Semiclassical evolution of dissipative Markovian systems

A semiclassical approximation for an evolving density operator, driven by a `closed` Hamiltonian operator and `open` Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra `open` term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further `small-chord` approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.

Defect centre responsible for production of 110 degrees C TL peak in quartz

110 degrees C thermoluminescence (TL) peak in quartz is well known due to its pre-dose effect, which is used in dating technique. The generally accepted mechanism for the production of this peak is based on Ge impurity contained in quartz. Its role is to substitute for Si in SiO(4) tetrahedron and under irradiation gives rise to [GeO(4)/e(-)](-) electron centre. Heating for TL read out liberates electron that recombines with hole in [AlO(4)/h]degrees or [H(3)O(4)/h]degrees centres emitting photon. The investigation, carried out on blue quartz, green quartz, black quartz, pink quartz, red quartz, sulphurous quartz, milky quartz, alpha quartz and synthetic quartz, has shown that the 110 degrees C TL peak in all these varieties of quartz has no correlation with the respective Ge content. Electron paramagnetic resonance (EPR) measurements on any of these varieties of quartz revealed a signal with g(1) = 2.0004, g(2) = 1.9986 and g(3) = 1.974 and this signal does not appear to correspond to any known EPR signals in alpha quartz. Furthermore, isothermal decay measurements are carried out on the above mentioned EPR signal and 110 degrees C TL peak in alpha, blue and green quartz. A close correlation has been observed in the decay behavior. A new mechanism is proposed based on an interstitial O(-) centre. (C) 2009 Elsevier Ltd. All rights reserved.