Lie symmetries of Einstein's vacuum equations in N dimensions

We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on Einstein's equations. Instead of setting to zero the coefficients of all independent partial derivatives (which involves a very complicated substitution of Einstein's equations), we set to zero the coefficients of derivatives that do not appear in Einstein's equations. This considerably constrains the coefficients of symmetry generating vector fields. Using the Lie algebra property of generators of symmetries and the fact that general coordinate transformations are symmetries of Einstein's equations, we are then able to obtain all the Lie symmetries. The method we have used can likely be applied to other types of equations

Entanglement for all quantum states

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.Comment: 9 page

Manipulation of single-photon states encoded in transverse spatial modes: possible and impossible tasks

Controlled generation and manipulation of photon states encoded in their spatial degrees of freedom is a crucial ingredient in many quantum information tasks exploiting higher-than-two dimensional encoding. Here, we prove the impossibility to arbitrarily modify $d$-level state superpositions (qu$d$its) for $d>2$, encoded in the transverse modes of light, with optical components associated to the group of symplectic transforms (Gaussian operations). Surprisingly, we also provide an explicit construction of how non-Gaussian operations acting on mode subspaces do enable to overcome the limit $d=2$. In addition, this set of operations realizes the full SU(3) algebra.Comment: Published in PR

Observation of a nanophase segregation in LiCl aqueous solutions from Transient Grating Experiments

Transient Grating experiments performed on supercooled LiCl, RH2O solutions with R>6 reveal the existence of a strong, short time, extra signal which superposes to the normal signal observed for the R=6 solution and other glass forming systems. This extra signal shows up below 190 K, its shape and the associated timescale depend only on temperature, while its intensity increases with R. We show that the origin of this signal is a phase separation between clusters with a low solute concentration and the remaining, more concentrated, solution. Our analysis demonstrates that these clusters have a nanometer size and a composition which are rather temperature independent, while increasing R simply increases the number of these clusters.Comment: 19 pages+ 8 figures+ 2 table

Optical and plasmonic properties of twisted bilayer graphene: Impact of interlayer tunneling asymmetry and ground-state charge inhomogeneity

We present a theoretical study of the local optical conductivity, plasmon spectra, and thermoelectric properties of twisted bilayer graphene (TBG) at different filling factors and twist angles $\theta$. Our calculations are based on the electronic band structures obtained from a continuum model that has two tunable parameters, $u_0$ and $u_1$, which parametrize the intra-sublattice inter-layer and inter-sublattice inter-layer tunneling rate, respectively. In this Article we focus on two key aspects: i) we study the dependence of our results on the value of $u_0$, exploring the whole range $0\leq u_0\leq u_1$; ii) we take into account effects arising from the intrinsic charge density inhomogeneity present in TBG, by calculating the band structures within the self-consistent Hartree approximation. At zero filling factor, i.e. at the charge neutrality point, the optical conductivity is quite sensitive to the value of $u_0$ and twist angle, whereas the charge inhomogeneity brings about only modest corrections. On the other hand, away from zero filling, static screening dominates and the optical conductivity is appreciably affected by the charge inhomogeneity, the largest effects being seen on the intra-band contribution to it. These findings are also reflected by the plasmonic spectra. We compare our results with existing ones in the literature, where effects i) and ii) above have not been studied systematically. As natural byproducts of our calculations, we obtain the Drude weight and Seebeck coefficient. The former displays an enhanced particle-hole asymmetry stemming from the inhomogeneous ground-state charge distribution. The latter is shown to display a broad sign-changing feature even at low temperatures ($\approx 5~{\rm K}$) due to the reduced slope of the bands, as compared to those of single-layer graphene.Comment: 28 pages, 16 figures, 6 appendice

Financial globalization : unequal blessings

The authors present a framework to analyze financial globalization. They argue that financial globalization needs to take into account the relation between money (particularly in its role as store of value), asset and factor price flexibility, and contractual and regulatory institutions. Countries that have the"blessed trinity"(international currency, flexible exchange rate regime, and sound contractual and regulatory environment) can integrate successfully into the world financial markets. But developing countries normally display the"unblessed trinity"(weak currency, fear of floating, and weak institutional framework). The authors define and discuss two alternative avenues (a"dollar trinity"and a"peso trinity") for developing countries to safely embrace international financial integration while the blessed trinity remains beyond reach.Economic Theory&Research,Fiscal&Monetary Policy,Banks&Banking Reform,Payment Systems&Infrastructure,Financial Intermediation,Financial Economics,Macroeconomic Management,Economic Stabilization,Economic Theory&Research,Fiscal&Monetary Policy

Capital market development : whither Latin America ?

Over the past decades, many countries have implemented significant reforms to foster capital market development. Latin American countries were at the forefront of this process. The authors analyze where Latin American capital markets stand after these reforms. They find that despite the intense reform effort, capital markets in Latin America remain underdeveloped relative to markets in other regions. Furthermore, stock markets are below what can be expected, given Latin America's economic and institutional fundamentals. The authors discuss alternative ways of interpreting this evidence. They argue that it is difficult to pinpoint which policies Latin American countries should pursue to overcome their poor capital market development. Moreover, they argue that expectations about the outcome of the reform process may need to be revisited to take into account intrinsic characteristics of emerging economies. The latter may limit the scope for developing deep domestic capital markets in a context of international financial integration.Markets and Market Access,Economic Theory&Research,Access to Markets,Financial Economics,Financial Intermediation

Financial globalization: Unequal blessings

This paper presents a framework to analyze financial globalization. It argues that financial globalization needs to take into account the relation between money (particularly in its role as store of value), asset and factor price flexibility, and contractual and regulatory institutions. Countries that have the “blessed trinity” (international currency, flexible exchange rate regime, and sound contractual and regulatory environment) can integrate successfully into the (imperfect) world financial markets. But developing countries normally display the “unblessed trinity” (weak currency, fear of floating, and weak institutional framework). The paper defines and discusses two alternative avenues (a “dollar trinity” and a “peso trinity”) for developing countries to safely embrace international financial integration while the blessed trinity remains beyond reach.

Share Opportunity Sets and Cooperative Games

In many share problems there is a priori given a natural set of possible divisions to solve the sharing problem.Cooperative games related to such share sets are introduced, which may be helpful in solving share problems.Relations between properties of share sets and properties of games are investigated.The average lexicographic value for share sets and for cooperative games is studied.cooperative games;bankruptcy games;average lexicographic value;opportunity sets