Efficient Refocussing of One Spin and Two Spin Interactions for NMR Quantum Computation

The use of spin echoes to refocus one spin interactions (chemical shifts) and two spin interactions (spin-spin couplings) plays a central role in both conventional NMR experiments and NMR quantum computation. Here we describe schemes for efficient refocussing of such interactions in both fully and partially coupled spin systems.Comment: 4 pages, RevTeX, including 4 LaTeX figure

Proposal for a race-track microtron with high peak current

In order to obtain high gain in a free electron laser a high-quality electron beam with high peak current is required. It is well-known that a microtron is able to produce a high-quality beam having low emittance and small energy spread (1%). Because a circular microtron has a limited high-current capability a race-track design is adopted for providing flexibility, better beam quality and of course higher peak current in the microbunch. Space charge problems may be severe in a microtron. It can be shown that bunching on certain specific subharmonic frequencies will lead to a strong reduction of the space charge problems. The general layout of our microtron design will be presented. The characteristics are: energy 25 MeV, micropulse 10° of the rf frequency of 3 GHz. Our aim is to come beyond the present state of the art with the following characteristics: relative energy spread 0.001, emittance 3 mm mrad, current in the micropulse 100 A, macropulse length 50 μs and subharmonic bunching at 1:64

Collisional rates for the inelastic Maxwell model: application to the divergence of anisotropic high-order velocity moments in the homogeneous cooling state

The collisional rates associated with the isotropic velocity moments $$and the anisotropic moments$$ and $$ are exactly derived in the case of the inelastic Maxwell model as functions of the exponent $r$, the coefficient of restitution $\alpha$, and the dimensionality $d$. The results are applied to the evolution of the moments in the homogeneous free cooling state. It is found that, at a given value of $\alpha$, not only the isotropic moments of a degree higher than a certain value diverge but also the anisotropic moments do. This implies that, while the scaled distribution function has been proven in the literature to converge to the isotropic self-similar solution in well-defined mathematical terms, nonzero initial anisotropic moments do not decay with time. On the other hand, our results show that the ratio between an anisotropic moment and the isotropic moment of the same degree tends to zero.Comment: 7 pages, 2 figures; v2: clarification of some mathematical statements and addition of 7 new references; v3: Published in "Special Issue: Isaac Goldhirsch - A Pioneer of Granular Matter Theory

On the physical parametrization and magnetic analogs of the Emparan-Teo dihole solution

The Emparan-Teo non-extremal black dihole solution is reparametrized using Komar quantities and the separation distance as arbitrary parameters. We show how the potential $A_3$ can be calculated for the magnetic analogs of this solution in the Einstein-Maxwell and Einstein-Maxwell-dilaton theories. We also demonstrate that, similar to the extreme case, the external magnetic field can remove the supporting strut in the non-extremal black dihole too.Comment: 9 pages, 1 figur

Exact steady state solution of the Boltzmann equation: A driven 1-D inelastic Maxwell gas

The exact nonequilibrium steady state solution of the nonlinear Boltzmann equation for a driven inelastic Maxwell model was obtained by Ben-Naim and Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for the Fourier transform of the distribution function $f(c)$. In this paper we have inverted the Fourier transform to express $f(c)$ in the form of an infinite series of exponentially decaying terms. The dominant high energy tail is exponential, $f(c)\simeq A_0\exp(-a|c|)$, where $a\equiv 2/\sqrt{1-\alpha^2}$ and the amplitude $A_0$ is given in terms of a converging sum. This is explicitly shown in the totally inelastic limit ($\alpha\to 0$) and in the quasi-elastic limit ($\alpha\to 1$). In the latter case, the distribution is dominated by a Maxwellian for a very wide range of velocities, but a crossover from a Maxwellian to an exponential high energy tail exists for velocities $|c-c_0|\sim 1/\sqrt{q}$ around a crossover velocity $c_0\simeq \ln q^{-1}/\sqrt{q}$, where $q\equiv (1-\alpha)/2\ll 1$. In this crossover region the distribution function is extremely small, $\ln f(c_0)\simeq q^{-1}\ln q$.Comment: 11 pages, 4 figures; a table and a few references added; to be published in PR

An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux

In the steady Couette flow of a granular gas the sign of the heat flux gradient is governed by the competition between viscous heating and inelastic cooling. We show from the Boltzmann equation for inelastic Maxwell particles that a special class of states exists where the viscous heating and the inelastic cooling exactly compensate each other at every point, resulting in a uniform heat flux. In this state the (reduced) shear rate is enslaved to the coefficient of restitution $\alpha$, so that the only free parameter is the (reduced) thermal gradient $\epsilon$. It turns out that the reduced moments of order $k$ are polynomials of degree $k-2$ in $\epsilon$, with coefficients that are nonlinear functions of $\alpha$. In particular, the rheological properties ($k=2$) are independent of $\epsilon$ and coincide exactly with those of the simple shear flow. The heat flux ($k=3$) is linear in the thermal gradient (generalized Fourier's law), but with an effective thermal conductivity differing from the Navier--Stokes one. In addition, a heat flux component parallel to the flow velocity and normal to the thermal gradient exists. The theoretical predictions are validated by comparison with direct Monte Carlo simulations for the same model.Comment: 16 pages, 4 figures,1 table; v2: minor change

Tanaka Theorem for Inelastic Maxwell Models

We show that the Euclidean Wasserstein distance is contractive for inelastic homogeneous Boltzmann kinetic equations in the Maxwellian approximation and its associated Kac-like caricature. This property is as a generalization of the Tanaka theorem to inelastic interactions. Consequences are drawn on the asymptotic behavior of solutions in terms only of the Euclidean Wasserstein distance