Role of Modified Chaplygin Gas in Bianchi Type-I Universe

We have studied the evolution of a homogeneous, anisotropic universe given by a Bianchi type-I cosmological model with modified Chaplygin gas. We have assumed that the equation of state of this modified model is valid from the radiation era to the ΛCMD model. We have used state-finder parameters in characterizing different phase of the model.     

Modelling carrier dynamics and small-signal modulation response in quantum-well lasers

This paper discusses models of carrier dynamics and modulation response in quantum-well lasers. We present a detailed carrier dynamics model that takes into account the different roles played by holes and electrons in such quantum-well lasers, the internal Coulomb field resulting from the mutual interaction of electrons and holes, and the effect of that field on the energy bands. We further address the ability to construct a simpler model that in the limited context of small-signal excitations yields results that are reasonably consistent with those of the detailed model. We compare that simple model to other common simple models and demonstrate the significance of identifying the important parameters in a simple model via self-consistent extraction from detailed calculations. We identify the equilibrium ratio of confined carriers to confinement region carriers, the local capture time and the transport time as the crucial parameters of any simple model.     

Cosmology with a variable Chaplygin gas

We consider a new generalized Chaplygin gas model that includes the original Chaplygin gas model as a special case. In such a model the generalized Chaplygin gas evolves as from dust to quiescence or phantom. We show that the background evolution for the model is equivalent to that for a coupled dark energy model with dark matter. The constraints from the current type Ia supernova data favour a phantom-like Chaplygin gas model.     

A reflexive toy-model for financial market

We propose a reflexive toy model for market dynamics, based on the idea that existing reflexive loops are generated by the conviction, shared by many market operators, that a certain price follows a certain model. Their trading behaviour will therefore increase the probability that the model predictions are in fact fulfilled. We analytically write the equations generating a reflexive loop stemming from a simple linear regression model, and we show that the resulting toy model yields a peculiar intermittent behavior. The presence of two unstable fixed points is apparent from our numerical calculation and the residence-time distribution density in these points asymptotically follows an inverse-power-law tail. The exponent of this tail, as well as the scaling properties of the model output, are close to those stemming from real-price time series.     

Nonsaturation of the J/psi suppression at large transverse energy in the comovers approach

We explore the phenomenology of the localized gravity model of Randall and Sundrum where a 5-dimensional nonfactorizable geometry generates the gauge hierarchy by an exponential function called a warp factor. The Kaluza-Klein (KK) tower of gravitons in this scenario has different properties from those in factorizable models. We derive the KK graviton interactions with the standard model fields and obtain constraints from their direct production at hadron colliders as well as from virtual KK exchanges. We study the KK spectrum in e(+)e(-) annihilation and show how to determine the model parameters if the first KK state is observed.     

A stochastic model of tweet diffusion on the Twitter network

We introduce a stochastic model which describes the information diffusion on the network of a popular web service, Twitter. Restricting our attention to the daily diffusion from a popular account, we model the information diffusion as a random multiplicative process. We justify our model by directly observing the statistics of the multiplicative factors in the Twitter data.     

Mapping the parameter space of a T2-dependent model of water diffusion MR in brain tissue

We present a new model for describing the diffusion-weighted (DW) proton nuclear magnetic resonance signal obtained from normal grey matter. Our model is analytical and, in some respects, is an extension of earlier model schemes. We model tissue as composed of three separate compartments with individual properties of diffusion and transverse relaxation. Our study assumes slow exchange between compartments. We attempt to take cell morphology into account, along with its effect on water diffusion in tissues. Using this model, we simulate diffusion-sensitive MR signals and compare model output to experimental data from human grey matter. In doing this comparison, we perform a global search for good fits in the parameter space of the model. The characteristic nonmonoexponential behavior of the signal as a function of experimental b value is reproduced quite well, along with established values for tissue-specific parameters such as volume fraction, tortuosity and apparent diffusion coefficient. We believe that the presented approach to modeling diffusion in grey matter adds new aspects to the treatment of a longstanding problem.     

Decoherence and dynamical entropy generation in quantum field theory

We formulate a novel approach to decoherence based on neglecting observationally inaccessible correlators. We apply our formalism to a renormalised interacting quantum field theoretical model. Using out-of-equilibrium field theory techniques we show that the Gaussian von Neumann entropy for a pure quantum state increases to the interacting thermal entropy. This quantifies decoherence and thus measures how classical our pure state has become. The decoherence rate is equal to the single particle decay rate in our model. We also compare our approach to existing approaches to decoherence in a simple quantum mechanical model. We show that the entropy following from the perturbative master equation suffers from physically unacceptable secular growth.     

