Open String Descriptions of Space-like Singularities in Two Dimensional String Theory

The matrix model formulation of two dimensional string theory has been shown to admit time dependent classical solutions whose closed string duals are geodesically incomplete space-times with space-like boundaries. We investigate some aspects of the dynamics of fermions in one such background. We show that even though the background solution appears pathological, the time evolution of the system is smooth in terms of open string degrees of freedom, viz. the fermions. In particular, an initial state of fermions evolves smoothly into a well defined final state over an infinite open string time interval, while the time perceived by closed strings appears to end abruptly. We outline a method of calculating fermion correlators exactly using symmetry properties. The result for the two point function is consistent with the semiclassical picture.Comment: LaTeX 8 eps figures, referenced adde

Theory of weakly nonlinear self sustained detonations

We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced, unsteady, small disturbance, transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multi- dimensional detonations

Quasinormal modes and dispersion relations for quarkonium in a plasma

Recent investigations show that the thermal spectral function of heavy ${b \bar b }$ and ${c \bar c}$ vector mesons can be described using holography. These studies consider a bottom up model that captures the heavy flavour spectroscopy of masses and decay constants in the vacuum and is consistently extended to finite temperature. The corresponding spectral functions provide a picture of the dissociation process in terms of the decrease of the quasi-state peaks with temperature. Another related tool that provides important information about the thermal behaviour is the analysis of the quasinormal modes. They are field solutions in a curved background assumed to represent, in gauge/gravity duality, quasi-particle states in a thermal medium. The associated complex frequencies are related to the thermal mass and width. We present here the calculation of quasinormal modes for charmonium and bottomonium using the holographic approach. The temperature dependence of mass and thermal width are investigated. Solutions corresponding to heavy mesons moving into the plasma are also studied. They provide the dependence of the real and imaginary parts of the frequency with the quasi-particle momenta, the so called dispersion relations.Comment: V2: enlarged version with clarifications, more comparison with previous articles and additional references included. 11 figures, 2 tables, 62 references. Version accepted for publication in JHE

Bottomonium dissociation in a finite density plasma

We present a holographic description of the thermal behavior of $b \bar b$ heavy vector mesons inside a plasma at finite temperature and density. The meson dissociation in the medium is represented by the decrease in the height of the spectral function peaks. In order to find a description for the evolution of the quasi-states with temperature and chemical potential it is crucial to use a model that is consistent with the decay constant behavior. The reason is that the height of a spectral function peak is related to the value of the zero temperature decay constant of the corresponding particle. AdS/QCD holographic models are in general not consistent with the observation that decay constants of heavy vector mesons decrease with radial excitation level. However, it was recently shown that using a soft wall background and calculating the correlation functions at a finite position of anti-de Sitter space, associated with an ultraviolet energy scale, it is possible to describe the observed behavior. Here we extend this proposal to the case of finite temperature $T$ and chemical potential $\mu$. A clear picture of the dissociation of bottomonium states as a function of $\mu$ and $T$ emerges from the spectral function. The energy scales where the change in chemical potential leads to changes in the thermal properties of the mesons is consistent with QCD expectations.Comment: In V3: errors in reference citations corrected. Version published in Physics Letters B. 15 pages, 3 figure