Time-dependent backgrounds of two dimensional string theory from the c=1c=1 matrix model

The aim of this paper is to use correspondence between solutions in the $c=1$ matrix model collective field theory and coupled dilaton-gravity to a massless scalar field. First, we obtain the incoming and outgoing fluctuations for the time-dependent backgrounds with the lightlike and spacelike boundaries. In the case of spacelike boundaries, we have done here for the first time. Then by using the leg-pole transformations we find corresponding tachyon field in two dimensional string theory for lightlikes and spacelikes boundary.Comment: 10 page

Collective Field Description of Matrix Cosmologies

We study the Das-Jevicki collective field description of arbitrary classical solutions in the c=1 matrix model, which are believed to describe nontrivial spacetime backgrounds in 2d string theory. Our analysis naturally includes the case of a Fermi droplet cosmology: a finite size droplet of Fermi fluid, made up of a finite number of eigenvalues. We analyze properties of the coordinates in which the metric in the collective field theory is trivial, and comment on the form of the interaction terms in these coordinates.Comment: 16 pages, 1 figure. v2: Typos corrected, JHEP styl

Tachyon Backgrounds in 2D String Theory

We consider the construction of tachyonic backgrounds in two-dimensional string theory, focusing on the Sine-Liouville background. This can be studied in two different ways, one within the context of collective field theory and the other via the formalism of Toda integrable systems. The two approaches are seemingly different. The latter involves a deformation of the original inverted oscillator potential while the former does not. We perform a comparison by explicitly constructing the Fermi surface in each case, and demonstrate that the two apparently different approaches are in fact equivalent.Comment: 25 pages, no figure

Energy Quantisation in Bulk Bouncing Tachyon

We argue that the closed string energy in the bulk bouncing tachyon background is to be quantised in a simple manner as if strings were trapped in a finite time interval. We discuss it from three different viewpoints; (1) the timelike continuation of the sinh-Gordon model, (2) the dual matrix model description of the (1+1)-dimensional string theory with the bulk bouncing tachyon condensate, (3) the c_L=1 limit of the timelike Liouville theory with the dual Liouville potential turned on. There appears to be a parallel between the bulk bouncing tachyon and the full S-brane of D-brane decay. We find the critical value \lambda_c of the bulk bouncing tachyon coupling which is analogous to \lambda_o=1/2 of the full S-brane coupling, at which the system is thought to be at the bottom of the tachyon potential.Comment: 25 pages, minor changes, one reference adde

Matrix Model and Time-like Linear Dilaton Matter

We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple fermi surface. Indeed, after a Lorentz transformation, the corresponding 2d spacetime is a conventional linear dilaton background with a time-dependent tachyon field. We show that the tree level scattering amplitudes in the matrix model perfectly agree with those computed in the world-sheet theory. The classical trajectories of fermions correspond to the decaying D-branes in the time-like linear dilaton CFT. We also discuss the ground ring structure. Furthermore, we study the properties of the time-like Liouville theory by applying this matrix model description. We find that its ground ring structure is very similar to that of the minimal string.Comment: 30 pages, harvmac, typos corrected, acknowledgements and comments added(v2), published version (v3

On The Problem of Particle Production in c=1 Matrix Model

We reconsider and analyze in detail the problem of particle production in the time dependent background of $c=1$ matrix model where the Fermi sea drains away at late time. In addition to the moving mirror method, which has already been discussed in hep-th/0403169 and hep-th/0403275, we describe yet another method of computing the Bogolubov coefficients which gives the same result. We emphasize that these Bogolubov coefficients are approximately correct for small value of the deformation parameter. We also study the time evolution of the collective field theory stress-tensor with a special point-splitting regularization. Our computations go beyond the approximation of the previous treatments and are valid at large coordinate distances from the boundary at a finite time and up-to a finite coordinate distance from the boundary at late time. In this region of validity our regularization produces a certain singular term that is precisely canceled by the collective field theory counter term in the present background. The energy and momentum densities fall off exponentially at large distance from the boundary to the values corresponding to the static background. This clearly shows that the radiated energy reaches the asymptotic region signaling the space-time decay.Comment: 37 pages, 5 figures. Section 6 is modified to clarify main accomplishments of the paper including a discussion comparing stress-tensor analysis with those preexisted in literature. Other modifications include minor changes in the text and addition of one reference. Version accepted for publication in JHE

Dynamic Phenotypic Clustering in Noisy Ecosystems

In natural ecosystems, hundreds of species typically share the same environment and are connected by a dense network of interactions such as predation or competition for resources. Much is known about how fixed ecological niches can determine species abundances in such systems, but far less attention has been paid to patterns of abundances in randomly varying environments. Here, we study this question in a simple model of competition between many species in a patchy ecosystem with randomly fluctuating environmental conditions. Paradoxically, we find that introducing noise can actually induce ordered patterns of abundance-fluctuations, leading to a distinct periodic variation in the correlations between species as a function of the phenotypic distance between them; here, difference in growth rate. This is further accompanied by the formation of discrete, dynamic clusters of abundant species along this otherwise continuous phenotypic axis. These ordered patterns depend on the collective behavior of many species; they disappear when only individual or pairs of species are considered in isolation. We show that they arise from a balance between the tendency of shared environmental noise to synchronize species abundances and the tendency for competition among species to make them fluctuate out of step. Our results demonstrate that in highly interconnected ecosystems, noise can act as an ordering force, dynamically generating ecological patterns even in environments lacking explicit niches