دانلود مقاله : Universality of entanglement creation in low-energy two-dimensional scattering 2013

چکیده : 

We prove that the entanglement created in the low-energy scattering

of two particles in two dimensions is given by a universal

coefficient that is independent of the interaction potential. This is

strikingly different from the three dimensional case, where it is

proportional to the total scattering cross section. Before the collision

the state is a product of two normalized Gaussians. We take

the purity as the measure of the entanglement after the scattering.

We give a rigorous computation, with error bound, of the leading

order of the purity at low-energy. For a large class of potentials,

that are not-necessarily spherically symmetric, we prove that the

low-energy behavior of the purity, P, is universal. It is given by

− 1

(ln(σ /¯h))2 E, where σ is the variance of the Gaussians and

the entanglement coefficient, E, depends only on the masses of the

particles and not on the interaction potential. There is a strong dependence

of the entanglement in the difference of the masses