Kubo–Anderson oscillator and NMR of solid state

Sergeev, N. A.; Olszewski, Marcin

doi:10.1016/j.ssnmr.2008.07.003

Cited by 5 publications

(4 citation statements)

References 40 publications

(61 reference statements)

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“…Prior to this research, there were only two types of stochastic processes for which the relaxation function had been evaluated. Namely, for Gaussian processes [5,9] and for the Markov jump process [10,11,12,13,14,15,16]. Our results add the continuous-time random walk to this list.…”

Section: Final Remarksmentioning

confidence: 71%

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Dephasing by a continuous-time random walk process

Packwood

Tanimura²

2012

Phys. Rev. E

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Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require Q is the value of a stochastic process at time s, and the angular brackets denote ensemble averaging. This paper gives an exact evaluation of these functions for the case where Q is a continuous-time random walk process. The continuous time random walk describes an environment that undergoes slow, step-like changes in time. It also has a well-defined Gaussian limit, and so allows for non-Gaussian and Gaussian stochastic dynamics to be studied within a single framework. We apply the results to extract qubitlattice interaction parameters from dephasing data of P-doped Si semiconductors (data collected elsewhere), and to calculate the two-dimensional spectrum of a three level harmonic oscillator undergoing random frequency modulations.

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Section: Final Remarksmentioning

confidence: 71%

“…For interactions that take place on a slower time scale, we have stationary Markov jump processes (also known as the random telegraph process). The phase relaxation function in equation (1) (but apparently not the one in (2)) has been evaluated and applied for a variety of such cases [5,9,11,12,13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Dephasing by a continuous-time random walk process

Packwood

Tanimura²

2012

Phys. Rev. E

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“…We suppose that the molecule-environment coupling causes a stochastic modulation to the vibrational mode frequencies. This 'stochastic frequency modulation' approach is used extensively in the field of spectroscopy to model optical relaxation processes [31,32], and can be described by the Kubo oscillator model [33][34][35][36][37][38],…”

Section: Stochastic Boltzmann Equation (A) Stochastic Model For Magnetic Relaxation In High-spin Moleculesmentioning

confidence: 99%

Stochastic Boltzmann equation for magnetic relaxation in high-spin molecules

2016

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We introduce the stochastic Boltzmann equation (SBE) as an approach for exploring the spin dynamics of magnetic molecules coupled to a stochastic environment. The SBE is a time-evolution equation for the probability density of the spin density matrix of the system. This probability density is relevant to experiments which take measurements on single molecules, in which probabilities of observing particular spin states (rather than ensemble averages) are of interest. By analogy with standard treatments of the regular Boltzmann equation, we propose a relaxation-time approximation for the SBE, and show that solutions to the SBE under the relaxation-time approximation can be obtained by performing simple trajectory simulations for the case of a boson gas environment.Cases where the relaxation-time approximation are satisfied can therefore be investigated by careful choice of the parameters for the boson gas environment, even if the actual environment is quite different from a boson gas. The application of the SBE approach is demonstrated through an illustrative example.

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“…Recently, Sergeev and Olszewski have derived an analytical solution for the Kubo-Anderson oscillator with a fluctuating frequency ω for an arbitrary distribution function which has been applied to explain various dynamical problems of solid state NMR, when the potential barrier for the mobility of magnetic nuclei is a stochastic function of time. SR has also been studied on pattern formation, spatial order of spiral waves, Ising model, and so on.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Resonance in a Generalized Quantum Kubo Oscillator

Ghosh

Chattopadhyay

Chaudhuri³

2009

J. Phys. Chem. B

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We discuss stochastic resonance in a biased linear quantum system that is subject to multiplicative and additive noises. Starting from a microscopic system-reservoir Hamiltonian, we derive a c-number analogue of the generalized Langevin equation. The developed approach puts forth a quantum mechanical generalization of the "Kubo type" oscillator which is a linear system. Such a system is often used in the literature to study various phenomena in nonequilibrium systems via a particular interaction between system and the external noise. Our analytical results proposed here have the ability to reveal the role of external noise and vis-a-vis the mechanisms and detection of subtle underlying signatures of the stochastic resonance behavior in a linear system. In our development, we show that only when the external noise possesses a "finite correlation time" the quantum effect begins to appear. We observe that the quantum effect enhances the resonance in comparison to the classical one.

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Kubo–Anderson oscillator and NMR of solid state

Cited by 5 publications

References 40 publications

Dephasing by a continuous-time random walk process

Dephasing by a continuous-time random walk process

Stochastic Boltzmann equation for magnetic relaxation in high-spin molecules

Stochastic Resonance in a Generalized Quantum Kubo Oscillator

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