Analytic representations of finite quantum systems based on $SU(2)$ coherent states in $C\cup\{\infty\}$ and potential quantum applications to energy works

Mohammed, Aisha Faraj Abukhzam

doi:10.1109/gec55014.2022.9986916

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2024

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“…This connection was initially defined by [13] and [3]. In our recent paper [15], we further developed this work by providing a numerical implementation of these functions and exploring their behavior, including calculating their zeros through numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Dirac Contour Representation for Quantum Systems with Finite-Dimensional Hilbert Space in the Extended Complex Plane

Mohammed,

Mageed

2024

The 6th International Conference on Numerical Modelling in Engineering

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The Dirac contour representation functions fk(z) and fb(z) are employed to represent theket states |f ⟩ and bra states ⟨f |, respectively, in quantum systems with a finite-dimensional Hilbertspace H_2j+1. The scalar product within these quantum systems is defined using a contour integral.Moreover, a numerical approach is utilized to examine the time evolution of both periodic and non-periodic systems, utilizing several Hamiltonian matrices. Furthermore, the stability of periodic systemsis investigated. In addition to these aspects, we study the most significant application of the Dirac con-tour representation, which is its capability to handle an extended Hilbert space, suitable for describingquantum physics at negative temperatures.

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Section: Introductionmentioning

confidence: 99%