Adiabatic elimination in quantum stochastic models

We consider a physical system with a coupling to bosonic reservoirs via a quantum stochastic differential equation. We study the limit of this model as the coupling strength tends to infinity. We show that in this limit the solution to the quantum stochastic differential equation converges strongly to the solution of a limit quantum stochastic differential equation. In the limiting dynamics the excited states are removed and the ground states couple directly to the reservoirs.Comment: 17 pages, no figures, corrected mistake

Pion and kaon physics with improved staggered quarks

We compute pseudoscalar meson masses and decay constants using staggered quarks on lattices with three flavors of sea quarks and lattice spacings $\approx 0.12$ fm and $\approx 0.09$ fm. We fit partially quenched results to ``staggered chiral perturbation theory'' formulae, thereby taking into account the effects of taste-symmetry violations. Chiral logarithms are observed. From the fits we calculate $f_\pi$ and $f_K$, extract Gasser-Leutwyler parameters of the chiral Lagrangian, and (modulo rather large perturbative errors) find the light and strange quark masses.Comment: Lattice2003(spectrum); 3 pages, 1 eps figur

High Pressure Thermoelasticity of Body-centered Cubic Tantalum

We have investigated the thermoelasticity of body-centered cubic (bcc) tantalum from first principles by using the linearized augmented plane wave (LAPW) and mixed--basis pseudopotential methods for pressures up to 400 GPa and temperatures up to 10000 K. Electronic excitation contributions to the free energy were included from the band structures, and phonon contributions were included using the particle-in-a-cell (PIC) model. The computed elastic constants agree well with available ultrasonic and diamond anvil cell data at low pressures, and shock data at high pressures. The shear modulus $c_{44}$ and the anisotropy change behavior with increasing pressure around 150 GPa because of an electronic topological transition. We find that the main contribution of temperature to the elastic constants is from the thermal expansivity. The PIC model in conjunction with fast self-consistent techniques is shown to be a tractable approach to studying thermoelasticity.Comment: To be appear in Physical Review

Fermi's golden rule and exponential decay as a RG fixed point

We discuss the decay of unstable states into a quasicontinuum using models of the effective Hamiltonian type. The goal is to show that exponential decay and the golden rule are exact in a suitable scaling limit, and that there is an associated renormalization group (RG) with these properties as a fixed point. The method is inspired by a limit theorem for infinitely divisible distributions in probability theory, where there is a RG with a Cauchy distribution, i.e. a Lorentz line shape, as a fixed point. Our method of solving for the spectrum is well known; it does not involve a perturbation expansion in the interaction, and needs no assumption of a weak interaction. We use random matrices for the interaction, and show that the ensemble fluctuations vanish in the scaling limit. Thus the limit is the same for every model in the ensemble with probability one.Comment: 20 pages, 1 figur

Time-of-arrival distributions from position-momentum and energy-time joint measurements

The position-momentum quasi-distribution obtained from an Arthurs and Kelly joint measurement model is used to obtain indirectly an ``operational'' time-of-arrival (TOA) distribution following a quantization procedure proposed by Kocha\'nski and W\'odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA distribution is not time covariant. The procedure is generalized by using other phase-space quasi-distributions, and sufficient conditions are provided for time covariance that limit the possible phase-space quasi-distributions essentially to the Wigner function, which, however, provides a non-positive TOA quasi-distribution. These problems are remedied with a different quantization procedure which, on the other hand, does not guarantee normalization. Finally an Arthurs and Kelly measurement model for TOA and energy (valid also for arbitrary conjugate variables when one of the variables is bounded from below) is worked out. The marginal TOA distribution so obtained, a distorted version of Kijowski's distribution, is time covariant, positive, and normalized

Stochastic attractors for shell phenomenological models of turbulence

Recently, it has been proposed that the Navier-Stokes equations and a relevant linear advection model have the same long-time statistical properties, in particular, they have the same scaling exponents of their structure functions. This assertion has been investigate rigorously in the context of certain nonlinear deterministic phenomenological shell model, the Sabra shell model, of turbulence and its corresponding linear advection counterpart model. This relationship has been established through a "homotopy-like" coefficient $\lambda$ which bridges continuously between the two systems. That is, for $\lambda=1$ one obtains the full nonlinear model, and the corresponding linear advection model is achieved for $\lambda=0$. In this paper, we investigate the validity of this assertion for certain stochastic phenomenological shell models of turbulence driven by an additive noise. We prove the continuous dependence of the solutions with respect to the parameter $\lambda$. Moreover, we show the existence of a finite-dimensional random attractor for each value of $\lambda$ and establish the upper semicontinuity property of this random attractors, with respect to the parameter $\lambda$. This property is proved by a pathwise argument. Our study aims toward the development of basic results and techniques that may contribute to the understanding of the relation between the long-time statistical properties of the nonlinear and linear models

Vortices and dynamics in trapped Bose-Einstein condensates

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid $^4$He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.Comment: Accepted for publication in Journal of Low Temperature Physics, conference proceedings: Symposia on Superfluids under Rotation (Lammi, Finland, April 2010