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F. Cooper

Publications and source records attributed to F. Cooper.

10 recordsLinked to original sources
arXiv2015

PT Meets Supersymmetry and Nonlinearity: An Analytically Tractable Case Example

In the present work, we combine the notion of $\mathcal{PT}$-symmetry with that of super-symmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called P{\"o}schl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which the corresponding solution of the regular nonlinear Schr{\"o}dinger equation with arbitrary power law nonlinearity does not possess. The spectral properties and dynamical implications of this instability are examined. We believe that these findings may pave the way towards initiating a fruitful interplay between the notions of $\mathcal{PT}$-symmetry, super-symmetric partner potentials and nonlinear interactions.

nlin.PS↗
arXiv2009

Fermion particle production in semi-classical Boltzmann-Vlasov transport theory

We present numerical solutions of the semi-classical Boltzmann-Vlasov equation for fermion particle-antiparticle production by strong electric fields in boost-invariant coordinates in (1+1) and (3+1) dimensional QED. We compare the Boltzmann-Vlasov results with those of recent quantum field theory calculations and find good agreement. We conclude that extending the Boltzmann-Vlasov approach to the case of QCD should allow us to do a thorough investigation of how back-reaction affects recent results on the dependence of the transverse momentum distribution of quarks and anti-quarks on a second Casimir invariant of color SU(3).

hep-ph↗
arXiv2001

Classical Limit of Time-Dependent Quantum Field Theory-a Schwinger-Dyson Approach

We rewrite the Martin-Siggia-Rose (MSR) formalism for the statistical dynamics of classical fields in a covariant second order form appropriate for the statistical dynamics of relativistic field theory. This second order formalism is related to a rotation of Schwinger's closed time path (CTP) formalism for quantum dynamics, with the main difference being that certain vertices are absent in the classical theory. These vertices are higher order in an $\hbar$ expansion. The structure of the second order formulation of the Schwinger Dyson (S-D) equations is identical to that of the rotated CTP formalism apart from initial conditions on the Green's functions and the absence of these vertices. We then discuss self-consistent truncation schemes based on keeping certain graphs in the two-particle irreducible effective action made up of bare vertices and exact Green's functions.

hep-ph↗
arXiv2000

Equilibrium and nonequilibrium properties associated with the chiral phase transition at finite density in the Gross-Neveu Model

We study the dynamics of the chiral phase transition at finite density in the Gross-Neveu (GN) model in the leading order in large-N approximation. The phase structure of the GN model in this approximation has the property that there is a tricritical point at a fixed temperature and chemical potential separating regions where the chiral transition is first order from that where it is second order. We consider evolutions starting in local thermal and chemical equilibrium in the massless unbroken phase for conditions pertaining to traversing a first or second order phase transition. We assume boost invariant kinematics and determine the evolution of the order parameter $σ$, the energy density and pressure as well as the effective temperature, chemical potential and interpolating number densities as a function of the proper time $τ$. We find that before the phase transition, the system behaves as if it were an ideal fluid in local thermal equilibrium with equation of state $p=ε$. After the phase transition, the system quickly reaches its true broken symmetry vacuum value for the fermion mass and for the energy density. The single particle distribution functions for Fermions and anti-Fermions go far out of equilibrium as soon as the plasma traverses the chiral phase transition. We have also determined the spatial dependence of the "pion" Green's function $<\barψ(x) γ_5 ψ(x) \barψ(0) γ_5 ψ(0)>$ as a function of the proper time.

hep-ph↗
arXiv1998

Evolution of Inhomogeneous Condensates: Self-consistent Variational Approach

We establish a self-consistent variational framework that allows us to study numerically the non-equilibrium evolution of non-perturbative inhomogeneous field configurations including quantum backreaction effects. After discussing the practical merits and disadvantages of different approaches we provide a closed set of local and renormalizable update equations that determine the dynamical evolution of inhomogeneous condensates and can be implemented numerically. These incorporate self-consistently the backreaction of quantum fluctuations and particle production. This program requires the solution of a self-consistent inhomogeneous problem to provide initial Cauchy data for the inhomogeneous condensates and Green's functions. We provide a simple solvable ansatz for such an initial value problem for the Sine-Gordon and phi^4 quantum field theories in one spatial dimension. We compare exact known results of the Sine Gordon model to this simple ansatz. We also study the linear sigma model in the large N limit in three spatial dimensions as a microscopic model for pion production in ultrarelativistic collisions. We provide a solvable self- consistent ansatz for the initial value problem with cylindrical symmetry. For this case we also obtain a closed set of local and renormalized update equations that can be numerically implemented. A novel phenomenon of spinodal instabilities and pion production arises as a result of a Klein paradox for large amplitude inhomogeneous condensate configurations.

hep-ph↗
arXiv1996

Anomalous Transverse Distribution of Pions as a signal for the production of DCC's

We give evidence that the production of DCC's during a non-equilibrium phase transition can lead to an anomalous transverse distribution of secondary pions when compared to a more conventional boost invariant hydrodynamic flow in local thermal equilibrium. Our results pertain to the linear $σ$ model,treated in leading order in large-$N$, in a boost invariant approximation. We also show that the interpolating number density of the field theory calculation plays the role of a classical relativistic phase space number distribution in determining the momentum distribution of pions in the center of mass frame.

hep-ph↗
arXiv1995

Quantum evolution of the disoriented chiral condensates

We study the dynamics of the chiral phase transition expected during the expansion of the quark-gluon plasma produced in a high energy hadron or heavy ion collision, using the $O(4)$ linear sigma model in the mean field approximation. Imposing boost invariant initial conditions at an initial proper time $\tau_0$ and starting from an approximate equilibrium configuration, we investigate the possibility of formation of disoriented chiral condensate during the expansion. In order to create large domains of disoriented chiral condensates low-momentum instabilities have to last for long enough periods of time. Our simulations show no instabilities for an initial thermal configuration. For some of the out-of-equilibrium initial states studied, the fluctuation in the number of particles with low transverse momenta become large at late proper times.

hep-ph↗
arXiv1992

Particle production in the central rapidity region

We study pair production from a strong electric field in boost-invariant coordinates as a simple model for the central rapidity region of a heavy-ion collision. We derive and solve the renormalized equations for the time evolution of the mean electric field and current of the produced particles, when the field is taken to be a function only of the fluid proper time $τ= \sqrt{t^2-z^2}$. We find that a relativistic transport theory with a Schwinger source term modified to take Pauli blocking (or Bose enhancement) into account gives a good description of the numerical solution to the field equations. We also compute the renormalized energy-momentum tensor of the produced particles and compare the effective pressure, energy and entropy density to that expected from hydrodynamic models of energy and momentum flow of the plasma.

hep-ph↗
arXiv1992

Variational Method for Studying Solitons in the KdV equation

We use a class of trial wave functions which are generalizations of gaussians to study single soliton approximate analytic solutions to the KdV equations. The variational parameters obey a Hamiltonian dynamics obtained from the Principle of Least Action. We get extremely accurate approximate single soliton solutions including their time dependence using this method.

hep-ph↗