Semiclassical Quantum Markovian Master Equations. Case Study: Continuous Wave Magnetic Resonance of Multispin Systems

Gyamfi, Jerryman A.

doi:10.48550/arxiv.2004.10872

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“…In ordinary quantum mechanics in H d , the eigenvalues of observables-like the Hamiltonian or magnetization vector-, which are absolute quantities (at least, up to a constant), are the natural occurrences. Meanwhile, what we experimentally measure in spectroscopic experiments like nuclear magnetic resonance (NMR) are quantities related to the differences between these eigenvalues [67,68]. We need not look further than the resonance conditions of such experiments to see this is the case.…”

Section: Discussionmentioning

confidence: 99%

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Fundamentals of quantum mechanics in Liouville space

Gyamfi

2020

Eur. J. Phys.

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The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of a Kronecker product and what we have termed the ‘bra-flipper’ operator. One of the greater strengths of the formalism expatiated on here is the striking similarities it bears with Dirac’s bra-ket notation. For the purpose of illustrating how the formalism can be effectively employed, we use it to solve a quantum optical master equation for a two-level quantum system and find its Kraus operator sum representation. The paper is addressed to students and researchers with some basic knowledge of linear algebra who want to acquire a deeper understanding of the Liouville space formalism. The concepts are conveyed so as to make the application of the formalism to more complex problems in quantum physics straightforward and unencumbered.

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Section: Discussionmentioning

confidence: 99%

“…as it is expected of Kraus operators in quantum Markovian master equations (290). where we have made use of the definition of L a , (251), and the Kronecker product property we saw in (68) (see also the derivation of (157)). But from (311) and (313), we know e tL b |ρ S (0) = where…”

Section: 33mentioning

confidence: 99%

Fundamentals of quantum mechanics in Liouville space

Gyamfi

2020

Eur. J. Phys.

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show abstract

Semiclassical Quantum Markovian Master Equations. Case Study: Continuous Wave Magnetic Resonance of Multispin Systems

Cited by 1 publication

References 0 publications

Fundamentals of quantum mechanics in Liouville space

Fundamentals of quantum mechanics in Liouville space

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