Relativistic and Non-Relativistic Many-Body Procedure, Applied to Atomic Systems

V. A. Sidorovich

A new operator approach to the solution of the non-relativistic Schrödinger equation for few-body quantum systems with pair-wise interaction is presented. The problem is solved on the basis of the sequential account of configurations (SAC) method proposed. The wave-function of a few-body system determined with allowance for the configuration interaction (CI-wavefunction) is expressed in terms of the one-configuration wavefunctions with use of the configuration mixing operator (±) introduced in the paper. The examination is carried out with an example of a few-electron atomic system. An analytical expression for the (±) -operator has been represented and an integral equation for the CI-wavefunction has been obtained. It is shown that: (I) the correlation interaction inside an isolated configuration does not destroy the independent particle approximation; (ii) in the framework of the present approach the self-action is excluded. The present approach has enabled to receive an analytical expression for the (±) -operator without applying the non-physical procedure of 'switching-on' the interconfiguration interaction.

Lloyd Armstrong

Ingvar Lindgren

D Sherrington

In a discussion of the quantum dynamics of a non-relativistic many-particle system it is shown how a two-body interaction, quartic in the field operators, may be replaced by an interaction with an auxliary density-like field. An extension of the procedure of Edwards and Sherrington for expanding in terms of correlations about the state of maximal quantum randomness is applied to the coupled system to give the density correltions and excitations as well as the corresponding single-particle quantities. As an example, an explicit expression for the density excitations is obtained in terms of the quasi-particle energies, for the case in which quasi-particles exist as well-defined modes of single-particle excitation.

Ingvar Lindgren

Juan Carlos García-Escartín, Pedro Chamorro‐Posada

Grover's algorithm for quantum search can also be applied to classical energy transfer. The procedure takes a system in which the total energy is equally distributed among N subsystems and transfers most of it to one marked subsystem. We show that in a relativistic setting the efficiency of this procedure can be improved. We will consider the transfer of relativistic kinetic energy in a series of elastic collisions. In this case, the number of steps of the energy transfer procedure approaches 1 as the initial velocities of the objects become closer to the speed of light. This is a consequence of introducing nonlinearities in the procedure. However, the maximum attainable transfer will depend on the particular combination of speed and number of objects. In the procedure, we will use N elements, as in the classical non-relativistic case, instead of the log 2 ( N ) states of the quantum algorithm.