In this paper, we establish the dimension-free Harnack inequality on configuration spaces by using the coupling argument. Furthermore, a unified treatment is also used to prove the equivalence between the Harnack inequality on configuration space and that on the corresponding base space under a...

The algebraic expressions for the total spin operators expressed in terms of orthofermion creation and annihilation operators are combined into a single equation. The terms in this expressions are rearranged to provide representations of local spin operators. This task is essential for modelling...

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...

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...

Recent developments of the study on quantum mechanical effects on condensed matter phenomena are overviewed from the viewpoint of numerical investigations. Various phases and phase transitions inherent to quantum mechanical interactions are reviewed. Quantum mechanical dynamics in nanoscale...

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...

Non-adiabatic transitions are studied in a spin-boson model with multiple scattering points. In order to generalize the Landau–Zener formula, which describes the case of a single scattering point, we define an “effective gap” for a set of scattering points. The generalized formula agrees...

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...

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...

This paper examines volatility spillovers from mature to emerging stock markets and tests for changes in the transmission mechanismcontagionduring turbulences in mature markets. Tri-variate GARCH-BEKK models of returns in global (mature), regional, and local markets are estimated for 41 emerging...