Adiabatic interpretation of particle creation in a de Sitter universe

The choice of vacuum state for a quantum scalar field propagating in a de Sitter spacetime (massive and arbitrarily coupled to the gravitational field) is discussed. The problem of finite-time initial conditions for the mode functions is analyzed, as well as how these determine the vacuum state of the quantum system. The principle guiding the choice of vacuum state is the following: one wants the vacuum contribution to the energy-momentum tensor to contain all the ultraviolet divergent terms, so that the particle creation terms are finite, and covariantly conserved. There is a suitable set of modes (instantaneous adiabatic basis) in which this splitting of the expectation value of the energy-momentum tensor can be carried out. Numerical results are presented for different finite-time initial conditions (m = 0.6, {zeta} = 1/6). The nature of the particle creation effect is described and its relationship to the concept of a horizon crossing time is shown. These numerical results imply that back-reaction can be important and should be the subject of further research

Diffusion in a Disk with a Circular Inclusion

We consider diffusion in a disk, representing a cell with a circular interior compartment. Using bipolar coordinates, we perform exact calculations, not restricted by the size or location of the intracellular compartment. We find Green functions, hitting densities and mean times to move from the compartment to the cellular surface and vice versa. For molecules with diffusivity $D$, mean times are proportional to $R^2/D$, where $R$ is the radius of the cell. We find explicit expressions for the dependence on $a^2$ (the fraction of the cell occupied by the intracellular compartment) and on the displacement of the compartment from the center of the cell. We consider distributions of initial conditions that are (i) uniform on the nuclear surface, (ii) uniform on the cellular surface, or (iii) given by the hitting density of particles diffusing from the nuclear to the cellular surface

Sampling from T cell receptor repertoires

Modern single-cell sequencing techniques allow the unique TCR signature of each of a sample of hundreds of T cells to be read. The mathematical challenge is to extrapolate from the properties of a sample to those of the whole repertoire of an individual, made up of many millions of T cells. We consider the distribution of the number of repeats of any TCR in a sample, the mean number of samples needed to find a repeat with probability one half, and the relationship between the true distribution of clonal sizes and that experimentally observed in the sample. We consider two special cases, where the distribution of clonal sizes is geometric, and where a subset of clones in the repertoire is expanded

Sonoluminescence as a QED vacuum effect: Probing Schwinger's proposal

Several years ago Schwinger proposed a physical mechanism for sonoluminescence in terms of photon production due to changes in the properties of the quantum-electrodynamic (QED) vacuum arising from a collapsing dielectric bubble. This mechanism can be re-phrased in terms of the Casimir effect and has recently been the subject of considerable controversy. The present paper probes Schwinger's suggestion in detail: Using the sudden approximation we calculate Bogolubov coefficients relating the QED vacuum in the presence of the expanded bubble to that in the presence of the collapsed bubble. In this way we derive an estimate for the spectrum and total energy emitted. We verify that in the sudden approximation there is an efficient production of photons, and further that the main contribution to this dynamic Casimir effect comes from a volume term, as per Schwinger's original calculation. However, we also demonstrate that the timescales required to implement Schwinger's original suggestion are not physically relevant to sonoluminescence. Although Schwinger was correct in his assertion that changes in the zero-point energy lead to photon production, nevertheless his original model is not appropriate for sonoluminescence. In other works (see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/9905034) we have developed a variant of Schwinger's model that is compatible with the physically required timescales.Comment: 18 pages, ReV_TeX 3.2, 9 figures. Major revisions: This document is now limited to providing a probe of Schwinger's original suggestion for sonoluminescence. For details on our own variant of Schwinger's ideas see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/990503

A new mechanism shapes the naïve CD8+ T cell repertoire: the selection for full diversity

During thymic T cell differentiation, TCR repertoires are shaped by negative, positive and agonist selection. In the thymus and in the periphery, repertoires are also shaped by strong inter-clonal and intra-clonal competition to survive death by neglect. Understanding the impact of these events on the T cell repertoire requires direct evaluation of TCR expression in peripheral naïve T cells. Several studies have evaluated TCR diversity, with contradictory results. Some of these studies had intrinsic technical limitations since they used material obtained from T cell pools, preventing the direct evaluation of clone sizes. Indeed with these approaches, identical TCRs may correspond to different cells expressing the same receptor, or to several amplicons from the same T cell. We here overcame this limitation by evaluating TCRB expression in individual naïve CD8+ T cells. Of the 2269 Tcrb sequences we obtained from 13 mice, 99% were unique. Mathematical analysis of this data showed that the average number of naïve peripheral CD8+ T cells expressing the same TCRB is 1.1 cell. Since TCRA co-expression studies could only increase repertoire diversity, these results reveal that the number of naïve T cells with unique TCRs approaches the number of naïve cells. Since thymocytes undergo multiple rounds of divisions after TCRB rearrangement; and 3–5% of thymocytes survive thymic selection events; the number of cells expressing the same TCRB was expected to be much higher. Thus, these results suggest a new repertoire selection mechanism, which strongly selects for full TCRB diversity