Statistical distribution of quantum particles

G. Kaniadakis, P. Quarati

Ahmad Adel Abutaleb

SERGEI B. ISAKOV

Generalized statistical distributions for identical particles are introduced for the case where filling a single-particle quantum state by particles depends on filling states of different momenta. The system of one-dimensional bosons with a two-body potential that can be solved by means of the thermodynamic Bethe ansatz is shown to be equivalent thermodynamically to a system of free particles obeying statistical distributions of the above class. The quantum statistics arising in this way are completely determined by the two-particle scattering phases of the corresponding interacting systems. An equation determining the statistical distributions for these statistics is derived.

Won-Young Hwang, Kicheon Kang

We propose an experimental scheme to probe the quantum statistics of two identical particles. The transition between the quantum and classical statistics of two identical particles is described by the particles having identical multiple internal energy levels. We show that effective distinguishability emerges as the thermal energy increases with respect to the energy level spacing, and the mesoscopic regime bridges quantum indistinguishability and classical distinguishability. A realistic experimental approach is proposed using a two-particle interferometer, where the particles reach statistical equilibrium before the two-particle distribution is measured. The unitarity of the scattering/separation process ensures the preservation of the equilibrium distribution and allows a direct measurement of the two-particle statistical distribution. Our results show the transition between quantum and classical behavior of the two-particle distribution, which can be directly probed by a realistic experiment.

Won-Young Hwang, Kicheon Kang

We propose an experimental scheme to probe the quantum statistics of two identical particles. The transition from quantum to classical statistics of two identical particles can be described by introducing multiple identical internal energy levels for each particle. We show that as the thermal energy exceeds the level spacing, the particles acquire effective distinguishability. This gives rise to a mesoscopic regime that smoothly connects quantum indistinguishability and classical distinguishability. A realistic experimental approach is proposed using a two-particle interferometer, where the particles reach statistical equilibrium before the two-particle distribution is measured. The unitarity of the scattering and separation processes guarantees preservation of the equilibrium distribution, enabling a direct measurement of the two-particle statistical distribution. Our results show the transition between quantum and classical behavior of the two-particle distribution, which can be directly probed by a realistic experiment.

Mark Kon