Foundering of mafic lower continental crust into underlying convecting mantle has been proposed as one means to explain the unusually evolved chemical composition of Earth's continental crust, yet direct evidence of this process has been scarce. Here we report that Late Jurassic high-magnesium andesites, dacites and adakites (siliceous lavas with high strontium and low heavy-rare-earth element and yttrium contents) from the North China craton have chemical and petrographic features consistent with their origin as partial melts of eclogite that subsequently interacted with mantle peridotite. Similar features observed in adakites and some Archaean sodium-rich granitoids of the tonalite-trondhjemite-granodiorite series have been interpreted to result from interaction of slab melts with the mantle wedge. Unlike their arc-related counterparts, however, the Chinese magmas carry inherited Archaean zircons and have neodymium and strontium isotopic compositions overlapping those of eclogite xenoliths derived from the lower crust of the North China craton. Such features cannot be produced by crustal assimilation of slab melts, given the high Mg#, nickel and chromium contents of the lavas. We infer that the Chinese lavas derive from ancient mafic lower crust that foundered into the convecting mantle and subsequently melted and interacted with peridotite. We suggest that lower crustal foundering occurred within the North China craton during the Late Jurassic, and thus provides constraints on the timing of lithosphere removal beneath the North China craton.

The phase diagram for staggered fermions is discussed in the context of the staggered chiral Lagrangian, extending previous work on the subject. When the discretization errors are significant, there may be an Aoki-like phase for staggered fermions, where the remnant SO4 taste-symmetry is broken down to SO3. We solve explicitly for the mass spectrum in the 3-flavor degenerate mass case and discuss qualitatively the 2 1-flavor case. From numerical results we find that current simulations are outside the staggered-Aoki phase. As for near-future simulations with more-improved versions of the staggered action, it seems unlikely that these will be in the Aoki phase for any realistic value of the quark mass, although the evidence is not conclusive.

In a previous paper [1], it was shown that the worldline expression for the nonperturbative imaginary part of the QED effective action can be approximated by the contribution of a special closed classical path in Euclidean spacetime, known as a worldline instanton. Here we extend this formalism to compute also the prefactor arising from quantum fluctuations about this classical closed path. We present a direct numerical approach for determining this prefactor, and we find a simple explicit formula for the prefactor in the cases where the inhomogeneous electric field is a function of just one spacetime coordinate. We find excellent agreement between our semiclassical approximation, conventional WKB, and recent numerical results using numerical worldline loops.

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Under a general framework, shortcuts to adiabatic processes are shown to be possible in classical systems. We then study the distribution function of the work done on a small system initially prepared at thermal equilibrium. It is found that the work fluctuations can be significantly reduced via shortcuts to adiabatic processes. For example, in the classical case probabilities of having very large or almost zero work values are suppressed. In the quantum case negative work may be totally removed from the otherwise non-positive-definite work values. We also apply our findings to a micro Otto-cycle-based heat engine. It is shown that the use of shortcuts, which directly enhances the engine output power, can also increase the heat engine efficiency substantially, in both quantum and classical regimes.

We document strong comovement in the stock returns of firms headquartered in the same geographic area. Moreover, stocks of companies that change their headquarters location experience a decrease in their comovement with stocks from the old location and an increase in their comovement with stocks from the new location. The local comovement of stock returns is not explained by economic fundamentals and is stronger for smaller firms with more individual investors and in regions with less financially sophisticated residents. We argue that price formation in equity markets has a significant geographic component linked to the trading patterns of local residents. Copyright 2006 by The American Finance Association.

The Lee model was introduced in the 1950s as an elementary quantum field theory in which mass, wave function, and charge renormalization could be carried out exactly. In early studies of this model it was found that there is a critical value of g 2 , the square of the renormalized coupling constant, above which g 2 0 , the square of the unrenormalized coupling constant, is negative. Thus, for g 2 larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. It was also discovered that in this non-Hermitian regime a new state appears whose norm is negative. This state is called a ghost state. It has always been assumed that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess PT symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having PT symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a new time-independent operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore, it has been shown that time evolution in such a theory is unitary. In this paper the C operator for the Lee model in the ghost regime is constructed in the V /N θ sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum field theory for all values of g 2 .

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