Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes

We compute the {\it exact} equation of state of circular strings in the (2+1) dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting and expanding) strings. The string equation of state has the perfect fluid form $P=(\gamma-1)E,$ with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient $\gamma$ depending on the elliptic modulus. We semi-classically quantize the oscillating circular strings. The string mass is $m=\sqrt{C}/(\pi H\alpha'),\;C$ being the Casimir operator, $C=-L_{\mu\nu}L^{\mu\nu},$ of the $O(3,1)$-dS [$O(2,2)$-AdS] group, and $H$ is the Hubble constant. We find \alpha'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0), and a {\it finite} number of states N_{\mbox{dS}}\approx 0.17/(H^2\alpha') in de Sitter spacetime; m^2_{\mbox{AdS}}\approx 4H^2n^2 (large $n\in N_0$) and N_{\mbox{AdS}}=\infty in anti de Sitter spacetime. The level spacing grows with $n$ in AdS spacetime, while is approximately constant (although larger than in Minkowski spacetime) in dS spacetime. The massive states in dS spacetime decay through tunnel effect and the semi-classical decay probability is computed. The semi-classical quantization of {\it exact} (circular) strings and the canonical quantization of generic string perturbations around the string center of mass strongly agree.Comment: Latex, 26 pages + 2 tables and 5 figures that can be obtained from the authors on request. DEMIRM-Obs de Paris-9404

Web based system architecture for long pulse remote experimentation

Remote experimentation (RE) methods will be essential in next generation fusion devices. Requirements for long pulse RE will be: on-line data visualization, on-line data acquisition processes monitoring and on-line data acquisition systems interactions (start, stop or set-up modifications). Note that these methods are not oriented to real-time control of fusion plant devices. INDRA Sistemas S.A., CIEMAT (Centro de Investigaciones Energéticas Medioambientales y Tecnológicas) and UPM (Universidad Politécnica de Madrid) have designed a specific software architecture for these purposes. The architecture can be supported on the BeansNet platform, whose integration with an application server provides an adequate solution to the requirements. BeansNet is a JINI based framework developed by INDRA, which makes easy the implementation of a remote experimentation model based on a Service Oriented Architecture. The new software architecture has been designed on the basis of the experience acquired in the development of an upgrade of the TJ-II remote experimentation system

String Driven Cosmology and its Predictions

We present a minimal model for the Universe evolution fully extracted from effective String Theory. This model is by its construction close to the standard cosmological evolution, and it is driven selfconsistently by the evolution of the string equation of state itself. The inflationary String Driven stage is able to reach enough inflation, describing a Big Bang like evolution for the metric. By linking this model to a minimal but well established observational information, (the transition times of the different cosmological epochs), we prove that it gives realistic predictions on early and current energy density and its results are compatible with General Relativity. Interestingly enough, the predicted current energy density is found Omega = 1 and a lower limit Omega \geq 4/9 is also found. The energy density at the exit of the inflationary stage also gives | Omega |_{inf}=1. This result shows an agreement with General Relativity (spatially flat metric gives critical energy density) within an inequivalent Non-Einstenian context (string low energy effective equations). The order of magnitude of the energy density-dilaton coupled term at the beginning of the radiation dominated stage agrees with the GUT scale. The predicted graviton spectrum is computed and analyzed without any free parameters. Peaks and asymptotic behaviours of the spectrum are a direct consequence of the dilaton involved and not only of the scale factor evolution. Drastic changes are found at high frequencies: the dilaton produces an increasing spectrum (in no string cosmologies the spectrum is decreasing). Without solving the known problems about higher order corrections and graceful exit of inflation, we find this model closer to the observational Universe than the current available string cosmology scenarii.Comment: LaTex, 22 pages, Lectures delivered at the Chalonge School, Nato ASI: Phase Transitions in the Early Universe: Theory and Observations. To appear in the Proceedings, Editors H. J. de Vega, I. Khalatnikov, N. Sanchez. (Kluwer Pub

