Damping and decoherence of Fock states in a nanomechanical resonator due to two level systems

We numerically investigate the decay of initial quantum Fock states and their superpositions for a mechanical resonator mode coupled to an environment comprising interacting, damped tunneling two level system (TLS) defects. The cases of one, three, and six near resonant, interacting TLS's are considered in turn and it is found that the resonator displays Ohmic bath like decay behavior with as few as three TLS's.Comment: 28 pages, 24 figures; submitted to Physical Review

Spontaneous Raman scattering for simultaneous measurements of in-cylinder species

A technique for multi-species mole fraction measurement in internal combustion engines is described. The technique is based on the spontaneous Raman scattering. It can simultaneously provide the mole fractions of several species of N-2, O-2, H2O, CO2 and fuel. Using the system, simultaneous measurement of air/fuel ratio and burnt residual gas are carried out during the mixture process in a Controlled Auto Ignition (CAI) combustion engine. The accuracy and consistency of the measured results were confirmed by the measured air fuel ratio using an exhaust gas analyzer and independently calculated mole fraction values. Measurement of species mole fractions during combustion process has also been demonstrated. It shows that the SRS can provide valuable data on this process in a CAI combustion engine

Challenging the empire

This paper considers how Paul Gilroy transformed hitherto dominant understandings of the relationship between race and class by developing an innovative account that foregrounded questions of racist oppression and collective resistance amid the organic crisis of British capitalism. The returns from this rethinking were profound in that he was able to make transparent both the structuring power of racism within the working class, and the necessity for autonomous black resistance. At the same time, significant lacunae in his account are identified, including the neglect of the episodic emergence of working-class anti-racism and the part played by socialists, particularly those of racialized minority descent in fashioning a major anti-racist social movement. The paper concludes with a lament for the disappearance of such work informed by a ‘Marxism without guarantees’ in the contemporary field of racism studies, and asks readers to consider the gains to be derived from such a re-engagement

Betti number signatures of homogeneous Poisson point processes

The Betti numbers are fundamental topological quantities that describe the k-dimensional connectivity of an object: B_0 is the number of connected components and B_k effectively counts the number of k-dimensional holes. Although they are appealing natural descriptors of shape, the higher-order Betti numbers are more difficult to compute than other measures and so have not previously been studied per se in the context of stochastic geometry or statistical physics. As a mathematically tractable model, we consider the expected Betti numbers per unit volume of Poisson-centred spheres with radius alpha. We present results from simulations and derive analytic expressions for the low intensity, small radius limits of Betti numbers in one, two, and three dimensions. The algorithms and analysis depend on alpha-shapes, a construction from computational geometry that deserves to be more widely known in the physics community.Comment: Submitted to PRE. 11 pages, 10 figure

Dynamical systems arising from elliptic curves

We exhibit a family of dynamical systems arising from rational points on elliptic curves in an attempt to mimic the familiar toral automorphisms. At the non-archimedean primes, a continuous map is constructed on the local elliptic curve whose topological entropy is given by the local canonical height. Also, a precise formula for the periodic points is given. There follows a discussion of how these local results may be glued together to give a map on the adelic curve. We are able to give a map whose entropy is the global canonical height and whose periodic points are counted asymptotically by the real division polynomial (although the archimedean component of the map is artificial). Finally, we set out a precise conjecture about the existence of elliptic dynamical systems and discuss a possible connection with mathematical physics