Convergence radius of perturbative Lindblad driven non-equilibrium steady states

We address the problem of analyzing the radius of convergence of perturbative expansion of non-equilibrium steady states of Lindblad driven spin chains. A simple formal approach is developed for systematically computing the perturbative expansion of small driven systems. We consider the paradigmatic model of an open $XXZ$ spin 1/2 chain with boundary supported ultralocal Lindblad dissipators and treat two different perturbative cases: (i) expansion in system-bath coupling parameter and (ii) expansion in driving (bias) parameter. In the first case (i) we find that the radius of convergence quickly shrinks with increasing the system size, while in the second case (ii) we find that the convergence radius is always larger than $1$, and in particular it approaches $1$ from above as we change the anisotropy from easy plane ($XY$) to easy axis (Ising) regime

Regional differences in intelligence and per capita income in Portugal

Regional differences in IQ and per capita incomes are presented for five regions of Portugal: North, North Central, Lisbon-Central, Lisbon-Suburb, and South. Regional IQs were calculated from a representative sample of 4548 Portuguese school students from 5th to 12th grades. The average IQ and average incomes are highest in Central Lisbon. The results show a positive association between IQs and average regional incomes, as it has been observed in other countries

False vacuum decay: effective one-loop action for pair creation of domain walls

An effective one-loop action built from the soliton field itself for the two-dimensional (2D) problem of soliton pair creation is proposed. The action consists of the usual mass term and a kinetic term in which the simple derivative of the soliton field is replaced by a covariant derivative. In this effective action the soliton charge is treated no longer as a topological charge but as a Noether charge. Using this effective one-loop action, the soliton-antisoliton pair production rate is calculated and one recovers Stone's exponential factor and the prefactor of Kiselev, Selivanov and Voloshin. The results are also valid straightforwardly to the problem of pair creation rate of domain walls in dimensions greater than 2.Comment: 12 pages, Late

The Two-Dimensional Analogue of General Relativity

General Relativity in three or more dimensions can be obtained by taking the limit $\omega\rightarrow\infty$ in the Brans-Dicke theory. In two dimensions General Relativity is an unacceptable theory. We show that the two-dimensional closest analogue of General Relativity is a theory that also arises in the limit $\omega\rightarrow\infty$ of the two-dimensional Brans-Dicke theory.Comment: 8 pages, LaTeX, preprint DF/IST-17.9

Collapsing and static thin massive charged dust shells in a Reissner-Nordstr\"om black hole background in higher dimensions

The problem of a spherically symmetric charged thin shell of dust collapsing gravitationally into a charged Reissner-Nordstr\"om black hole in $d$ spacetime dimensions is studied within the theory of general relativity. Static charged shells in such a background are also analyzed. First a derivation of the equation of motion of such a shell in a $d$-dimensional spacetime is given. Then a proof of the cosmic censorship conjecture in a charged collapsing framework is presented, and a useful constraint which leads to an upper bound for the rest mass of a charged shell with an empty interior is derived. It is also proved that a shell with total mass equal to charge, i.e., an extremal shell, in an empty interior, can only stay in neutral equilibrium outside its gravitational radius. This implies that it is not possible to generate a regular extremal black hole by placing an extremal dust thin shell within its own gravitational radius. Moreover, it is shown, for an empty interior, that the rest mass of the shell is limited from above. Then several types of behavior of oscillatory charged shells are studied. In the presence of a horizon, it is shown that an oscillatory shell always enters the horizon and reemerges in a new asymptotically flat region of the extended Reissner-Nordstr\"om spacetime. On the other hand, for an overcharged interior, i.e., a shell with no horizons, an example showing that the shell can achieve a stable equilibrium position is presented. The results presented have applications in brane scenarios with extra large dimensions, where the creation of tiny higher dimensional charged black holes in current particle accelerators might be a real possibility, and generalize to higher dimensions previous calculations on the dynamics of charged shells in four dimensions.Comment: 21 pages, 2 figure

Thermodynamics of toroidal black holes

The thermodynamical properties of toroidal black holes in the grand canonical ensemble are investigated using York's formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow one to compute the relevant thermodynamical quantities, e.g. thermal energy, entropy and specific heat. This black hole is thermodynamically stable and dominates the grand partition function. This means that there is no phase transition, as the one encountered for spherical black holes.Comment: 11 pages, 2 eps figures, revte

Sub-femtosecond electron bunches created by direct laser acceleration in a laser wakefield accelerator with ionization injection

In this work, we will show through three-dimensional particle-in-cell simulations that direct laser acceleration in laser a wakefield accelerator can generate sub-femtosecond electron bunches. Two simulations were done with two laser pulse durations, such that the shortest laser pulse occupies only a fraction of the first bubble, whereas the longer pulse fills the entire first bubble. In the latter case, as the trapped electrons moved forward and interacted with the high intensity region of the laser pulse, micro-bunching occurred naturally, producing 0.5 fs electron bunches. This is not observed in the short pulse simulation.Comment: AAC 201

Two-Dimensional Black Holes and Planar General Relativity

The Einstein-Hilbert action with a cosmological term is used to derive a new action in 1+1 spacetime dimensions. It is shown that the two-dimensional theory is equivalent to planar symmetry in General Relativity. The two-dimensional theory admits black holes and free dilatons, and has a structure similar to two-dimensional string theories. Since by construction these solutions also solve Einstein's equations, such a theory can bring two-dimensional results into the four-dimensional real world. In particular the two-dimensional black hole is also a black hole in General Relativity.Comment: 11 pages, plainte

The Tolman-Bondi--Vaidya Spacetime: matching timelike dust to null dust

The Tolman-Bondi and Vaidya solutions are two solutions to Einstein equations which describe dust particles and null fluid, respectively. We show that it is possible to match the two solutions in one single spacetime, the Tolman-Bondi--Vaidya spacetime. The new spacetime is divided by a null surface with Tolman-Bondi dust on one side and Vaidya fluid on the other side. The differentiability of the spacetime is discussed. By constructing a specific solution, we show that the metric across the null surface can be at least $C^1$ and the stress-energy tensor is continuous.Comment: 5 pages, no figur