Resumming the large-N approximation for time evolving quantum systems

In this paper we discuss two methods of resumming the leading and next to leading order in 1/N diagrams for the quartic O(N) model. These two approaches have the property that they preserve both boundedness and positivity for expectation values of operators in our numerical simulations. These approximations can be understood either in terms of a truncation to the infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a particular two-particle irreducible vacuum energy graph in the effective action of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the case of quantum mechanics where the Lagrangian is $L(x,\dot{x}) = (1/2) \sum_{i=1}^{N} \dot{x}_i^2 - (g/8N) [ \sum_{i=1}^{N} x_i^2 - r_0^2 ]^{2}$. The key to these approximations is to treat both the $x$ propagator and the $x^2$ propagator on similar footing which leads to a theory whose graphs have the same topology as QED with the $x^2$ propagator playing the role of the photon. The bare vertex approximation is obtained by replacing the exact vertex function by the bare one in the exact Schwinger-Dyson equations for the one and two point functions. The second approximation, which we call the dynamic Debye screening approximation, makes the further approximation of replacing the exact $x^2$ propagator by its value at leading order in the 1/N expansion. These two approximations are compared with exact numerical simulations for the quantum roll problem. The bare vertex approximation captures the physics at large and modest $N$ better than the dynamic Debye screening approximation.Comment: 30 pages, 12 figures. The color version of a few figures are separately liste

An improved time-dependent Hartree-Fock approach for scalar \phi^4 QFT

The $\lambda \phi^4$ model in a finite volume is studied within a non-gaussian Hartree-Fock approximation (tdHF) both at equilibrium and out of equilibrium, with particular attention to the structure of the ground state and of certain dynamical features in the broken symmetry phase. The mean-field coupled time-dependent Schroedinger equations for the modes of the scalar field are derived and the suitable procedure to renormalize them is outlined. A further controlled gaussian approximation of our tdHF approach is used in order to study the dynamical evolution of the system from non-equilibrium initial conditions characterized by a uniform condensate. We find that, during the slow rolling down, the long-wavelength quantum fluctuations do not grow to a macroscopic size but do scale with the linear size of the system, in accordance with similar results valid for the large $N$ approximation of the O(N) model. This behavior undermines in a precise way the gaussian approximation within our tdHF approach, which therefore appears as a viable mean to correct an unlikely feature of the standard HF factorization scheme, such as the so-called ``stopping at the spinodal line'' of the quantum fluctuations. We also study the dynamics of the system in infinite volume with particular attention to the asymptotic evolution in the broken symmetry phase. We are able to show that the fixed points of the evolution cover at most the classically metastable part of the static effective potential.Comment: Accepted for publication on Phys. Rev.

Time evolution of the chiral phase transition during a spherical expansion

We examine the non-equilibrium time evolution of the hadronic plasma produced in a relativistic heavy ion collision, assuming a spherical expansion into the vacuum. We study the $O(4)$ linear sigma model to leading order in a large-$N$ expansion. Starting at a temperature above the phase transition, the system expands and cools, finally settling into the broken symmetry vacuum state. We consider the proper time evolution of the effective pion mass, the order parameter $\langle \sigma \rangle$, and the particle number distribution. We examine several different initial conditions and look for instabilities (exponentially growing long wavelength modes) which can lead to the formation of disoriented chiral condensates (DCCs). We find that instabilities exist for proper times which are less than 3 fm/c. We also show that an experimental signature of domain growth is an increase in the low momentum spectrum of outgoing pions when compared to an expansion in thermal equilibrium. In comparison to particle production during a longitudinal expansion, we find that in a spherical expansion the system reaches the ``out'' regime much faster and more particles get produced. However the size of the unstable region, which is related to the domain size of DCCs, is not enhanced.Comment: REVTex, 20 pages, 8 postscript figures embedded with eps

Comparison of optical model results from a microscopic Schr\"odinger approach to nucleon-nucleus elastic scattering with those from a global Dirac phenomenology

