A C++ library using quantum trajectories to solve quantum master equations.pdf

a r X i v : q u a n t - p h / 9 6 0 8 0 0 4 v 1 5 A u g 1 9 9 6 A C++ library using quantum trajectories to solve quantum master equations Ru?diger Schack? (a,b) and Todd A. Brun? (b) (a)Department of Mathematics, Royal Holloway, University of London Egham, Surrey TW20 0EX, England (b)Department of Physics, Queen Mary and Westfield College University of London, London E1 4NS, England July 18, 1996 Abstract Quantum trajectory methods can be used for a wide range of open quantum systems to solve the master equation by unraveling the density operator evolution into individual stochastic trajectories in Hilbert space. This C++ class library of- fers a choice of integration algorithms for three important unravelings of the master equation. Different physical systems are modeled by different Hamiltonians and en- vironment operators. The program achieves flexibility and user friendliness, without sacrificing execution speed, through the way it represents operators and states in Hilbert space. Primary operators, implemented in the form of simple routines acting on single degrees of freedom, can be used to build up arbitrarily complex operators in product Hilbert spaces with arbitrary numbers of components. Standard alge- braic notation is used to build operators and to perform arithmetic operations on operators and states. States can be represented in a local moving basis, often lead- ing to dramatic savings of computing resources. The state and operator classes are very general and can be used independently of the quantum trajectory algorithms. Only a rudimentary knowledge of C++ is required to use this package. ?Email: r.schack@rhbnc.ac.uk ?Email: t.brun@qmw.ac.uk 1 Program Summary Title of program: Quantum trajectory class library Program obtainable from: http://galisteo.ma.rhbnc.ac.uk/applied/QSD.html and the au- thors. Licensing provisions : none Operating systems under which the program has been tested : UNIX (Gnu g++), DOS (Turbo C++), VMS (DEC C++) Programming