Bloch equations

Bloch equations

Bloch equations are a set of differential equations that describe the behavior of a single spin magnetization vector in a magnetic field. They are used to describe the interaction of a system with a single electromagnetic field and are satisfied by the density matrix in this case.From: Encyclopaedia of Medical Physics [2020], Detuning-induced stimulated Raman adiabatic passage in dense two-level systems [2018], Nonlinear transport theory in the metal with tunnel barrier [2018]

Introduction to Magnetic Resonance Imaging

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Published in Jianming Jin, in Magnetic Resonance Imaging, 2018

Jianming Jin

The Bloch equations, as they are commonly known, provide one of the simplest models for the behavior of a nuclear spin system after pulse excitations. The only limitation the model has is that it is based on classical principles, and, as such, cannot explain the finer details of NMR spectra, since these are typically due to complex quantum effects. According to Canet (1996), the Bloch equations may be written () dMx,ydt = γ(M × B)x,y − Mx,yT2 () dMzdt = γ(M × B)z + M0 − MzT1

M

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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017

Splinter Robert

The Bloch equation describes the magnetization vector behavior under the NMR phenomenon: dM/dt = M × γB, where M = magnetization vector, B = magnetic field, t = time, and γ is the gyromagnetic ratio. The operator × (i.e., cross-product) in this case represents vector multiplication (see Figure M.23).

Detuning-induced stimulated Raman adiabatic passage in dense two-level systems

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Published in Journal of Modern Optics, 2018

Li Deng, Gongwei Lin, Yueping Niu, Shangqing Gong

The two-level system we consider here is shown in Figure 1(a). When the system interacts with a single electromagnetic field, it can be described by the Bloch equation. In the high density case, the Bloch equation should take into account the NDD interaction, which can be written in the following [21–23]

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Introduction to Magnetic Resonance Imaging

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Detuning-induced stimulated Raman adiabatic passage in dense two-level systems