Two-dimensional Toy Model Research Articles

Kink-boundary collisions in a two-dimensional scalar field theory

In a two-dimensional toy model, motivated from five-dimensional heterotic M-theory, we study the collision of scalar field kinks with boundaries. By numerical simulation of the full two-dimensional theory, we find that the kink is always inelastically reflected with a model-independent fraction of its kinetic energy converted into radiation. We show that the reflection can be analytically understood as a fluctuation around the scalar field vacuum. This picture suggests the possibility of spontaneous emission of kinks from the boundary due to small perturbations in the bulk. We verify this picture numerically by showing that the radiation emitted from the collision of an initial single kink eventually leads to a bulk populated by many kinks. Consequently, processes changing the boundary charges are practically unavoidable in this system. We speculate that the system has a universal final state consisting of a stack of kinks, their number being determined by the initial energy.

A dynamical approach to protein folding.

In this paper we show that a dynamical description of the protein folding process provides an effective representation of equilibrium properties and it allows for a direct investigation of the mechanisms ruling the approach towards the native configuration. The results reported in this paper have been obtained fora two-dimensional toy-model of aminoacid sequences, whosenative configurations were previously determined byMonte Carlo techniques.The somewhat controversial scenario emerging from the comparison among different thermodynamical indicators is definitely better resolved with the help of a truly dynamical description. In particular,we are able to identify the metastable states visited during the folding process by monitoring the temporal evolution of the `long-range' potentialenergy. Moreover, the resulting dynamical scenario is consistent with the picture arising from a reconstruction of the energy landscape in the vicinity of the global minimum. This suggests that the introduction of efficient `static' indicators too should properly account for the complex `orography' of the landscape.

Induced Chern-Simons terms

We examine the claim that the effective action of four-dimensional SU(2)_L gauge theory at high and low temperature contains a three-dimensional Chern-Simons term with coefficient being the chemical potential for baryon number. We perform calculations in a two-dimensional toy model and find that the existence of the term is rather subtle.

A quantum S-matrix for two-dimensional black hole formation and evaporation

We study the black hole information paradox in the context of a two-dimensional toy model given by dilaton gravity coupled to N massless scalar fields. After making the model well-defined by imposing reflecting boundary conditions at a critical value of the dilaton field, we quantize the theory and define a quantum S-matrix for the case that N = 24. This S-matrix maps pure initial states to pure out-states and we further argue that in the semiclassical regime it describes the formation and subsequent Hawking evaporation of two-dimensional black holes. Finally, we note an interesting correspondence between the dilaton gravity S-matrix and that of the c = 1 matrix model.

Gauge invariance and anomalous theories at finite fermionic density.

We investigate the issue of stability of anomalous matter at finite fermionic density using a two-dimensional toy model. In particular, we pay careful attention to the issue of gauge invariance. We find that, contrary to some recent claims, the effective free energy (obtained by integrating out the fermions) cannot be obtained by the simple inclusion of a Chern-Simons term multiplying the fermionic chemical potential. We obtain some conditions for stability of anomalous charges when some finite density of conserved charge is present as well as for the neutral case. We also show that, under reasonable conditions, no sphaleron-type solution can exist in the toy model unless the anomalous charge density vanishes. We argue that this could be the case for more realistic models as well.