Abstract:
The number of fixed mutations accumulated in an evolving population often displays a variance that is significantly larger than the mean (the overdispersed molecular clock). By examining a generic evolutionary process on a neutral network of high-fitness genotypes, we establish a formalism for computing all cumulants of the full probability distribution of accumulated mutations in terms of graph properties of the neutral network, and use the formalism to prove overdispersion of the molecular clock. We further show that significant overdispersion arises naturally in evolution when the neutral network is highly sparse, exhibits large global fluctuations in neutrality, and small local fluctuations in neutrality. The results are also relevant for elucidating the topological structure of a neutral network from empirical measurements of the substitution process.

Abstract:
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are studied: pure duplication growth, and two two-parameter models in which duplication forms one element of the growth dynamics. A power-law degree distribution is found to emerge in all three models. However, the parameter space of the latter two models is characterized by a range of parameter values for which duplication is the predominant mechanism of graph growth. For parameter values that lie in this ``duplication-dominated'' regime, it is shown that the degree distribution either approaches zero asymptotically, or approaches a non-zero power-law degree distribution very slowly. In either case, the approach to the true asymptotic degree distribution is characterized by a dependence of the scaling exponent on properties of the initial degree distribution. It is therefore conjectured that duplication-dominated, scale-free networks may contain identifiable remnants of their early structure. This feature is inherited from the idealized model of pure duplication growth, for which the exact finite-size degree distribution is found and its asymptotic properties studied.

Abstract:
In a new model that we proposed, nonperturbative vacuum contributions to the effective action of a free quantized massive scalar field lead to a cosmological solution in which the scalar curvature becomes constant after a time $t_j$ (when the redshift $z \sim 1$) that depends on the mass of the scalar field and its curvature coupling. This spatially-flat solution implies an accelerating universe at the present time and gives a good one-parameter fit to high-redshift Type Ia supernovae (SNe-Ia) data, and the present age and energy density of the universe. Here we show that the imaginary part of the nonperturbative curvature term that causes the cosmological acceleration, implies a particle production rate that agrees with predictions of other methods and extends them to non-zero mass fields. The particle production rate is very small after the transition and is not expected to alter the nature of the cosmological solution. We also show that the equation of state of our model undergoes a transition at $t_j$ from an equation of state dominated by non-relativistic pressureless matter (without a cosmological constant) to an effective equation of state of mixed radiation and cosmological constant, and we derive the equation of state of the vacuum. Finally, we explain why nonperturbative vacuum effects of this ultralow-mass particle do not significantly change standard early universe cosmology.

Abstract:
We show that the vacuum energy of a free quantized field of very low mass can significantly alter the recent expansion of the universe. The effective action of the theory is obtained from a non-perturbative sum of scalar curvature terms in the propagator. We numerically investigate the semiclassical Einstein equations derived from it. As a result of non-perturbative quantum effects, the scalar curvature of the matter-dominated universe stops decreasing and approaches a constant value. The universe in our model evolves from an open matter-dominated epoch to a mildly inflating de Sitter expansion. The Hubble constant during the present de Sitter epoch, as well as the time at which the transition occurs from matter-dominated to de Sitter expansion, are determined by the mass of the field and by the present matter density. The model provides a theoretical explanation of the observed recent acceleration of the universe, and gives a good fit to data from high-redshift Type Ia supernovae, with a mass of about 10^{-33} eV, and a current ratio of matter density to critical density, Omega_0 <0.4 . The age of the universe then follows with no further free parameters in the theory, and turns out to be greater than 13 Gyr. The model is spatially open and consistent with the possibility of inflation in the very early universe. Furthermore, our model arises from the standard renormalizable theory of a free quantum field in curved spacetime, and does not require a cosmological constant or the associated fine-tuning.

Abstract:
We show that there exists a choice of scalar field modes, such that the evolution of the quantum field in the zero-mass and large-mass limits is consistent with the Einstein equations for the background geometry. This choice of modes is also consistent with zero production of these particles and thus corresponds to a preferred vacuum state preserved by the evolution. In the zero-mass limit, we find that the quantum field equation implies the Einstein equation for the scale factor of a radiation-dominated universe; in the large-mass case, it implies the corresponding Einstein equation for a matter-dominated universe. Conversely, if the classical radiation-dominated or matter-dominated Einstein equations hold, there is no production of scalar particles in the zero and large mass limits, respectively. The suppression of particle production in the large mass limit is over and above the expected suppression at large mass. Our results hold for a certain class of conformally ultrastatic background geometries and therefore generalize previous results by one of us for spatially flat Robertson-Walker background geometries. In these geometries, we find that the temporal part of the graviton equations reduces to the temporal equation for a massless minimally coupled scalar field, and therefore the results for massless particle production hold also for gravitons. Within the class of modes we study, we also find that the requirement of zero production of massless scalar particles is not consistent with a non-zero cosmological constant. Possible implications are discussed.

