Unstable particles as open quantum systems

Abstract

We present the probability preserving description of the decaying particle within the framework of quantum mechanics of open systems taking into account the superselection rule prohibiting the superposition of the particle and vacuum. In our approach the evolution of the system is given by a family of completely positive trace preserving maps forming one-parameter dynamical semigroup. We give the Kraus representation for the general evolution of such systems which allows one to write the evolution for systems with two or more particles. Moreover, we show that the decay of the particle can be regarded as a Markov process by finding explicitly the master equation in the Lindblad form. We also show that there are remarkable restrictions on the possible strength of decoherence.Comment: 11 pp, 2 figs (published version

Quantum spin correlations in relativistic Møller scattering

“…It depends on particles momenta [7][8][9], moreover in some energy ranges this dependence may be non-monotonic (in systems containing at least one massive particle) [8][9][10][11]. It can be seen in The relativistic correlation function for a pure singlet state as a function of kinetic energy of one particle.The kinetic energy of the second particle equals 5MeV, a = (0, 0, 1), b = (1, 0, 0),…”

A project to measure quantum spin correlations of relativistic electron pairs in Møller scattering

“…Since the pioneering paper by Czachor [6] one can notice a raise of interest in relativistic aspects of the quantum information theory, expressed in the most important papers on that subject [6,[9][10][11][12][13], including the papers of our group [7,8,[14][15][16][17][18][19]. However, the theoretical analysis of spin correlations in relativistic regime given in these papers is full of ambiguities and interpretational difficulties.…”

“…They arise mostly due to the fact of an apparent conflict between nonlocality of the relativistic quantum mechanics and the Lorentz symmetry. Rembieliński et al exhaustively discussed the a e-mail: cib@fuw.edu.pl relativistic EPR correlation function for a bipartite system of spin-1/2 fermions in the framework of the relativistic quantum mechanics [17] and the quantum field theory [18]. The function was calculated in both pseudoscalar and vector state, which are the relativistic counterparts of the non-relativistic singlet and triplet states, respectively.…”

Formulae for partial widths derived from the Lindblad equation

“…In literature, several examples of combining formalism for open quantum systems with explicitly non-Hermitian Hamiltonians are found, see, e.g., [27][28][29][30][31][32]. The term "open" in regard to a quantum system indicate that the system is interacting with some environment.…”

“…(The terms "open" and "unbound" are sometimes used interchangeably.) In [28,29] it was demonstrated how the Lindblad equation may be used to describe the dynamics of spontaneously decaying particles, i.e. to systems in which the number of particles is not constant.…”