Entanglement, BEC, and superfluid-like behavior of two-mode photon systems

A system of two interacting photon modes, without constraints on the photon number, in the presence of a Kerr nonlinearity, exhibits BEC if the transfer amplitude is greater than the mode frequency. A symmetry-breaking field (SBF) can be introduced by taking into account a classical electron current. The ground state, in the limit of small nonlinearity, becomes a squeezed state, and thus the modes become entangled. The smaller is the SBF, the greater is entanglement. Superfluid-like behavior is observed in the study of entanglement growth from an initial coherent state, since in the short-time range the growth does not depend on the SBF amplitude, and on the initial state amplitude. On the other hand, the latter is the only parameter which determines entanglement in the absence of the SBF

Power calculation for gravitational radiation: oversimplification and the importance of time scale

A simplified formula for gravitational-radiation power is examined. It is shown to give completely erroneous answers in three situations, making it useless even for rough estimates. It is emphasized that short timescales, as well as fast speeds, make classical approximations to relativistic calculations untenable.Comment: Three pages, no figures, accepted for publication in Astronomische Nachrichte

Integrated geophysical surveys to assess the structural conditions of a karstic cave of archaeological importance

An integrated geophysical survey using both the electrical resistivity tomography (ERT) and ground-penetrating radar (GPR) methods was undertaken over a cave of great archaeological interest in southern Italy. The survey was performed to assess the stability of the carbonate rock roof of the cave. A geophysical survey was preferred to boreholes and geotechnical tests, in order to avoid the risk of mass movements. The interpretation of integrated data from ERT and GPR resulted in an evaluation of some of the electromagnetic (EM) characteristics (such as the EM wave velocity) and the detection of discontinuities (fractures) in the carbonate rock. It is well known that rock fractures constitute a serious problem in cave maintenance, and progressive cracking within the bed rock is considered to be one of the main causes of collapse. An analysis of the back-scattered energy was also required for the GPR data interpretation. Cracks within the bedrock were detected to a depth of about 2 m by using GPR, which allowed for the identification of the loosened zone around the cave

Amplified spontaneous emission and lasing in lead halide perovskites: State of the art and perspectives

Lead halide perovskites are currently receiving increasing attention due to their potential to combine easy active layers fabrication, tunable electronic and optical properties with promising performance of optoelectronic and photonic device prototypes. In this paper, we review the main development steps and the current state of the art of the research on lead halide perovskites amplified spontaneous emission and on optically pumped lasers exploiting them as active materials

SBV regularity for Hamilton-Jacobi equations in Rn\mathbb R^n

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$\partial_t u + H(D_{x} u)=0 \qquad \textrm{in} \Omega\subset \mathbb R\times \mathbb R^{n} .$$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.Comment: 15 page

Droplet minimizers for the Gates-Lebowitz-Penrose free energy functional

We study the structure of the constrained minimizers of the Gates-Lebowitz-Penrose free-energy functional ${\mathcal F}_{\rm GLP}(m)$, non-local functional of a density field $m(x)$, $x\in {\mathcal T}_L$, a $d$-dimensional torus of side length $L$. At low temperatures, ${\mathcal F}_{\rm GLP}$ is not convex, and has two distinct global minimizers, corresponding to two equilibrium states. Here we constrain the average density L^{-d}\int_{{\cal T}_L}m(x)\dd x to be a fixed value $n$ between the densities in the two equilibrium states, but close to the low density equilibrium value. In this case, a "droplet" of the high density phase may or may not form in a background of the low density phase, depending on the values $n$ and $L$. We determine the critical density for droplet formation, and the nature of the droplet, as a function of $n$ and $L$. The relation between the free energy and the large deviations functional for a particle model with long-range Kac potentials, proven in some cases, and expected to be true in general, then provides information on the structure of typical microscopic configurations of the Gibbs measure when the range of the Kac potential is large enough

Regularity of higher codimension area minimizing integral currents

This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of the partial regularity of area minimizing integer rectifiable currents in higher codimension, due originally to F. Almgren, which is contained in a series of papers in collaboration with C. De Lellis (University of Zurich).Comment: This text will appear in "Geometric Measure Theory and Real Analysis", pp. 131--192, Proceedings of the ERC school in Pisa (2013), L. Ambrosio Ed., Edizioni SNS (CRM Series

Determination of the best empiric method to quantify the amplified spontaneous emission threshold in polymeric active waveguides

Amplified Spontaneous Emission (ASE) threshold represents a crucial parameter often used to establish if a material is a good candidate for applications to lasers. Even if the ASE properties of conjugated polymers have been widely investigated, the specific literature is characterized by several methods to determine the ASE threshold, making comparison among the obtained values impossible. We quantitatively compare 9 different methods employed in literature to determine the ASE threshold, in order to find out the best candidate to determine the most accurate estimate of it. The experiment has been performed on thin films of an homopolymer, a copolymer and a host:guest polymer blend, namely poly(9,9-dioctylfluorene) (PFO), poly(9,9-dioctylfluorene-cobenzothiadiazole) (F8BT) and F8BT:poly(3- hexylthiophene) (F8BT:rrP3HT), applying the Variable Pump Intensity (VPI) and the Variable Stripe Length (VSL) methods. We demonstrate that, among all the spectral features affected by the presence of ASE, the most sensitive is the spectral linewidth and that the best way to estimate the ASE threshold is to determine the excitation density at the beginning of the line narrowing. We also show that the methods most frequently used in literature always overestimate the threshold up to more than one order of magnitude

A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows

In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric, recently introduced and defined on the space of positive Radon measure with varying masses. We perform successively a time step for the quadratic Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao distance. Exploiting some inf-convolution structure of the metric we show convergence of the whole process for the standard class of energy functionals under suitable compactness assumptions, and investigate in details the case of internal energies. The interest is double: On the one hand we prove existence of weak solutions for a certain class of reaction-advection-diffusion equations, and on the other hand this process is constructive and well adapted to available numerical solvers.Comment: Final version, to appear in SIAM SIM