Abstract:
In recent work, we showed that non-perturbative vacuum effects of a very low mass particle could induce, at a redshift of order 1, a transition from a matter-dominated to an accelerating universe. In that work, we used the simplification of a sudden transition out of the matter-dominated stage and were able to fit the Type Ia supernovae (SNe-Ia) data points with a spatially-open universe. In the present work, we find a more accurate, smooth {\it spatially-flat} analytic solution to the quantum-corrected Einstein equations. This solution gives a good fit to the SNe-Ia data with a particle mass parameter $m_h$ in the range $6.40 \times 10^{-33}$ eV to $7.25 \times 10^{-33}$ eV. It follows that the ratio of total matter density (including dark matter) to critical density, $\O_0$, is in the range 0.58 to 0.15, and the age $t_0$ of the universe is in the range $8.10 h^{-1}$ Gyr to $12.2 h^{-1}$ Gyr, where $h$ is the present value of the Hubble constant, measured as a fraction of the value 100 km/(s Mpc). This spatially-flat model agrees with estimates of the position of the first acoustic peak in the small angular scale fluctuations of the cosmic background radiation, and with light-element abundances of standard big-bang nucleosynthesis. Our model has only a single free parameter, $m_h$, and does not require that we live at a special time in the evolution of the universe.

Abstract:
We show that nonperturbative vacuum effects can produce a vacuum-driven transition from a matter-dominated universe to one in which the effective equation of state is that of radiation plus cosmological constant. The actual material content of the universe after the transition remains that of non-relativistic matter. This metamorphosis of the equation of state can be traced to nonperturbative vacuum effects that cause the scalar curvature to remain nearly constant at a well-defined value after the transition, and is responsible for the observed acceleration of the recent expansion of the universe.

Abstract:
Mesoscopic physics deals with three fundamental issues: quantum coherence, fluctuations and correlations. Here we analyze these issues for atom optics, using a simplified model of an assembly of atoms (or detectors, which are particles with some internal degree of freedom) moving in arbitrary trajectories in a quantum field. Employing the influence functional formalism, we study the self-consistent effect of the field on the atoms, and their mutual interactions via coupling to the field. We derive the coupled Langevin equations for the atom assemblage and analyze the relation of dissipative dynamics of the atoms with the correlation and fluctuations of the quantum field. This provides a useful theoretical framework for analysing the coherent properties of atom-field systems.

Abstract:
The thermal radiance felt by a uniformly accelerated detector/oscillator/atom--the Unruh effect-- is often mistaken to be some emitted radiation detectable by an observer/probe/sensor. Here we show by an explicit calculation of the energy momentum tensor of a quantum scalar field that, at least in 1+1 dimension, while a polarization cloud is found to exist around the particle trajectory, there is no emitted radiation from a uniformly accelerated oscillator in equilibrium conditions. Under nonequilibrium conditions which can prevail for non-uniformly accelerated trajectories or before the atom or oscillator reaches equilibrium, there is conceivably radiation emitted, but that is not what Unruh effect entails.

Abstract:
In analyzing the nature of thermal radiance experienced by an accelerated observer (Unruh effect), an eternal black hole (Hawking effect) and in certain types of cosmological expansion, one of us proposed a unifying viewpoint that these can be understood as arising from the vacuum fluctuations of the quantum field being subjected to an exponential scale transformation. This viewpoint, together with our recently developed stochastic theory of particle-field interaction understood as quantum open systems described by the influence functional formalism, can be used to address situations where the spacetime possesses an event horizon only asymptotically, or none at all. Examples studied here include detectors moving at uniform acceleration only asymptotically or for a finite time, a moving mirror, and a collapsing mass. We show that in such systems radiance indeed is observed, albeit not in a precise Planckian spectrum. The deviation therefrom is determined by a parameter which measures the departure from uniform acceleration or from exact exponential expansion. These results are expected to be useful for the investigation of non-equilibrium black hole thermodynamics and the linear response regime of backreaction problems in semiclassical gravity.