Instability in the Hartmann-Hahn double resonance

Levi, Roei; Masis, Sergei; Buks, Eyal

doi:10.1103/physreva.102.053516

Cited by 9 publications

(20 citation statements)

References 25 publications

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“…The system's stability depends on the set of eigenvalues of the Jacobian matrix J, which is denoted by S. The system is stable provided that real (ξ) < 0 for any ξ ∈ S. It was shown in appendix B of Ref. [8] that such a system is stable provided that J u , J A and J B are all real, J u is antisymmetric, all diagonal elements of J A + J B are positive, and d H is finite. Properties of the matrices J u , J A and J B are analyzed below.…”

Section: It Is Convenient To Express the Perturbation ǫVmentioning

confidence: 99%

“…[17] (see also appendix B of Ref. [8]) that such a linear master equation is stable provided that γ E > 0. Below we analyze the stability of the nonlinear GME (2).…”

mentioning

confidence: 99%

“…For the first one, which is henceforth referred to as unitary nonlinearity, the unitary term Θ u (ρ) is replaced by a nonlinear term. In most cases, unitary nonlinearity originates from either the mean field approximation [5][6][7][8], or from a transformation mapping the Hilbert space of finite dimension d H into a space having infinite dimensionality (e.g. the Holstein-Primakoff transformation [9], which can yield a parametric instability in ferromagnetic resonators [10]).…”

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confidence: 99%

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Stability of the Grabert master equation

Buks,

Schwartz

2021

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We study the dynamics of a quantum system having Hilbert space of finite dimension dH. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the nonlinear master equation derived by Grabert. The dynamics near a fixed point is analyzed by using the method of linearization, and by evaluating the eigenvalues of the Jacobian matrix. We find that all these eigenvalues are non-negative, and conclude that the fixed point is stable. This finding raises the question: under what conditions instability is possible in a quantum system having finite dH?

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Section: It Is Convenient To Express the Perturbation ǫVmentioning

confidence: 99%

“…[17] (see also appendix B of Ref. [8]) that such a linear master equation is stable provided that γ E > 0. Below we analyze the stability of the nonlinear GME (2).…”

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Stability of the Grabert master equation

Buks,

Schwartz

2021

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“…Limit cycle solutions for the modified Schrödinger equation are found in the instability region. The instability of the modified Schrödinger equation is closely related to an instability found with a similar spin-spin system [19], when the equations of motion generated by the standard Schrödinger equation are analyzed using the mean field approximation [20][21][22][23]. * eyal@ee.technion.ac.il…”

Section: Introductionmentioning

confidence: 99%

Disentanglement and a nonlinear Schrödinger equation

Buks¹

2022

J. Phys. A: Math. Theor.

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“…We explore the effect of the added disentanglement nonlinear term for the case of a two-spin 1/2 system. With externally applied driving the two-spin 1/2 system can become unstable [17,18] when the Hartmann Hahn matching condition [19,20] is nearly satisfied. We find that in the same region the added nonlinear disentangling term has a relatively large effect on the dynamics.…”

Section: Introductionmentioning

confidence: 99%

The mean field approximation and disentanglement

Buks¹

2021

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The mean field approximation becomes applicable when entanglement is sufficiently weak. We explore a nonlinear term that can be added to the Schrödinger equation without violating unitarity of the time evolution. We find that the added term suppresses entanglement, without affecting the evolution of any product state. The dynamics generated by the modified Schrödinger equation is explored for the case of a two-spin 1/2 system. We find that for this example the added term strongly affects the dynamics when the Hartmann Hahn matching condition is nearly satisfied.

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Instability in the Hartmann-Hahn double resonance

Cited by 9 publications

References 25 publications

Stability of the Grabert master equation

Stability of the Grabert master equation

Disentanglement and a nonlinear Schrödinger equation

The mean field approximation and disentanglement

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