Impulse Correlation for Partially Filled Detonation Tubes

The effect of nozzles on the impulse obtained from a detonation tube of circular cross section has been the focus of many experimental and numerical studies. In these cases, the simplified detonation tube is closed at one end (forming the thrust surface) and open at the other end, enabling the attachment of an extension. A flowfield analysis of a detonation tube with an extension requires considering unsteady wave interactions making analytical and accurate numerical predictions difficult (especially in complicated extension geometries). To predict the impulse obtained from a detonation tube with an extension (considered a partially filled detonation tube), we utilize data from other researchers to generate a partial-fill correlation

Chaos in Time Dependent Variational Approximations to Quantum Dynamics

Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational approximation to the dynamics of a quantum system based on the Dirac action principle leads to a classical Hamiltonian dynamics for the variational parameters. Since this Hamiltonian is generically nonlinear and nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exact quantum evolution. We then restrict attention to a system of two biquadratically coupled quantum oscillators and study two variational schemes, the leading order large N (four canonical variables) and Hartree (six canonical variables) approximations. The chaos seen in the approximate dynamics is an artifact of the approximations: this is demonstrated by the fact that its onset occurs on the same characteristic time scale as the breakdown of the approximations when compared to numerical solutions of the time-dependent Schrodinger equation.Comment: 10 pages (12 figures), RevTeX (plus macro), uses epsf, minor typos correcte

Exact and approximate dynamics of the quantum mechanical O(N) model

We study a quantum dynamical system of N, O(N) symmetric, nonlinear oscillators as a toy model to investigate the systematics of a 1/N expansion. The closed time path (CTP) formalism melded with an expansion in 1/N is used to derive time evolution equations valid to order 1/N (next-to-leading order). The effective potential is also obtained to this order and its properties areelucidated. In order to compare theoretical predictions against numerical solutions of the time-dependent Schrodinger equation, we consider two initial conditions consistent with O(N) symmetry, one of them a quantum roll, the other a wave packet initially to one side of the potential minimum, whose center has all coordinates equal. For the case of the quantum roll we map out the domain of validity of the large-N expansion. We discuss unitarity violation in the 1/N expansion; a well-known problem faced by moment truncation techniques. The 1/N results, both static and dynamic, are also compared to those given by the Hartree variational ansatz at given values of N. We conclude that late-time behavior, where nonlinear effects are significant, is not well-described by either approximation.Comment: 16 pages, 12 figrures, revte

Non-equilibrium dynamics in quantum field theory at high density: the tsunami

The dynamics of a dense relativistic quantum fluid out of thermodynamic equilibrium is studied in the framework of the Phi^4 scalar field theory in the large N limit. The time evolution of a particle distribution in momentum space (the tsunami) is computed. The effective mass felt by the particles in such a high density medium equals the tree level mass plus the expectation value of the squared field. The case of negative tree level squared mass is particularly interesting. In such case dynamical symmetry restoration as well as dynamical symmetry breaking can happen. Furthermore, the symmetry may stay broken with vanishing asymptotic squared mass showing the presence of out of equilibrium Goldstone bosons. We study these phenomena and identify the set of initial conditions that lead to each case. We compute the equation of state which turns to depend on the initial state. Although the system does not thermalize, the equation of state for asymptotically broken symmetry is of radiation type. We compute the correlation functions at equal times. The two point correlator for late times is the sum of different terms. One stems from the initial particle distribution. Another term accounts for the out of equilibrium Goldstone bosons created by spinodal unstabilities when the symmetry is asymptotically broken.Both terms are of the order of the inverse of the coupling for distances where causal signals can connect the two points. The contribution of the out of equilibrium Goldstones exhibits scaling behaviour in a generalized sense.Comment: LaTex, 49 pages, 15 .ps figure

The Vector Analyzing Power in Elastic Electron-Nucleus Scattering

The vector analyzing power A_n is calculated for elastic electron scattering from a variety of spin zero nuclei at energies from 14 MeV to 3 GeV. Time reversal symmetry insures that A_n vanish in first Born approximation. Therefore A_n depends on Coulomb distortions and can be large for scattering from heavy nuclei. The vector analyzing power is a potential source of systematic error for parity violation experiments. We find that A_n=-0.361 ppm for the kinematics of the Parity Radius Experiment (PREX) involving 850 MeV electrons scattering at six degrees from 208Pb. This is comparable to the parity violating asymmetry. However for HAPPEX He involving 3 GeV electrons scattering on 4He we find that A_n is very small.Comment: 6 pages, 6 figures, submitted to Phys. Rev.

Exact factorization of the time-dependent electron-nuclear wavefunction

We present an exact decomposition of the complete wavefunction for a system of nuclei and electrons evolving in a time-dependent external potential. We derive formally exact equations for the nuclear and electronic wavefunctions that lead to rigorous definitions of a time-dependent potential energy surface (TDPES) and a time-dependent geometric phase. For the $H_2^+$ molecular ion exposed to a laser field, the TDPES proves to be a useful interpretive tool to identify different mechanisms of dissociation.Comment: 4 pages, 2 figure

Renormalized broken-symmetry Schwinger-Dyson equations and the 2PI-1/N expansion for the O(N) model

We derive the renormalized Schwinger-Dyson equations for the one- and two-point functions in the auxiliary field formulation of $\lambda \phi^4$ field theory to order 1/N in the 2PI-1/N expansion. We show that the renormalization of the broken-symmetry theory depends only on the counter terms of the symmetric theory with $\phi = 0$. We find that the 2PI-1/N expansion violates the Goldstone theorem at order 1/N. In using the O(4) model as a low energy effective field theory of pions to study the time evolution of disoriented chiral condensates one has to {\em{explicitly}} break the O(4) symmetry to give the physical pions a nonzero mass. In this effective theory the {\em additional} small contribution to the pion mass due to the violation of the Goldstone theorem in the 2-PI-1/N equations should be numerically unimportant

Gauge Fields Out-Of-Equilibrium: A Gauge Invariant Formulation and the Coulomb Gauge

We study the abelian Higgs model out-of-equilibrium in two different approaches, a gauge invariant formulation, proposed by Boyanovsky et al. \cite{Boyanovsky:1996dc} and in the Coulomb gauge. We show that both approaches become equivalent in a consistent one loop approximation. Furthermore, we carry out a proper renormalization for the model in order to prepare the equations for a numerical implementation. The additional degrees of freedom, which arise in gauge theories, influence the behavior of the system dramatically. A comparison with results in the 't Hooft-Feynman background gauge found by us recently, shows very good agreement.Comment: 32 pages, 8 figure

Zero mode in the time-dependent symmetry breaking of λϕ4\lambda\phi^4 theory

We apply the quartic exponential variational approximation to the symmetry breaking phenomena of scalar field in three and four dimensions. We calculate effective potential and effective action for the time-dependent system by separating the zero mode from other non-zero modes of the scalar field and treating the zero mode quantum mechanically. It is shown that the quantum mechanical properties of the zero mode play a non-trivial role in the symmetry breaking of the scalar $\lambda \phi^4$ theory.Comment: 10 pages, 3 figure

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