This book offers an introduction to quantum technology that is specifically tailored to economists, students of economics, and professionals in the financial and payments industries. The book reviews quantum speedups that have been identified for algorithms used to solve and estimate economic...

Quantum decision models provide a theoretical framework to study decision making and opinion dynamics. The role of Lie algebras is fundamental in these models to get the opinion dynamics without violating the uncertainty principle. A particular case is developed to show the potentiality of our...

We demonstrate that when the Gibbs entropy is an invariant of motion, following Information Theory procedures it is possible to define a generalized metric phase space for the temporal evolution of the mean values of a given Hamiltonian. The metric is positive definite and this fact leads to a...

In this paper we continue our description of stock markets in terms of some non-abelian operators which are used to describe the portfolio of the various traders and other observable quantities. After a first prototype model with only two traders, we discuss a more realistic model of market...

Using the generalized Ehrenfest theorem the dynamics of the mean values of a complete set of non-commuting observables (CSNCO) associated to a given Hamiltonian is expressed. We found refined time-dependent invariants of motion (TDIM) for the CSNCO, and associated them with different Lie...

Invariants of motion are constructed departing from the Gibbs entropy. The method we applied also allows us to find the subspace of a real vector space to which the system is confined to during its temporal evolution. We also find that the Uncertainty Principle is itself an invariant of motion...

We investigate an undamped random phase-space dynamics in deterministic external force fields (conservative and magnetic ones). By employing the hydrodynamical formalism for those stochastic processes we analyze microscopic kinetic-type “collision invariants” and their relationship to local...