Collision dynamics of two interacting particles

S. P. Khare

Pang Xiao‐feng

The dynamic and collision features of microscopic particles described by nonlinear Schrodinger equation are investigated deeply using the analytic and the Runge-Kutta method of numerical simulation. The results show that the microscopic particles have a wave-corpuscle duality and are stable in propagation. When the two microscopic particles are collided, they can go through each other and retain their form after their collision of head-on from opposite directions, This feature is the same with that of the classical particles. However, a wave peak of large amplitude, which is a result of complicated superposition of two solitary waves, occurs in the colliding process. This displays the wave feature of microscopic particles. Therefore, the collision process shows clearly that the solutions of the nonlinear Schrodinger equation have a both corpuscle and wave feature, then the microscopic particles represented by the solutions have a wave-corpuscle duality. Obviously, this is due to the nonlinear interaction b||2. Thus we can determine the nonlinear Schrodinger equation can describe correctly the natures and properties of microscopic particles in quantum systems. Key words: Microscopic particle Schrodinger equation; Wave-corpuscle duality; Nonlinear interaction; Collision; Propagation; Quantum mechanics

X. Z. Zhang, Z. Song

We study the dynamics of the collision between two fermions in Hubbard model with on-site interaction strength U. The exact solution shows that the scattering matrix for two-wavepacket collision is separable into two independent parts, operating on spatial and spin degrees of freedom, respectively. The S-matrix for spin configuration is equivalent to that of Heisenberg-type pulsed interaction with the strength depending on U and relative group velocity vr. This can be applied to create distant EPR pair, through a collision process for two fermions with opposite spins in the case of |vr/U| = 1, without the need for temporal control and measurement process. Multiple collision process for many particles is also discussed.

Max Born

Qingze Guan, Vincent M. Klinkhamer, Ralf Klemt +5 more

Access to single particle momenta provides new means of studying the dynamics of few interacting particles. In a joint theoretical and experimental effort, we observe and analyze the effects of a finite number of ultracold two-body collisions on the relative and single-particle densities by quenching two ultracold atoms with initial narrow wave packet into a wide trap with inverted aspect ratio. The experimentally observed spatial oscillations of the relative density are reproduced by a parameter-free zero-range theory and interpreted in terms of cross-dimensional flux. We theoretically study the long time dynamics and find that the system does not approach its thermodynamic limit. The set-up can be viewed as an advanced particle-collider that allows one to watch the collision process itself.