Generalized Boltzmann equation describing the dynamics of bosons and fermions

Esteban Cárdenas, Thomas Chen

Haotian Tang, Philip John Siemens

Mushfiq Ahmad, Muhammad O. G. Talukder

The differential equation for Boltzmann's function is replaced by the corresponding discrete finite difference equation. The difference equation is, then, symmetrized so that the equation remains invariant when step d is replaced by -d. The solutions of this equation come in Boson-Fermion pairs. Reciprocal symmetric Boltzmann's function, thus, unifies both Bosonic and Fermionic distributions.

G. F. Bertsch

Jeffrey Yepez

Presented is a second quantized technology for representing fermionic and bosonic entanglement in terms of generalized joint ladder operators, joint number operators, interchangers, and pairwise entanglement operators. The joint number operators generate conservative quantum logic gates that are used for pairwise entanglement in quantum dynamical systems. These are most useful for quantum computational physics. The generalized joint operator approach provides a pathway to represent the Temperley-Lieb algebra and to represent braid group operators for either fermionic or bosonic many-body quantum systems. Moreover, the entanglement operators allow for a representation of quantum measurement, quantum maps (associated with quantum Boltzmann equation dynamics), and for a way to completely and efficiently extract all accessible bits of joint information from entangled quantum systems in terms of quantum propositions.

Shigeji Fujita