Ergodic and non-ergodic clustering of inertial particles

We compute the fractal dimension of clusters of inertial particles in mixing flows at finite values of Kubo (Ku) and Stokes (St) numbers, by a new series expansion in Ku. At small St, the theory includes clustering by Maxey's non-ergodic 'centrifuge' effect. In the limit of St to infinity and Ku to zero (so that Ku^2 St remains finite) it explains clustering in terms of ergodic 'multiplicative amplification'. In this limit, the theory is consistent with the asymptotic perturbation series in [Duncan et al., Phys. Rev. Lett. 95 (2005) 240602]. The new theory allows to analyse how the two clustering mechanisms compete at finite values of St and Ku. For particles suspended in two-dimensional random Gaussian incompressible flows, the theory yields excellent results for Ku < 0.2 for arbitrary values of St; the ergodic mechanism is found to contribute significantly unless St is very small. For higher values of Ku the new series is likely to require resummation. But numerical simulations show that for Ku ~ St ~ 1 too, ergodic 'multiplicative amplification' makes a substantial contribution to the observed clustering.Comment: 4 pages, 2 figure

Comparing the correlation length of grain markets in China and France

In economics comparative analysis plays the same role as experimental research in physics. In this paper we closely examine several methodological problems related to comparative analysis by investigating the specific example of grain markets in China and France respectively. This enables us to answer a question in economic history which has so far remained pending, namely whether or not market integration progressed in the 18th century. In economics as in physics, before being accepted any new result has to be checked and re-checked by different researchers. This is what we call the replication and comparison procedures. We show how these procedures should (and can) be implemented.Comment: 16 pages, 7 figures, to appear in International Journal of Modern Physics

Perturbation theory for a stochastic process with Ornstein-Uhlenbeck noise

The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two dimensions. In the case of motion in the vicinity of an attractive fixed point, it is shown how the solution of this equation can be developed as a power series. The coefficients are determined exactly by using algebraic properties of a system of annihilation and creation operators.Comment: 7 pages, 0 figure

A quantum Peierls-Nabarro barrier

Kink dynamics in spatially discrete nonlinear Klein-Gordon systems is considered. For special choices of the substrate potential, such systems support continuous translation orbits of static kinks with no (classical) Peierls-Nabarro barrier. It is shown that these kinks experience, nevertheless, a lattice-periodic confining potential, due to purely quantum effects anaolgous to the Casimir effect of quantum field theory. The resulting ``quantum Peierls-Nabarro potential'' may be calculated in the weak coupling approximation by a simple and computationally cheap numerical algorithm, which is applied, for purposes of illustration, to a certain two-parameter family of substrates.Comment: 13 pages LaTeX, 7 figure

A model for alignment between microscopic rods and vorticity

Numerical simulations show that microscopic rod-like bodies suspended in a turbulent flow tend to align with the vorticity vector, rather than with the dominant eignevector of the strain-rate tensor. This paper investigates an analytically solvable limit of a model for alignment in a random velocity field with isotropic statistics. The vorticity varies very slowly and the isotropic random flow is equivalent to a pure strain with statistics which are axisymmetric about the direction of the vorticity. We analyse the alignment in a weakly fluctuating uniaxial strain field, as a function of the product of the strain relaxation time $\tau_{\rm s}$ and the angular velocity $\omega$ about the vorticity axis. We find that when $\omega\tau_{\rm s}\gg 1$, the rods are predominantly either perpendicular or parallel to the vorticity

Perfect State Transfer, Effective Gates and Entanglement Generation in Engineered Bosonic and Fermionic Networks

We show how to achieve perfect quantum state transfer and construct effective two-qubit gates between distant sites in engineered bosonic and fermionic networks. The Hamiltonian for the system can be determined by choosing an eigenvalue spectrum satisfying a certain condition, which is shown to be both sufficient and necessary in mirror-symmetrical networks. The natures of the effective two-qubit gates depend on the exchange symmetry for fermions and bosons. For fermionic networks, the gates are entangling (and thus universal for quantum computation). For bosonic networks, though the gates are not entangling, they allow two-way simultaneous communications. Protocols of entanglement generation in both bosonic and fermionic engineered networks are discussed.Comment: RevTeX4, 6 pages, 1 figure; replaced with a more general example and clarified the sufficient and necessary condition for perfect state transfe

Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks

In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum for a general type of tree-like networks. Close to the percolation threshold we find characteristic scaling functions for the density of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for small lambda, where alpha_1 holds below and alpha_2 at the percolation threshold. In the range where the spectra are accessible from a numerical diagonalization procedure the two methods lead to very similar results.Comment: 9 pages, 6 figure

Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle

Both in atomic physics and in mesoscopic physics it is sometimes interesting to consider the energy time-dependence of a parametrically-driven chaotic system. We assume an Hamiltonian ${\cal H}(Q,P;x(t))$ where $x(t)=Vt$. The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy-spreading is studied. The associated irreversible growth of the average energy has the meaning of dissipation. It is found that a dimensionless velocity $v_{PR}$ determines the nature of the dynamics, and controls the route towards quantal-classical correspondence (QCC). A perturbative regime and a non-perturbative semiclassical regime are distinguished.Comment: 4 pages, clear presentation of the main poin

The potential of the ground state of NaRb

The X$^{1}\Sigma ^{+}$ state of NaRb was studied by Fourier transform spectroscopy. An accurate potential energy curve was derived from more than 8800 transitions in isotopomers $^{23}$Na$^{85}$Rb and $^{23}$Na$^{87}$Rb. This potential reproduces the experimental observations within their uncertainties of 0.003 \rcm to 0.007 \rcm. The outer classical turning point of the last observed energy level ($v''=76$, $J''=27$) lies at $\approx 12.4$ \AA, leading to a energy of 4.5 \rcm below the ground state asymptote.Comment: 8 pages, 6 figures and 2 table