The evolution of pionium, the $π^+ π^-$ hydrogen-like atom, while passing through matter is solved within the density matrix formalism in the first Born approximation. We compare the influence on the pionium break-up probability between the standard probabilistic calculations and the more precise picture of the density matrix formalism accounting for interference effects. We focus our general result in the particular conditions of the DIRAC experiment at CERN.The evolution of pionium, the $π^+ π^-$ hydrogen-like atom, while passing through matter is solved within the density matrix formalism in the first Born approximation. We compare the influence on the pionium break-up probability between the standard probabilistic calculations and the more precise picture of the density matrix formalism accounting for interference effects. We focus our general result in the particular conditions of the DIRAC experiment at CERN.

arXiv:physics/0407110Journal of Physics B Atomic Molecular and Optical PhysicsDec 7, 20046 citations

Dirac density matrix and the Legendre transform of the kinetic energy generated by one-dimensional model potentials

I. A. Howard, Norman Henry March

In density functional theory, the single-particle kinetic energy is still not known in an orbital-free form. The natural tool to calculate such kinetic energy for a given one-body potential V is the Dirac density matrix y. Here, by first taking solvable one-dimensional examples, and in particular the sech 2 (x) potential, forms for the Dirac density matrix are exhibited in terms of the potential.This in turn generates the Legendre transform of the single-particle kinetic energy. Finally, one-dimensional perturbation theory for the kinetic energy density, summed to all orders in V, is presented in the appendix.In density functional theory, the single-particle kinetic energy is still not known in an orbital-free form. The natural tool to calculate such kinetic energy for a given one-body potential V is the Dirac density matrix y. Here, by first taking solvable one-dimensional examples, and in particular the sech 2 (x) potential, forms for the Dirac density matrix are exhibited in terms of the potential.This in turn generates the Legendre transform of the single-particle kinetic energy. Finally, one-dimensional perturbation theory for the kinetic energy density, summed to all orders in V, is presented in the appendix.

Journal of Physics A Mathematical and GeneralDec 21, 20050 citations

Generalization and Solution of the Dirac Statistical Equation

CRC Press eBooksMay 21, 20040 citations

Spectral Densities

P. Weinberger

Abstract The previous two chapters were devoted entirely to the concept of multiple scattering, the concept of structure constants, and approximations dealing with the problem of disorder. Since the same formal language was used for both ordered and disordered systems, it is now comparatively easy to discuss spectral densities quite generally. A spectral density is defined in terms of the imaginary part of a representation of a given resolvent. The configuration space representation of the resolvent of the (one-electron) Hamiltonian (see also Chapter 4), for example, yields the (second-order) Dirac density matrix γ(r, r′, ϵ).Abstract The previous two chapters were devoted entirely to the concept of multiple scattering, the concept of structure constants, and approximations dealing with the problem of disorder. Since the same formal language was used for both ordered and disordered systems, it is now comparatively easy to discuss spectral densities quite generally. A spectral density is defined in terms of the imaginary part of a representation of a given resolvent. The configuration space representation of the resolvent of the (one-electron) Hamiltonian (see also Chapter 4), for example, yields the (second-order) Dirac density matrix γ(r, r′, ϵ).

Feb 22, 19900 citations

A new representation for the density matrix

G. Ramachandran, M. V. N. Murthy

Nuclear Physics AMar 1, 198016 citations

The evolution of pionium, the

π^+ π^-

hydrogen-like atom, while passing through matter is solved within the density matrix formalism in the first Born approximation. We compare the influence on the pionium break-up probability between the standard probabilistic calculations and the more precise picture of the density matrix formalism accounting for interference effects. We focus our general result in the particular conditions of the DIRAC experiment at CERN.