The Stability Of Charged Multi-body Particles In Periodic Potential Wells

In this paper,we study the stability of odd-numbered charged particles in one-dimensional periodic potentials Vtrap =V0(-cos(27??)+ 1).From the principle of minimum energy can be seen:a number of particles together,the lowest energy state is the most stable equilibrium state.Assuming that the particles are only affected by periodic potential wells and Coulomb force,the energy of 2N + 1 charges is given by Hamiltonian(?)Firstly,we proved the stability of three particles and five particles system.Sec-ondly,we used the proposition 2.5 to prove that when V0>7q2/8?2?0.(2N + 1),2N + 1 particles system also had a stable equilibrium position.In particular,when N??,the particles still had a stable equilibrium state.