Non-Markovian quantum trajectories: an exact result

We analyze the non-Markovian stochastic Schroedinger equation describing a particle subject to spontaneous collapses in space (in the language of collapse models), or subject to a continuous measurement of its position (in the language of continuous quantum measurement). For the first time, we give the explicit general solution for the free particle case (H = p^2/2m), and discuss the main properties. We analyze the case of an exponential correlation function for the noise, giving a quantitative description of the dynamics and of its dependence on the correlation time.Comment: 4 pages, RevTeX. Minor revision

Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: general solution and main properties

We analyze the non-Markovian dynamics of a quantum system subject to spontaneous collapse in space. After having proved, under suitable conditions, the separation of the center-of-mass and relative motions, we focus our analysis on the time evolution of the center of mass of an isolated system (free particle case). We compute the explicit expression of the Green's function, for a generic Gaussian noise, and analyze in detail the case of an exponential correlation function. We study the time evolution of average quantities, such as the mean position, momentum and energy. We eventually specialize to the case of Gaussian wave functions, and prove that all basic facts about collapse models, which are known to be true in the white noise case, hold also in the more general case of non-Markovian dynamics.Comment: 37 pages, LaTeX. Title changed. Other minor correction

Test of gravitomagnetism with satellites around the Earth

We focus on the possibility of measuring the gravitomagnetic effects due to the rotation of the Earth, by means of a space-based experiment that exploits satellites in geostationary orbits. Due to the rotation of the Earth, there is an asymmetry in the propagation of electromagnetic signals in opposite directions along a closed path around the Earth. We work out the delays between the two counter-propagating beams for a simple configuration, and suggest that accurate time measurements could allow, in principle, to detect the gravitomagnetic effect of the EarthComment: 6 pages, 3 figures; revised to match the version accepted for publication in EPJ

Lorentz contraction and accelerated systems

The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising when the world lines correspond to physically connected or disconnected objects. In all cases the special theory of relativity proves to be completely self-consistentComment: 7 pages, LaTeX, to be published in European Journal of Physic

Mapping Cartesian Coordinates into Emission Coordinates: some Toy Models

After briefly reviewing the relativistic approach to positioning systems based on the introduction of the emission coordinates, we show how explicit maps can be obtained between the Cartesian coordinates and the emission coordinates, for suitably chosen set of emitters, whose world-lines are supposed to be known by the users. We consider Minkowski space-time and the space-time where a small inhomogeineity is introduced (i.e. a small "gravitational" field), both in 1+1 and 1+3 dimensions.Comment: 13 pages, 7 figures, Accepted for publication in International Journal of Modern Physics

The efficiency view of corporate boards: theory and evidence

We build a simple model in which corporate governance may allow for institutions acting as commitment devices (e.g., the introduction of independent and minority members in the board). The model predicts that the incentive to adopt an institution — letting the general interest of shareholders prevail over private benefits of control by dominant shareholders — is decreasing in ownership concentration and increasing in free cash flow. We take the predictions of our theoretical model to the data, by providing empirical evidence on the board structure of Italian listed companies over the period 2004-2007. We find that board composition favors independent members in firms where the free cash flow is large, and executive members in firms with high ownership concentration and in family firms, supporting the view of corporate governance as a mechanism to control agency costs. More ambiguous conclusions are reached as for the link between governance and firm value, as the presence of minority lists in the board appears to improve value while that of independent members reduces performance.corporate boards, agency problems, private benefits, firms’ performance.

A kinetic model for the finite-time thermodynamics of small heat engines

We study a molecular engine constituted by a gas of $N \sim 10^2$ molecules enclosed between a massive piston and a thermostat. The force acting on the piston and the temperature of the thermostat are cyclically changed with a finite period $\tau$. In the adiabatic limit $\tau \to \infty$, even for finite size $N$, the average work and heats reproduce the thermodynamic values, recovering the Carnot result for the efficiency. The system exhibits a stall time $\tau^*$ where net work is zero: for $\tau<\tau^*$ it consumes work instead of producing it, acting as a refrigerator or as a heat sink. At $\tau>\tau^*$ the efficiency at maximum power is close to the Curzorn-Ahlborn limit. The fluctuations of work and heat display approximatively a Gaussian behavior. Based upon kinetic theory, we develop a three-variables Langevin model where the piston's position and velocity are linearly coupled together with the internal energy of the gas. The model reproduces many of the system's features, such as the inversion of the work's sign, the efficiency at maximum power and the approximate shape of fluctuations. A further simplification in the model allows to compute analytically the average work, explaining its non-trivial dependence on $\tau$.Comment: 8 pages, 6 figures, accepted for publication on Physical Review

Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations

We investigate a kinetic heat engine model constituted by particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period $\tau$ : their relative excursions, $\delta$ and $\epsilon$ respectively, constitute the thermodynamic forces dragging the system out-of-equilibrium. The analysis of the entropy production of the system allows to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. In the limit of small $\delta$ and $\epsilon$ the fluxes are linear in the forces through a $\tau$-dependent Onsager matrix whose off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which - in the linear regime - yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon-Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e. outside of the linear regime. In all our analysis the adiabatic limit $\tau \to \infty$ and the the small force limit $\delta,\epsilon \to 0$ are not directly related.Comment: 10 pages, 9 figure

A relativistic navigation system for space

We present here a method for the relativistic positioning in spacetime based on the reception of pulses from sources of electromagnetic signals whose worldline is known. The method is based on the use of a fourdimensional grid covering the whole spacetime and made of the null hypersurfaces representing the propagating pulses. In our first approach to the problem of positioning we consider radio-pulsars at infinity as primary sources of the required signals. The reason is that, besides being very good clocks, pulsars can be considered as being fixed stars for reasonably long times. The positioning is obtained linearizing the worldline of the observer for times of the order of a few periods of the signals. We present an exercise where the use of our method applied to the signals from four real pulsars permits the reconstruction of the motion of the Earth with respect to the fixed stars during three days. The uncertainties and the constraints of the method are discussed and the possibilities of using mov- ing artificial sources carried around by celestial bodies or spacecrafts in the Solar System is also discusse