Transition Probability (Fidelity) and Its Relatives

Transition Probability (Fidelity) and its Relatives

Transition Probability (fidelity) for pairs of density operators can be defined as a “functor” in the hierarchy of “all” quantum systems and also within any quantum system. The Introduction of “amplitudes” for density operators allows for a more intuitive treatment of these quantities, also pointing to a natural parallel transport. The latter is governed by a remarkable gauge theory with strong...

Fractional Probability Measure and Its Properties

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

Life and Its Close Relatives

When driven by an external thermodynamic gradient, nonbiological physical systems can exhibit a wide range of behaviours usually associated with living systems. Consequently, Artificial Life researchers should be open to the possibility that there is no hard-and-fast distinction between the biological and the physical. This suggests a novel field of research: the application of biologists’ meth...

Geometric Range Searching and Its Relatives Geometric Range Searching and Its Relatives

Transition Probability and Preferential Gauge

This paper is concerned with whether or not the preferential gauge can ensure the uniqueness and correctness of results obtained from the standard time-dependent perturbation theory, in which the transition probability is formulated in terms of matrix elements of Hamiltonian. For a dynamical quantum process, the major objective of the existing perturbation theory is to calculate the transition ...