Lyapunov exponents and poles in a non Hermitian dynamics

Gomez, Ignacio S.

doi:10.1016/j.chaos.2017.04.009

Cited by 5 publications

(3 citation statements)

References 47 publications

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“…Transient chaos can be characterized by studying the maximal FT LE with a moving window of finite timeseries. We have chosen the Gram-Schmidt orthogonalization method to calculate the maximal FT LE [40][41][42]. So, accordingly, in our numerical computation, we have chosen to evaluate the FT LE for a sufficiently long temporal evolution of the system.…”

Section: Analysis Of Fixed Points and Time-seriesmentioning

confidence: 99%

Problems and Prospects of Development in Guwahati, Assam

Deka

Devi

2017

The Urban Book Series

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We propose a parity-time symmetric dielectric-nanofilm-dielectric multilayered structure that could facilitate highly amplified transmission of optical power in the infrared spectrum. We have theoretically studied our model using the transfer matrix formalism. The reflection and the transmission coefficients of the S-matrix are evaluated. The theoretical results are validated by FDTD numerical simulation. We have shown how the thickness of the layers and the gain/loss coefficient of the active layers could generate spectral singularities in the S-matrix and how these singularities could be exploited to achieve amplified transmission of a single wavelength through the structure.

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Section: Analysis Of Fixed Points and Time-seriesmentioning

confidence: 99%

Problems and Prospects of Development in Guwahati, Assam

Deka

Devi

2017

The Urban Book Series

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“…More precisely, the Kolmogorov-Sinai (KS) entropy of continuous and discrete chaotic systems tend to coincide for a certain finite time range. In this sense, the KS-entropy represents a robust indicator in the field [6][7][8][9][10][11][12][13][14]. The coarse-graining of the quantum phase space, as a consequence of the Uncertainty Principle (UP), has an intimate relationship with quantum chaos time scales [15][16][17][18][19], and quantum extensions for the KS-entropy have been proposed [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A unified time scale for quantum chaotic regimes

Gomez¹,

Borges²

2018

J. Stat. Mech.

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We present a generalised time scale for quantum chaos dynamics, motivated by nonextensive statistical mechanics. It recovers, as particular cases, the relaxation (Heisenberg) and the random (Ehrenfest) time scales. Moreover, we show that the generalised time scale can also be obtained from a nonextensive version of the Kolmogorov-Sinai entropy by considering the graininess of quantum phase space and a generalised uncorrelation between subsets of the phase space. Lyapunov and regular regimes for the fidelity decay are obtained as a consequence of a nonextensive generalisation of the mth point correlation function for a uniformly distributed perturbation in the classical limit.

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“…The use of such tool makes the significant progress in study of the finite-dimensional flow systems [18,19], discrete maps [20] and timeseries [21] (including the cases with the presence of noise, see, e.g, [22]). In recent works Lyapunov exponents are applied for analysis of non Hermitian Hamiltonian systems [23] and neural systems [24]. In the case of spatiotemporal dynamics the calculation of LEs is more complicated [25,26].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov analysis of the spatially discrete-continuous system dynamics

Maksimenko

Hramov

Короновский

et al. 2017

Chaos, Solitons & Fractals

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Citation: MAXIMENKO, V.A. ... et al, 2017. Lyapunov analysis of the spatially discrete-continuous system dynamics. Chaos, Solitons and Fractals, 104, Additional Information:• This paper was accepted for publication in the journal Chaos, Soli- AbstractThe spatially discrete-continuous dynamical systems, that are composed of a spatially extended medium coupled with a set of lumped elements, are frequently met in different fields, ranging from electronics to multicellular structures in living systems. Due to the natural heterogeneity of such systems, the calculation of Lyapunov exponents for them appears to be a challenging task, since the conventional techniques in this case often become unreliable andPreprint submitted to Elsevier August 31, 2017inaccurate. The paper suggests an effective approach to calculate Lyapunov exponents for discrete-continuous dynamical systems, which we test in stability analysis of two representative models from different fields. Namely, we consider a mathematical model of a 1D transferred electron device coupled with a lumped resonant circuit, and a phenomenological neuronal model of spreading depolarization, which involves 2D diffusive medium. We demonstrate that the method proposed is able reliably recognize regular, chaotic and hyperchaotic dynamics in the systems under study.

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Lyapunov exponents and poles in a non Hermitian dynamics

Cited by 5 publications

References 47 publications

Problems and Prospects of Development in Guwahati, Assam

Problems and Prospects of Development in Guwahati, Assam

A unified time scale for quantum chaotic regimes

Lyapunov analysis of the spatially discrete-continuous system dynamics

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