A Classical View of the Euler Angles and the Euler Kinematic Equations in NMR

Siminovitch, D.

doi:10.1006/jmra.1995.0767

Cited by 7 publications

(2 citation statements)

References 22 publications

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“…The velocity of the evolution can be regarded as the classical speed of the state point r(t) on the Bloch sphere, and the expression can be derived [46,[56][57][58][59][60][61][62] as…”

Section: Discussionmentioning

confidence: 99%

“…where ω(t) is the angular velocity determined by 1 2 ω • σ ≡ H. This equation can also be derived by the quantum dynamics expressed in (3a)-(3c) (see appendix B.6), which can be viewed as the Euler kinematic equations [58][59][60][61][62]. From another perspective, if we can solve the vector differential equation ( 15) for a classical ω(t), the quantum dynamics will also be obtained by (1) or (2).…”

Section: Discussionmentioning

confidence: 99%

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Generating arbitrary analytically solvable two-level systems

Liang

2024

J. Phys. A: Math. Theor.

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We present a new approach for generating arbitrary analytically solvable two-level systems.This method offers the ability to completely derive all analytically solvable Hamiltonians for any analytical evolutions of two-level systems.To demonstrate the effectiveness of this approach, we reconstruct the Rosen-Zener model and generate several new exact solutions.Using this approach, we present the exact evolution of the semi-classical Rabi model with new analytical properties.The parameters used to generate Hamiltonians have direct physical interpretations within the Bloch sphere, the quantum speed limit, and the geometric phase.As a result, the physical properties of the generated Hamiltonian are highly controllable, which plays a significant role in the fields of quantum control, quantum computing, and quantum information.

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“…The velocity of the evolution can be regarded as the classical speed of the state point r(t) on the Bloch sphere, and the expression can be derived [46,[56][57][58][59][60][61][62] as…”

Section: Discussionmentioning

confidence: 99%