Abstract

The imperceptible identical particle systems such as electron gas in metals have been the concern of experimental and theoretical studies mostly aiming to understand the properties of these systems. Hartree-Fock equation of electron gas, a fermion quantum plasma, has been established by the method of “equation of motion”, and by using Dirac field. The goal of this paper is to establish regarding the same method, the Hartree-Fock equation for a non-neutral plasma of identical ions of spin zero at high density and low temperature in a Paul trap, by using the complex scalar field.

Highlights

  • Cooled ions are used as quantum memories [1]. These identical ions comply with different statistics according to whether it is concerned with fermions or bosons

  • When the spin of these ions is zero, the dynamics of the system at high density and low temperature is given by the approximation equation which is the concern of this study

  • The usual constraints with a drawing of a trap are the precision of the parts, that of their position and the pertubations of the electrical field created by the environment of the electrodes, notably the fixing structure. These traps are Fernand Tshizanga Mpinga: Hartree-Fock Equation for a Non-neutral Plasma of Spin Zero Ions in a Paul Trap used in ultra-vacuum chambers; which requires a choice of suitable materials

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Summary

Introduction

Cooled ions are used as quantum memories [1] These identical ions comply with different statistics according to whether it is concerned with fermions or bosons. HartreeFock equation is an approximated equation of the dynamics of a system at low temperature [2] [3]. When the spin of these ions is zero, the dynamics of the system at high density and low temperature is given by the approximation equation which is the concern of this study. Cylindrical bars are parallely set out and diagonally paired. They are referred to as electrodes pair RF and electrodes pair DC. 2. Hartree-Fock Equation for a Non-neutral Plasma of Spin Zero Ions in a Paul Trap

Non-neutral Plasma in a Paul Trap
Laser Cooling Technique
Microscopic Theory
Complex Scalar Field and Its Quantization
Boson Operators and Commutation Relations
Space of Quantum States of Boson Operators
Hamiltonian Operator of Non- Neutral Plasma
Temporal Evolution of the Field Operator of Zero Spin Ion
2.10. Hartree- Fock Equation of Identical Ions of Spin Zero
Conclusion
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