Quantum collision theory with phase-space distributions

Quantum-mechanical phase-space distributions, introduced by Wigner in 1932, provide an intuitive alternative to the usual wave-function approach to problems in scattering and reaction theory. The aim of the present work is to collect and extend previous efforts in a unified way, emphasizing the parallels among problems in ordinary quantum theory, nuclear physics, chemical physics, and quantum field theory. The method is especially useful in providing easy reductions to classical physics and kinetic regimes under suitable conditions. Section II, dealing in detail with potential scattering of a spinless nonrelativistic particle, provides the background for more complex problems. Following a brief description of the two-body problem, the authors address the N-body problem with special attention to hierarchy closures, Boltzmann-Vlasov equations, and hydrodynamic aspects. The final section sketches past and possibly future applications to a wide variety of problems

Universal features of the off-equilibrium fragmentation with the Gaussian dissipation

We investigate universal features of the off-equilibrium sequential and conservative fragmentation processes with the dissipative effects which are simulated by the Gaussian random inactivation process. The relation between the fragment multiplicity scaling law and the fragment size distribution is studied and a dependence of scaling exponents on the parameters of fragmentation and inactivation rate functions is established.Comment: 10 pages, 2 figure

Integral correlation measures for multiparticle physics

We report on a considerable improvement in the technique of measuring multiparticle correlations via integrals over correlation functions. A modification of measures used in the characterization of chaotic dynamical sytems permits fast and flexible calculation of factorial moments and cumulants as well as their differential versions. Higher order correlation integral measurements even of large multiplicity events such as encountered in heavy ion collisons are now feasible. The change from ``ordinary'' to ``factorial'' powers may have important consequences in other fields such as the study of galaxy correlations and Bose-Einstein interferometry.Comment: 23 pages, 6 tar-compressed uuencoded PostScript figures appended, preprint TPR-92-4

Simulating lattice gauge theories on a quantum computer

We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one and two qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the lattice. The number of qubits required for storing a particular state is found to have a linear dependence with the total number of lattice sites. The number of qubit operations required for performing the time evolution corresponding to the Hamiltonian is found to be between a linear to quadratic function of the number of lattice sites, depending on the arrangement of qubits in the quantum computer. We remark that our results may also be easily generalized to higher SU(N) gauge theories.Comment: 15 pages, 4 figures, 3 table

Private languages and private theorists

Simon Blackburn objects that Wittgenstein's private language argument overlooks the possibility that a private linguist can equip himself with a criterion of correctness by confirming generalizations about the patterns in which his private sensations occur. Crispin Wright responds that appropriate generalizations would be too few to be interesting. But I show that Wright's calculations are upset by his failure to appreciate both the richness of the data and the range of theories that would be available to the private linguist

Linking metacognition and mindreading: Evidence from autism and dual-task investigations

Questions of how we know our own and other minds, and whether metacognition and mindreading rely on the same processes, are longstanding in psychology and philosophy. In Experiment 1, children/adolescents with autism (who tend to show attenuated mindreading) showed significantly lower accuracy on an explicit metacognition task than neurotypical children/adolescents, but not on an allegedly metacognitive implicit one. In Experiment 2, neurotypical adults completed these tasks in a single-task condition, or a dual-task condition that required concurrent completion of a secondary task that tapped mindreading. Metacognitive accuracy was significantly diminished by the dual-mindreading-task on the explicit task, but not the implicit task. In Experiment 3, we included additional dual-tasks to rule out the possibility that any secondary task (regardless of whether it required mindreading) would diminish metacognitive accuracy. Finally, in both experiments 1 and 2, metacognitive accuracy on the explicit task, but not the implicit task, was associated significantly with performance on a measure of mindreading ability. These results suggest that explicit metacognitive tasks (used frequently to measure metacognition in humans) share metarepresentational processing resources with mindreading, whereas implicit tasks (which are claimed by some comparative psychologists to measure metacognition in non-human animals) do not

Relativistic quantum transport theory approach to multiparticle production

The field-theoretic description of multiparticle production processes is cast in a form analogous to ordinary transport theory. Inclusive differential cross sections are shown to be given by integrals of covariant phasespace distributions. The single-particle distribution function F(p, R) is defined as the Fourier transform of a suitable correlation function in analogy with the nonrelativistic (Wigner) phase-space distribution function. Its transform F(p, q) is observed to be essentially the discontinuity of a multiparticle scattering amplitude. External-field problems are studied to exhibit the physical content of the formalism. When q=0 one recovers the single-particle distribution exactly. The equation of motion for F(p, R) generates an infinite hierarchy of coupled equations for various distribution functions. In the Hartree approximation one obtains nonlinear integral equations analogous to the Vlasov equation in plasma physics. Such equations are convenient for exhibiting collective motions; in particular it appears that a collective mode exists in a φ^4 theory for a uniform infinite medium. It is speculated that such collective modes could provide a theoretical basis for clustering effects in multiparticle production

High-energy scattering of quarks in gauge theories

High-energy quark-quark scattering is calculated in quantum chromodynamics (QCD) using the infrared equation of Cornwall and Tiktopoulos. In contrast to ordinary quantum electrodynamics, the high-energy behavior is determined by the infrared structure. The infrared divergence is regulated by introduction of a small gluon mass; the amplitudes obtained agree with previous perturbation calculations (for t fixed, s→∞) in QCD modified by the addition of a Higgs meson in the limit of small gluon mass. A proposal to calculate the infrared-finite behavior at fixed angle using asymptotic freedom is made, based on the hypothesis that the infrared divergence can be factored from an infrared-finite and renormalization-point-dependent part. The latter is calculable for the colorless exchange amplitude but not for the color exchange amplitude