We develop a numerical scheme for the wave front computation of complete transmissions and reflections in geometrical optics. Such a problem can be formulated by a reduced Liouville equation with a discontinuous local wave speed or index of refraction, arising in the high frequency limit of linear waves through inhomogeneous media. The key idea is to incorporate Snell’s Law of Refraction into t...

A simple scheme, capable of treating transport in molecular junctions in the language of many-body states, is presented. By introducing an ansatz in Liouville space, similar to the generalized Kadanoff-Baym approximation, a quantum master equation QME -like expression is derived starting from the exact equation of motion for Hubbard operators. Using an effective Liouville space propagation, a d...

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): thus 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 interaction with th...

abstract.   the sturm-liouville boundary value problem of the multi-order fractional differential equation  is studied. results on the existence of solutions are established. the analysis relies on a weighted function space and a fixed point theorem. an example is given to illustrate the efficiency of the main theorems.

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument in favour of the procedure we prove the Liouville equation of motion on the level of three-point functions. The analytical structure of the correlation functi...

We give a non-trivially interacting field theory example of scale invariant but non-conformal field theory. The model is based on the exactly solvable Liouville field theory coupled with free scalars deformed by an exactly marginal operator. We show non-vanishing of the trace of the energy-momentum tensor by using the quantum Schwinger-Dyson equation for the Liouville field theory, which is a s...

We study a process of anomalous diffusion, based on intermittent velocity fluctuations , and we show that its scaling depends on whether we observe the motion of many independent trajectories or that of a Liouville-like equation driven density. The reason for this discrepancy seems to be that the Liouville-like equation is unable to reproduce the multi-scaling properties emerging from trajector...

The variational iterationmethod VIM 1–4 and homotopy perturbationmethod HPM 5– 8 , proposed byHe, are powerful analytical methods for various kinds of linear and nonlinear problems. For example, the variational iteration method has been applied to autonomous ordinary differential equation 9 and delay differential equation 10 . Abdou and Soliman applied this method to Schrodinger-KDV, generalize...