Comparisons are made between results of calculations for intermediate energy nucleon-nucleus scattering for 12C, 16O, 40Ca, 90Zr, and 208Pb, using optical potentials obtained from global Dirac phenomenology and from a microscopic Schr\"odinger model. Differential cross sections and spin observables for scattering from the set of five nuclei at 65 MeV and 200 MeV have been studied to assess the relative merits of each approach. Total reaction cross sections from proton-nucleus and total cross sections from neutron-nucleus scattering have been evaluated and compared with data for those five targets in the energy range 20 MeV to 800 MeV. The methods of analyses give results that compare well with experimental data in those energy regimes for which the procedures are suited.Comment: 22 pages, 12 figure

The Importance of DNA Repair in Tumor Suppression

The transition from a normal to cancerous cell requires a number of highly specific mutations that affect cell cycle regulation, apoptosis, differentiation, and many other cell functions. One hallmark of cancerous genomes is genomic instability, with mutation rates far greater than those of normal cells. In microsatellite instability (MIN tumors), these are often caused by damage to mismatch repair genes, allowing further mutation of the genome and tumor progression. These mutation rates may lie near the error catastrophe found in the quasispecies model of adaptive RNA genomes, suggesting that further increasing mutation rates will destroy cancerous genomes. However, recent results have demonstrated that DNA genomes exhibit an error threshold at mutation rates far lower than their conservative counterparts. Furthermore, while the maximum viable mutation rate in conservative systems increases indefinitely with increasing master sequence fitness, the semiconservative threshold plateaus at a relatively low value. This implies a paradox, wherein inaccessible mutation rates are found in viable tumor cells. In this paper, we address this paradox, demonstrating an isomorphism between the conservatively replicating (RNA) quasispecies model and the semiconservative (DNA) model with post-methylation DNA repair mechanisms impaired. Thus, as DNA repair becomes inactivated, the maximum viable mutation rate increases smoothly to that of a conservatively replicating system on a transformed landscape, with an upper bound that is dependent on replication rates. We postulate that inactivation of post-methylation repair mechanisms are fundamental to the progression of a tumor cell and hence these mechanisms act as a method for prevention and destruction of cancerous genomes.Comment: 7 pages, 5 figures; Approximation replaced with exact calculation; Minor error corrected; Minor changes to model syste

Skylab imagery: Application to reservoir management in New England

The author has identified the following significant results. S190B imagery is superior to the LANDSAT imagery for land use mapping and is as useful for level 1 and 2 land use mapping as the RB-57/RC8 high altitude imagery. Detailed land use mapping at levels 3 and finer from satellite imagery requires better resolution. For evaluating factors that are required to determine volume runoff potentials in a watershed, the S190B imagery was found to be as useful as the RB-57/RC8 high altitude aircraft imagery

Chaos in effective classical and quantum dynamics

We investigate the dynamics of classical and quantum N-component phi^4 oscillators in the presence of an external field. In the large N limit the effective dynamics is described by two-degree-of-freedom classical Hamiltonian systems. In the classical model we observe chaotic orbits for any value of the external field, while in the quantum case chaos is strongly suppressed. A simple explanation of this behaviour is found in the change in the structure of the orbits induced by quantum corrections. Consistently with Heisenberg's principle, quantum fluctuations are forced away from zero, removing in the effective quantum dynamics a hyperbolic fixed point that is a major source of chaos in the classical model.Comment: 6 pages, RevTeX, 5 figures, uses psfig, changed indroduction and conclusions, added reference

Microwave resonances of the bubble phases in 1/4 and 3/4 filled higher Landau levels

We have measured the diagonal conductivity in the microwave regime of an ultrahigh mobility two dimensional electron system. We find a sharp resonance in Re[sigma_{xx}] versus frequency when nu > 4 and the partial filling of the highest Landau level, nu^*, is ~ 1/4 or 3/4 and temperatures < 0.1 K. The resonance appears for a range of nu^* from 0.20 to 0.37 and again from 0.62 to 0.82. the peak frequency, f_{pk} changes from ~ 500 to ~ 150 as nu^* = 1/2 is approached. This range of f_{pk} shows no dependence on nu where the resonance is observed. The quality factor, Q, of the resonance is maximum at ~ nu^* = 0.25 and 0.74. We interpret the resonance as due to a pinning mode of the bubble phase crystal.Comment: revtex 4, 3 figures, minor corrections made. Accepted by pr