Extended uncertainty principle and the geometry of (anti)-de Sitter space

It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.Comment: 8 pages, plain TeX, references adde

Quantum Fluctuations in Open Pre-Big Bang Cosmology

We solve exactly the (linear order) equations for tensor and scalar perturbations over the homogeneous, isotropic, open pre-big bang model recently discussed by several authors. We find that the parametric amplification of vacuum fluctuations (i.e. particle production) remains negligible throughout the perturbative pre-big bang phase.Comment: 12 pages, ReVTeX, Discussion of relation to Ref.[8] modifie

Maxwell-Chern-Simons Theory With Boundary

The Maxwell-Chern-Simons (MCS) theory with planar boundary is considered. The boundary is introduced according to Symanzik's basic principles of locality and separability. A method of investigation is proposed, which, avoiding the straight computation of correlators, is appealing for situations where the computation of propagators, modified by the boundary, becomes quite complex. For MCS theory, the outcome is that a unique solution exists, in the form of chiral conserved currents, satisfying a Kac-Moody algebra, whose central charge does not depend on the Maxwell term.Comment: 30 page

A new CFD-Simulink based systems engineering approach applied to the modelling of a hydraulic safety relief valve

A safety relief valve is a simple hydro-mechanic device, needed to avoid overpressure transients inside hydraulic circuits. Such valves are a critical part of the hydraulic system of aircraft; hence their performances must be adapted to a specific nominal pressure level and design requirements. In the following paragraphs the authors will address the issue of designing and validating a safety valve through a hybrid CFD/MATLAB-Simulink® approach. The main constraints are the geometrical dimensions and the need to limit the weight of the device. A significant part of the work consists of gathering all the possible information available in the literature, dealing with the best design practices to achieve the performance objective. Thanks to a robust computational procedure, it should be possible to reduce the amount of “physical” prototypes required to validate the functionality of a safety relief valve. The process presented uses a numerical computational fluid dynamic (CFD) approach, to define the pressure field inside the valve and the forces acting on it; identifying the force distribution inside the valve is paramount to address the performance evaluation of the valve itself. The first step deals with the definition of a computer aided design (CAD) model of the valve. Then the CFD software uses the above-mentioned CAD model to define the domain of the problem. Once obtained the pressure field, it is possible to integrate it through the surface of the valve, thus obtaining the forces acting on the moving part (poppet). After the numerical scheme has been calibrated, some investigations are done to reduce the computational cost: the main aim is to run a complete simulation (meshing and solving) on a standard computer. Some of the positions (i.e. strokes) of the valve have been simulated as static, hence a steady-state calculation has been applied to solve the motion field. Another important result consists of creating a MATLAB-Simulink® model, capable to reach results comparable to the CFD simulation, but in shorter times. While the CFD model can provide high quality results, the MATLAB-Simulink® calculation should be used to create a “first guess” instrument, useful to address the very first valve geometry. The implementation of the Look-Up Tables (LUTs) links the MATLAB-Simulink® model to the CFD simulation, but increases the time required to obtain a solution: on the other hand, this reduces the amount of equation-modeled quantities, delivering a greater precision to the calculations

Some Aspects of Minimal Length Quantum Mechanics

String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and momentum space wave function for a "free particle". In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions.Comment: 9 pages, one eps figur

Key performance indicators of ‘good practices’ of energy efficiency in industry: application to real cases in Italy and in the European Union

With the publication of the Energy Efficiency Directive (EED) in 2012, energy savings in the Industry processes have gained more and more importance in the European Union (EU). Industry (with building and transport) is one of the three main sectors where Energy consumption and efficiency play a fundamental role, to accomplish the EU energy objectives. Many countries in EU have already adopted schemes and mechanisms to implement the Directive: however deep differences of approaches still remain among the Member States (MSs), especially with respect to the identification of the real benefits of measures and to the assessment of their efficiency and sustainability. As a consequence, a huge amount of the efficiency potential still remains untapped. This paper proposes some criteria for the evaluation of the applied Energy Efficiency measures, leading to the identification of Good Practices of Energy Efficiency. These criteria are taken from the ‘real world’ of industry, and are susceptible to be replicated in other contexts (e.g. different sectors or other countries). The proposed criteria have been developed in the EU H2020 project EU MERCI (nr 693845) and through a national research (part of the ‘Ricerca di Sistema’ national funding system) both coordinated by RSE. The starting point is the harmonization of data sets related to projects developed in different EU countries within local efficiency implementation schemes. The second step is the definition of Key Performance Indicators (KPIs) reflecting the impact of measures against Energy, Environment and Economic aspects. The last step is the extraction of efficiency ‘Good Practices’ ranked according to the identified KPIs and other factors, including social elements. The real added value of this approach is that it is full based on tangibly implemented projects, in opposition to similar attempts, essentially theoretical. Ultimately, it offers a key of assessment of the effectiveness of efficiency measures implementing local and EU policies

