction costs minimizing features of control rights and governance. Differently, needs theory of governance, as here presented, hypothesizes imperfect rationality, multiple needs, and reciprocity, in which case opportunism is reduced to an exception to individual behavior. Consistently, it presents a theory that links production governance with the wellbeing of those partaking in production. Building on Maslow’s human psychology, the governance model suggested in this paper is aimed at evidencing the self-actualization potential of control rights, organizational structures and practices. The application of Maslow’s theory to the institutional structure of organizations suggests that the deepest organizational layers (control rights and governance) broadly correspond to the most basic needs in Maslow’s theory (survival, security and belonging), while the outer layers (managerial models and employment relations) correspond to the fulfillment of the highest needs (self-esteem and self-actualization). Cooperative firms are used as an illustration of governance solutions consistent with needs theory in human psychology