Data reduction in the ITMS system through a data acquisition model with self-adaptive sampling rate

Long pulse or steady state operation of fusion experiments require data acquisition and processing systems that reduce the volume of data involved. The availability of self-adaptive sampling rate systems and the use of real-time lossless data compression techniques can help solve these problems. The former is important for continuous adaptation of sampling frequency for experimental requirements. The latter allows the maintenance of continuous digitization under limited memory conditions. This can be achieved by permanent transmission of compressed data to other systems. The compacted transfer ensures the use of minimum bandwidth. This paper presents an implementation based on intelligent test and measurement system (ITMS), a data acquisition system architecture with multiprocessing capabilities that permits it to adapt the system’s sampling frequency throughout the experiment. The sampling rate can be controlled depending on the experiment’s specific requirements by using an external dc voltage signal or by defining user events through software. The system takes advantage of the high processing capabilities of the ITMS platform to implement a data reduction mechanism based in lossless data compression algorithms which are themselves based in periodic deltas

Invariant Regions and Global Asymptotic Stability in an Isothermal Catalyst

A well-known model for the evolution of the (space-dependent) concentration and (lumped) temperature in a porous catalyst is considered. A sequence of invariant regions of the phase space is given, which converges to a globally asymptotically stable region $B$. Quantitative sufficient conditions are obtained for (the region $B$ to consist of only one point and) the problem to have a (unique) globally asymptotically stable steady state

A method for solve integrable A2A_2 spin chains combining different representations

A non homogeneous spin chain in the representations $\{3 \}$ and $\{3^*\}$ of $A_2$ is analyzed. We find that the naive nested Bethe ansatz is not applicable to this case. A method inspired in the nested Bethe ansatz, that can be applied to more general cases, is developed for that chain. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations different from that for a homogeneous chain. A conjecture about the form of the solutions for more general chains is presented. PACS: 75.10.Jm, 05.50+q 02.20 SvComment: PlainTeX, harvmac, 13 pages, 3 figures, to appear in Phys. Rev.

String dynamics in cosmological and black hole backgrounds: The null string expansion

We study the classical dynamics of a bosonic string in the $D$--dimensional flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a perturbative development in the string coordinates around a {\it null} string configuration; the background geometry is taken into account exactly. In the cosmological case we uncouple and solve the first order fluctuations; the string time evolution with the conformal gauge world-sheet $\tau$--coordinate is given by $X^0(\sigma, \tau)=q(\sigma)\tau^{1\over1+2\beta}+c^2B^0(\sigma, \tau)+\cdots$, $B^0(\sigma,\tau)=\sum_k b_k(\sigma)\tau^k$ where $b_k(\sigma)$ are given by Eqs.\ (3.15), and $\beta$ is the exponent of the conformal factor in the Friedmann--Robertson--Walker metric, i.e. $R\sim\eta^\beta$. The string proper size, at first order in the fluctuations, grows like the conformal factor $R(\eta)$ and the string energy--momentum tensor corresponds to that of a null fluid. For a string in the black hole background, we study the planar case, but keep the dimensionality of the spacetime $D$ generic. In the null string expansion, the radial, azimuthal, and time coordinates $(r,\phi,t)$ are $r=\sum_n A^1_{n}(\sigma)(-\tau)^{2n/(D+1)}~,$ $\phi=\sum_n A^3_{n}(\sigma)(-\tau)^{(D-5+2n)/(D+1)}~,$ and $t=\sum_n A^0_{n} (\sigma)(-\tau)^{1+2n(D-3)/(D+1)}~.$ The first terms of the series represent a {\it generic} approach to the Schwarzschild singularity at $r=0$. First and higher order string perturbations contribute with higher powers of $\tau$. The integrated string energy-momentum tensor corresponds to that of a null fluid in $D-1$ dimensions. As the string approaches the $r=0$ singularity its proper size grows indefinitely like $\sim(-\tau)^{-(D-3)/(D+1)}$. We end the paper giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure