Dynamical regimes of finite temperature discrete nonlinear Schrödinger chain

Chatterjee, Amit Kumar; Kulkarni, Manas; Kundu, Anupam

doi:10.48550/arxiv.2106.01267

Cited by 3 publications

(4 citation statements)

References 46 publications

(116 reference statements)

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“…Therefore, for large times ∆m(t) = S(−ω 0 )t. (11) In conclusion, in the linear rotator model, the breather mass feels a drift whose coefficient is the component of the power spectrum of the external signal at the breather frequency, S(−ω 0 ) = S(2|z 0 | 2 ). It is therefore useful to determine the power spectrum of the background signal w(t) = −z 1 − z −1 sampled at equilibrium in the absence of breathers.…”

Section: Necessary Ingredients For Frozen Dynamicsmentioning

confidence: 83%

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Frozen dynamics of a breather induced by an adiabatic invariant

Politi,

Iubini

2022

Preprint

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The Discrete Nonlinear Schrödinger (DNLS) equation is a Hamiltonian model displaying frozen dynamics when breathers appear in the system. We study breather relaxation in the thermal region, T < +∞, in a unidirectional version of the DNLS equation, where the rest of the system does not feel the breather. Breather dynamics is governed by a time-dependent onedimensional Hamiltonian with two distinct time scales, and we show that the stability of the breather is related to the existence of an adiabatic invariant (AI). Approximate expressions for the AI are obtained both by implementing a canonical perturbation theory and a more phenomenological approach based on the estimate of the energy flux. The close correspondence with the original model allows excluding that breather destabilization is induced by the formation of localized bound states such as dimers. Finally, the AI dynamics reveals an unexpected similarity with Levy processes, which deserves further investigations.

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Section: Necessary Ingredients For Frozen Dynamicsmentioning

confidence: 83%

“…The first study of the equilibrium properties of the DNLS equation is due to Rasmussen et al [7], who discuss the statistical mechanics for h ≤ h c within the grandcanonical ensemble (more recent studies can be found in Refs. [8,9,10,11]).…”

Section: Introductionmentioning

confidence: 99%

Frozen dynamics of a breather induced by an adiabatic invariant

Politi,

Iubini

2022

Preprint

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“…Further, specific features like butterfly speed has also been studied through collective field theory [29]. As in [28], the space time heat maps of OTOC are found prominent to differentiate the ultra-low, low and high temperature regimes that prevail in the discrete nonlinear Schrödinger chain [30].…”

Section: Introductionmentioning

confidence: 99%

Manifestation of strange nonchaotic attractors in extended systems: A study through out-of-time-ordered correlators

Muruganandam¹,

Senthilvelan²

2021

Preprint

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We study the spatial spread of out-of-time-ordered correlators (OTOCs) in coupled map lattices (CMLs) of quasiperiodically forced nonlinear maps. We use instantaneous speed (IS) and finite-time Lyapunov exponents (FTLEs) to investigate the role of strange non-chaotic attractors (SNAs) on the spatial spread of the OTOC. We find that these CMLs exhibit a characteristic on and off type of spread of the OTOC for SNA. Further, we provide a broad spectrum of the various dynamical regimes in a two-parameter phase diagram using IS and FTLEs. We substantiate our results by confirming the presence of SNA using established tools and measures, namely the distribution of finite-time Lyapunov exponents, phase sensitivity, spectrum of partial Fourier sums, and 0 − 1 test.

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“…The presence of two conservation laws (mass density a and energy density h, see section 2 for a precise definition) determines a non trivial microcanonical phase diagram, characterized by an infinite temperature-line at finite energy, h c (a) = 2a 2 . The first study of the equilibrium properties of the DNLS equation is due to Rasmussen et al [7], who discuss the statistical mechanics for h h c within the grandcanonical ensemble (more recent studies can be found in [8][9][10][11]).…”

Section: Introductionmentioning

confidence: 99%

Frozen dynamics of a breather induced by an adiabatic invariant

Politi¹,

Politi²,

Iubini³

2022

J. Stat. Mech.

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The discrete nonlinear Schrödinger (DNLS) equation is a Hamiltonian model displaying an extremely slow relaxation process when discrete breathers appear in the system. In (Iubini et al 2019 Phys. Rev. Lett. 122 084102), it was conjectured that the frozen dynamics of tall breathers is due to the existence of an adiabatic invariant (AI). Here, we prove the conjecture in the simplified context of a unidirectional DNLS equation, where the breather is ‘forced’ by a background unaffected by the breather itself. We first clarify that the nonlinearity of the breather dynamics and the deterministic nature of the forcing term are both necessary ingredients for the existence of a frozen dynamics. We then derive perturbative expressions of the AI by implementing a canonical perturbation theory and via a more phenomenological approach based on the estimate of the energy flux. The resulting accurate identification of the AI allows revealing the presence and role of sudden jumps as the main breather destabilization mechanism, with an unexpected similarity with Lévy processes.

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Dynamical regimes of finite temperature discrete nonlinear Schrödinger chain

Cited by 3 publications

References 46 publications

Frozen dynamics of a breather induced by an adiabatic invariant

Frozen dynamics of a breather induced by an adiabatic invariant

Manifestation of strange nonchaotic attractors in extended systems: A study through out-of-time-ordered correlators

Frozen dynamics of a breather induced by an adiabatic invariant

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