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arXiv · hep-lat/0309136

Quantum Markov Process on a Lattice

T. Hashimoto·M. Horibe·A. Hayashi
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Abstract

We develop a systematic description of Weyl and Fano operators on a lattice phase space. Introducing the so-called ghost variable even on an odd lattice, odd and even lattices can be treated in a symmetric way. The Wigner function is defined using these operators on the quantum phase space, which can be interpreted as a spin phase space. If we extend the space with a dichotomic variable, a positive distribution function can be defined on the new space. It is shown that there exits a quantum Markov process on the extended space which describes the time evolution of the distribution function.

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T. Hashimoto, M. Horibe, A. Hayashi. 2003-09-20. Quantum Markov Process on a Lattice. https://doi.org/10.1016/s0920-5632(03)02745-2

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