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New Aspects in Physics on Gel'fand Triplets

Tsunehiro Kobayashi

International Journal of Theoretical PhysicsOct 1, 20037 citations

Zero-Energy Flows and Vortex Patterns in Quantum Mechanics

We show that zero-energy flows appear in many particle systems as same as in single particle cases in 2-dimensions. Vortex patterns constructed from the zeroenergy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel’fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. We point out three interesting properties of the zero-energy flows; (i) the absolute economy as for the energy consumption, (ii) the infinite variety of the vortex patterns, and (iii) the absolute stability of the vortex patterns Keywords: Zero-energy solutions, vortex creations and annihilations, quantum mechanics, Gel’fand triplets,We show that zero-energy flows appear in many particle systems as same as in single particle cases in 2-dimensions. Vortex patterns constructed from the zeroenergy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel’fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. We point out three interesting properties of the zero-energy flows; (i) the absolute economy as for the energy consumption, (ii) the infinite variety of the vortex patterns, and (iii) the absolute stability of the vortex patterns Keywords: Zero-energy solutions, vortex creations and annihilations, quantum mechanics, Gel’fand triplets,

Jan 1, 20031 citation

One-dimensional infinite square well potential

David Thompson

Physics EducationJul 1, 19842 citations

Swanson Hamiltonian: non-PT-symmetry phase

Viviano Fernández, Romina Ramírez, M. Reboiro

In this work, we study the non-Hermitian Swanson Hamiltonian, particularly the non-parity-time symmetry phase. We use the formalism of Gel´fand triplet to construct the generalized eigenfunctions and the corresponding spectrum. Depending on the region of the parameter model space, we show that the Swanson Hamiltonian represents different physical systems, i.e. parabolic barrier, negative mass oscillators. We also discussed the presence of Exceptional Points of infinite order.

Dec 1, 202120 citations

INFINITELY DEEP SQUARE-WELL POTENTIAL

Shi‐Hai Dong

Springer eBooksJan 1, 20071 citation

Swanson Hamiltonian: non-PT-symmetry phase

Viviano Fernández, Romina Ramírez, M. Reboiro

Abstract In this work, we study the non-Hermitian Swanson Hamiltonian, particularly the non-parity-time symmetry phase. We use the formalism of Gel’fand triplet to construct the generalized eigenfunctions and the corresponding spectrum. Depending on the region of the parameter model space, we show that the Swanson Hamiltonian represents different physical systems, i.e. parabolic barrier, negative mass oscillators. We also discussed the presence of Exceptional Points of infinite order.

arXiv:2108.01004Journal of Physics A Mathematical and TheoreticalNov 17, 20210 citations

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