arXiv subjects
Publications and source records attributed to Eli Eisenberg.
The effect of diffusional relaxation on the random sequential deposition process is studied in the limit of fast deposition. Expression for the coverage as a function of time are analytically derived for both the short-time and long-time regimes. These results are tested and compared with numerical simulations.
We consider the quantum mechanical behavior of a driven particle in an infinite 1D potential well. We show that the time dependent perturbation series is induced by the delicate non-trivial properties of the momentum operator in this case, namely, its non-self-adjointness. Using this expansion, we calculate the first order contribution to the cross section and the energy gain, and discuss their classical limit. In this limit the one-period energy gain converges to its classical analog - the classical local (momentum space) diffusion coefficient. Both the classical and quantum mechanical results are compared with numerical simulations.
It has been previously shown, that classically chaotic kicked systems, whose unperturbed spectrum posseses one energy scale, admits a quantum anti-resonance (QAR) behavior. In this study we extend the conditions under which which this QAR occurs for the case of a two-sided kicked 1D infinite potential well. It is then shown by a perturbative argument that this QAR effects the behavior of the equivalent driven well, i.e., the number of periods needed to leave the initial state has a sharp peak around the QAR. We give a numerical evidence that the anti resonance persists even for large values of the perturbation parameter.
A direct and exact method for calculating the density of states for systems with localized potentials is presented. The method is based on explicit inversion of the operator $E-H$. The operator is written in the discrete variable representation of the Hamiltonian, and the Toeplitz property of the asymptotic part of the obtained {\it infinite} matrix is used. Thus, the problem is reduced to the inversion of a {\it finite} matrix.
It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively pure state can evolve under the usual unitary evolution to an effectively mixed state.