Within the density matrix formalism, it is shown that a simple way to get decoherence is through the introduction of a “quantum” of time (chronon): which implies replacing the differential Liouville–von Neumann equation with a finite-difference version of it. In this way, one is given the possibility of using a rather simple quantum equation to describe the decoherence effects due to dissipatio...

The dynamics of open quantum systems is formulated in terms of a probability distribution on the underlying Hilbert space. Deening the time{evolution of this probability distribution by means of a Liouville{master equation the time{dependent wave function of the system becomes a stochastic Markov process in the sense of classical probability theory. It is shown that the equation of motion for t...

In this paper we will compute the entropy of a Schwarzschild black hole by finding a classical central charge of the Virasoro algebra of a Liouville theory and using the Cardy formula. This is done by performing a dimensional reduction of the Einstein–Hilbert action with the Ansatz of spherical symmetry and writing the metric in conformally flat form. We obtain two coupled field equations using...

We consider the Liouville equations with highly heterogeneous Hamiltonians and their numerical solution by a time splitting algorithm. Such equations model the density of particles evolving according to the corresponding Hamiltonian dynamics as well as the propagation of high frequency waves with a wavelength much smaller than the correlation length of the random Hamiltonian. Our main results a...

In this paper we will compute the entropy of a Schwarzschild black hole by finding a classical central charge of the Virasoro algebra of a liouville theory and using the Cardy formula. This is done by performing a dimensional reduction of the Einstein-Hilbert action with the Ansatz of spherical symmetry and writing the metric in conformally flat form. We obtain two coupled field equations and u...