Symmetry and Natural Quantum Structures for Three-Particles in One-Dimension

B. Weinstein, Nathan L. Harshman, Jessica Uscinski

N. L. Harshman

How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical systems, from integrability to hard chaos. This article demonstrates that the related but distinct notions of integrability, separability, and solvability identify meaningful collective observables for Hamiltonians with sufficient symmetry. In turn, these observables induce tensor product structures on the Hilbert space that are especially useful for storing and processing quantum information and provide guidance to interpretation and phenomenology of quantum few-body physics.

Gianluca Stefanucci

Paolo Amore, Francisco Marcelo Fernández

Sayed Kazem Mousavi

This study presents a theory with a six-dimensional space-time structure, , in order to describe microscopic phenomena, the time arrow and complex phenomena of the quantum world. The interpretation of quantum world phenomena using four-dimensional space-time would be a very complicated and indescribable task. The dual wave-particle behavior, entanglement, quantum corridors, etc., represent the complex space-time structure. Previous studies indicate that complicated behaviors of particles in quantum mechanics are basically considered as the natural behavior of those particles. The theoretical framework of the nature of time is the transformation of imaginary dimensions into geometric dimensions and the description of quantum mechanical phenomena using external Euclidean geometry. The six-dimensional space-time structure consists of three space and three time dimensions, , and the time arrow is the result of the impossibility of the existence of matter in six space-time dimensions, and the direction of the arrow is aligned with the expansion of the universe.

Luis Grave de Peralta, Maricela Fernández Lozada, Hira Farooq +3 more