String deformations induced by retardation effects in mesons

The rotating-string model is an effective model of mesons, in which the quark and the antiquark are linked by a straight string. We previously developed a method to estimate the retardation effects in this model, but the string was still kept straight. We now go a step further and show that this kind of retardation effects cause a small deviation of the string from the straight line. We first give general arguments constraining the string shape. Then, we find analytical and numerical solutions for the string deformation induced by retardation effects. We finally discuss the influence of the curved string on the energy spectrum of the model.     

Anomalous vector-boson self-interactions

We study the possibility that vector-boson self-couplings may differ from their standard model values. We find that known constraints from loop effects and from unitary already imply that such deviations are of order 10⁻² or less. Consequently, even if the correct model differs from the standard model and even if the energy scale of new physics is as low as 1 TeV, a direct observation of anomalous couplings is very imporabable in the LEP-200 and Tevatron experiments.     

From regular to growing small-world networks

We propose a growing model which interpolates between one-dimensional regular lattice and small-world networks. The model undergoes an interesting phase transition from large to small worlds. We investigate the structural properties by both theoretical predictions and numerical simulations. Our growing model is a complementarity for the important static Watts-Strogatz network model.     

The equivalence of ensembles for lattice systems: Some examples and a counterexample

We describe the problem of the equivalence of ensembles at the level of states for classical lattice systems. We discuss circumstances where the vanishing of the specific information gain of a sequence of microcanonical measures with respect to a sequence of grand canonical measures implies the equivalence of ensembles. We give a simple derivation of a criterion for the vanishing of the specific information gain in terms of thermodynamic functions. The proof uses ideas from the theory of large deviations but is self-contained. We show how the criterion works in a simple model of a paramagnet and in the Ising model of a ferromagnet in any dimension but fails in the case of the Curie-Weiss mean-field model.     

Broken time‐reversal symmetry scattering at the Anderson transition

We study numerically the statistical properties of some scattering quantities for the Power‐law Banded Random Matrix model at criticality in the absence of time‐reversal symmetry, with a small number of single‐channel leads attached to it. We focus on the average scattering matrix elements, the conductance probability distribution, and the shot noise power as a function of the effective bandwidth b of the model. We find a smooth transition from insulating‐ to metallic‐like behavior in the scattering properties of the model by increasing b. We contrast our results with existing random matrix theory predictions.     

Quantum phase transitions in the bosonic single-impurity Anderson model

We consider a quantum impurity model in which a bosonic impurity level is coupled to a non-interacting bosonic bath, with the bosons at the impurity site subject to a local Coulomb repulsion U. Numerical renormalization group calculations for this bosonic single-impurity Anderson model reveal a zero-temperature phase diagram where Mott phases with reduced charge fluctuations are separated from a Bose-Einstein condensed phase by lines of quantum critical points. We discuss possible realizations of this model, such as atomic quantum dots in optical lattices. Furthermore, the bosonic single-impurity Anderson model appears as an effective impurity model in a dynamical mean-field theory of the Bose-Hubbard model.     

Recovering doping profiles in semiconductor devices with the Boltzmann–Poisson model

We investigate numerically an inverse problem related to the Boltzmann–Poisson system of equations for transport of electrons in semiconductor devices. The objective of the (ill-posed) inverse problem is to recover the doping profile of a device, presented as a source function in the mathematical model, from its current–voltage characteristics. To reduce the degree of ill-posedness of the inverse problem, we proposed to parameterize the unknown doping profile function to limit the number of unknowns in the inverse problem. We showed by numerical examples that the reconstruction of a few low moments of the doping profile is possible when relatively accurate time-dependent or time-independent measurements are available, even though the later reconstruction is less accurate than the former. We also compare reconstructions from the Boltzmann–Poisson (BP) model to those from the classical drift–diffusion-Poisson (DDP) model, assuming that measurements are generated with the BP model. We show that the two type of reconstructions can be significantly different in regimes where drift–diffusion-Poisson equation fails to model the physics accurately. However, when noise presented in measured data is high, no difference in the reconstructions can be observed.     

Quantum phase transitions in the interacting boson model: integrability, level repulsion, and level crossing

We study the quantum phase transition mechanisms that arise in the interacting boson model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.     

Stability and the maintenance of balance following a perturbation from quiet stance

We investigate stability and the maintenance of balance with the use of tools from dynamical systems. In particular we investigate the application of such tools to the study of the ground reaction forces resulting from an athlete being perturbed from quiet stance. We develop a nonlinear model consisting of a set of coupled vector fields for the derivative with respect to time of the angles between the resultant ground reaction forces and the vertical in the anteroposterior and mediolateral directions. This model contains a basin of attraction bound by a closed curve which we call the critical curve. It is only inside this curve that perturbations can be corrected, with the orbit spiraling onto an attractor corresponding to quiet stance. We show how the critical curve and also the strength of the attractor found in the basin of attraction can be fit to model the experimental data (time series) for an individual athlete. We also discuss how our model can be used to identify nonsymmetric behavior caused by muscle imbalances and differences in the ranges of motion on either side of the body.