On the relation between pseudo-Hermiticity and dissipation

Brizard, Alain J.

doi:10.1016/0375-9601(94)91112-6

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…Proof : The consistency of the relations (24) follows from Corollary 1 so the statement (26) is true. This is easily seen to be equivalent to the operator identity (25).…”

Section: Consider Now Any Curve Onmentioning

confidence: 92%

See 1 more Smart Citation

The Hamiltonian-Adjoint Equation and Perturbation Theory

Larsson¹

1998

Phys. Scr.

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“…Proof : The consistency of the relations (24) follows from Corollary 1 so the statement (26) is true. This is easily seen to be equivalent to the operator identity (25).…”

Section: Consider Now Any Curve Onmentioning

confidence: 92%

“…Theory including lowest order nonlinear terms is obtained if, in addition to the relations (24), the three new relations involving also and are used. Then a relation u 2 m 2 similar to (25), but now also involving the operators X 0 (2), and is obtained. These relations are not included in Y 0…”

Section: Consider Now Any Curve Onmentioning

confidence: 99%

The Hamiltonian-Adjoint Equation and Perturbation Theory

Larsson¹

1998

Phys. Scr.

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“…This makes Ĥ pseudo-Hermitian. 78,79 Consider a variable transformation w = Q1/2 η, so Eq. ( 21) becomes…”

Section: B Kelvin-helmholtz Instabilitymentioning

confidence: 99%

Wave-kinetic approach to zonal-flow dynamics: recent advances

Zhu,

Dodin

2021

Preprint

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Basic physics of drift-wave turbulence and zonal flows has long been studied within the framework of wavekinetic theory. Recently, this framework has been re-examined from first principles, which has led to more accurate yet still tractable "improved" wave-kinetic equations. In particular, these equations reveal an important effect of the zonal-flow "curvature" (the second radial derivative of the flow velocity) on dynamics and stability of drift waves and zonal flows. We overview these recent findings and present a consolidated high-level picture of (mostly quasilinear) zonal-flow physics within reduced models of drift-wave turbulence.

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“…If fluid plasma has inhomogeneous density and finite temperature (or average flow velocity), then it has free energy [29,30,31,32] that can drive linear instabilities. Although the corresponding dynamics remains Hamiltonian in the general sense of the word, the "quantumlike" Hamiltonian that enters the corresponding Schrödinger equation ceases to be Hermitian and becomes pseudo-Hermitian instead [33,34,35]. This means that plasma dynamics is governed by…”

Section: Introductionmentioning

confidence: 99%

On applications of quantum computing to plasma simulations

Dodin¹,

Startsev²

2020

Preprint

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Quantum computing is gaining increased attention as a potential way to speed up simulations of physical systems, and it is also of interest to apply it to simulations of classical plasmas. However, quantum information science is traditionally aimed at modeling linear Hamiltonian systems of a particular form that is found in quantum mechanics, so extending the existing results to plasma applications remains a challenge. Here, we report a preliminary exploration of the long-term opportunities and likely obstacles in this area. First, we show that many plasma-wave problems are naturally representable in a quantumlike form and thus are naturally fit for quantum computers. Second, we consider more general plasma problems that include non-Hermitian dynamics (instabilities, irreversible dissipation) and nonlinearities. We show that by extending the configuration space, such systems can also be represented in a quantumlike form and thus can be simulated with quantum computers too, albeit that requires more computational resources compared to the first case. Third, we outline potential applications of hybrid quantum-classical computers, which include analysis of global eigenmodes and also an alternative approach to nonlinear simulations.

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On the relation between pseudo-Hermiticity and dissipation

Cited by 8 publications

References 19 publications

The Hamiltonian-Adjoint Equation and Perturbation Theory

The Hamiltonian-Adjoint Equation and Perturbation Theory

Wave-kinetic approach to zonal-flow dynamics: recent advances

On applications of quantum computing to plasma simulations

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