Entanglement generation in relativistic quantum fields

We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the mode decompositions of observers in different regions of curved spacetimes, and describe observers moving along non-stationary trajectories. We focus on a quantum optical example in a cavity quantum electrodynamics setting: an uncharged scalar field within a cavity provides a model for an optical resonator, in which entanglement is created by non-uniform acceleration. We show that the amount of generated entanglement can be magnified by initial single-mode squeezing, for which we provide an explicit formula. Applications to quantum fields in curved spacetimes, such as an expanding universe, are discussed.Comment: 8 pages, 2 figures, Ivette Fuentes previously published as Ivette Fuentes-Guridi and Ivette Fuentes-Schuller; v2: published version (online), to appear in the J. Mod. Opt. Special Issue on the Physics of Quantum Electronic

Stationary distributions of sums of marginally chaotic variables as renormalization group fixed points

We determine the limit distributions of sums of deterministic chaotic variables in unimodal maps assisted by a novel renormalization group (RG) framework associated to the operation of increment of summands and rescaling. In this framework the difference in control parameter from its value at the transition to chaos is the only relevant variable, the trivial fixed point is the Gaussian distribution and a nontrivial fixed point is a multifractal distribution with features similar to those of the Feigenbaum attractor. The crossover between the two fixed points is discussed and the flow toward the trivial fixed point is seen to consist of a sequence of chaotic band mergers.Comment: 7 pages, 2 figures, to appear in Journal of Physics: Conf.Series (IOP, 2010

Seeding hESCs to achieve optimal colony clonality

Human embryonic stem cells (hESCs) and induced pluripotent stem cells (iPSCs) have promising clinical applications which often rely on clonally-homogeneous cell populations. To achieve this, it is important to ensure that each colony originates from a single founding cell and to avoid subsequent merging of colonies during their growth. Clonal homogeneity can be obtained with low seeding densities; however, this leads to low yield and viability. It is therefore important to quantitatively assess how seeding density affects clonality loss so that experimental protocols can be optimised to meet the required standards. Here we develop a quantitative framework for modelling the growth of hESC colonies from a given seeding density based on stochastic exponential growth. This allows us to identify the timescales for colony merges and over which colony size no longer predicts the number of founding cells. We demonstrate the success of our model by applying it to our own experiments of hESC colony growth; while this is based on a particular experimental set-up, the model can be applied more generally to other cell lines and experimental conditions to predict these important timescales

Correlated random walks of human embryonic stem cells in vitro

We perform a detailed analysis of the migratory motion of human embryonic stem cells in two-dimensions, both when isolated and in close proximity to another cell, recorded with time-lapse microscopic imaging. We show that isolated cells tend to perform an unusual locally anisotropic walk, moving backwards and forwards along a preferred local direction correlated over a timescale of around 50 min and aligned with the axis of the cell elongation. Increasing elongation of the cell shape is associated with increased instantaneous migration speed. We also show that two cells in close proximity tend to move in the same direction, with the average separation of m or less and the correlation length of around 25 μm, a typical cell diameter. These results can be used as a basis for the mathematical modelling of the formation of clonal hESC colonies

Key environmental stress biomarker candidates for the optimisation of chemotherapy treatment of leukaemia

The impact of fluctuations of environmental parameters such as oxygen and starvation on the evolution of leukaemia is analysed in the current review. These fluctuations may occur within a specific patient (in different organs) or across patients (individual cases of hypoglycaemia and hyperglycaemia). They can be experienced as stress stimuli by the cancerous population, leading to an alteration of cellular growth kinetics, metabolism and further resistance to chemotherapy. Therefore, it is of high importance to elucidate key mechanisms that affect the evolution of leukaemia under stress. Potential stress response mechanisms are discussed in this review. Moreover, appropriate cell biomarker candidates related to the environmental stress response and/or further resistance to chemotherapy are proposed. Quantification of these biomarkers can enable the combination of macroscopic kinetics with microscopic information, which is specific to individual patients and leads to the construction of detailed mathematical models for the optimisation of chemotherapy. Due to their nature, these models will be more accurate and precise (in comparison to available macroscopic/black box models) in the prediction of responses of individual patients to treatment, as they will incorporate microscopic genetic and/or metabolic information which is patient-specific.peer-reviewe

Renormalization group structure for sums of variables generated by incipiently chaotic maps

We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated to the operation of increment of summands and rescaling. In this structure - where the only relevant variable is the difference in control parameter from its value at the transition to chaos - the trivial fixed point is the Gaussian distribution and a novel nontrivial fixed point is a multifractal distribution that emulates the Feigenbaum attractor, and is universal in the sense of the latter. The crossover between the two fixed points is explained and the flow toward the trivial fixed point is seen to be comparable to the chaotic band merging sequence. We discuss the nature of the Central Limit Theorem for deterministic variables.Comment: 14 pages, 5 figures, to appear in Journal of Statistical Mechanic