New Results on N=4 SuperYang-Mills Theory

The N=4 SuperYang--Mills theory is covariantly determined by a U(1) \times SU(2) \subset SL(2,R) \times SU(2) internal symmetry and two scalar and one vector BRST topological symmetry operators. This determines an off-shell closed sector of N=4 SuperYang-Mills, with 6 generators, which is big enough to fully determine the theory, in a Lorentz covariant way. This reduced algebra derives from horizontality conditions in four dimensions. The horizontality conditions only depend on the geometry of the Yang-Mills fields. They also descend from a genuine horizontality condition in eight dimensions. In fact, the SL(2,R) symmetry is induced by a dimensional reduction from eight to seven dimensions, which establishes a ghost-antighost symmetry, while the SU(2) symmetry occurs by dimensional reduction from seven to four dimensions. When the four dimensional manifold is hyperKahler, one can perform a twist operation that defines the N=4 supersymmetry and its SL(2,H)\sim SU(4) R-symmetry in flat space. (For defining a TQFT on a more general four manifold, one can use the internal SU(2)-symmetry and redefine a Lorentz SO(4) invariance). These results extend in a covariant way the light cone property that the N=4 SuperYang-Mills theory is actually determined by only 8 independent generators, instead of the 16 generators that occur in the physical representation of the superPoincare algebra. The topological construction disentangles the off-shell closed sector of the (twisted) maximally supersymmetric theory from the (irrelevant) sector that closes only modulo equations of motion. It allows one to escape the question of auxiliary fields in N=4 SuperYang-Mills theory.Comment: 14 page

A Statistical Interpretation of Space and Classical-Quantum duality

By defining a prepotential function for the stationary Schr\"odinger equation we derive an inversion formula for the space variable $x$ as a function of the wave-function $\psi$. The resulting equation is a Legendre transform that relates $x$, the prepotential ${\cal F}$, and the probability density. We invert the Schr\"odinger equation to a third-order differential equation for ${\cal F}$ and observe that the inversion procedure implies a $x$-$\psi$ duality. This phenomenon is related to a modular symmetry due to the superposition of the solutions of the Schr\"odinger equation. We propose that in quantum mechanics the space coordinate can be interpreted as a macroscopic variable of a statistical system with $\hbar$ playing the role of a scaling parameter. We show that the scaling property of the space coordinate with respect to $\tau=\partial_{\psi}^2{\cal F}$ is determined by the ``beta-function''. We propose that the quantization of the inversion formula is a natural way to quantize geometry. The formalism is extended to higher dimensions and to the Klein-Gordon equation.Comment: 11 pages. Standard Latex. Final version to appear in Physical Review Letters. Revised and extended version. The formalism is extended to higher dimensions and to the Klein-Gordon equation. A possible connection with string theory is considered. The $x-\psi$ duality is emphasized by a minor change in the title. The new title is: Duality of $x$ and $\psi$ and a statistical interpretation of space in quantum mechanic

Minimal Length and the Quantum Bouncer: A Nonperturbative Study

We present the energy eigenvalues of a quantum bouncer in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP) via quantum mechanical and semiclassical schemes. In this paper, we use two equivalent nonperturbative representations of a deformed commutation relation in the form [X,P]=i\hbar(1+\beta P^2) where \beta is the GUP parameter. The new representation is formally self-adjoint and preserves the ordinary nature of the position operator. We show that both representations result in the same modified semiclassical energy spectrum and agrees well with the quantum mechanical description.Comment: 14 pages, 2 figures, to appear in Int. J. Theor. Phy

Pre-Big Bang Cosmology and Quantum Fluctuations

The quantum fluctuations of a homogeneous, isotropic, open pre-big bang model are discussed. By solving exactly the equations for tensor and scalar perturbations we find that particle production is negligible during the perturbative Pre-Big Bang phase.Comment: 4 pages, use esprc2.sty. Talk given at the 3rd Meeting on Constrained Dynamics and Quantum Gravity (QG 99), Villasimius, Sardinia, Italy, 14-18 Sep 199