Momentum autocorrelation function of an impurity in a classical oscillator chain with alternating masses— I. General theory

Yu, Ming B.

doi:10.1016/j.physa.2013.11.023

Cited by 20 publications

(10 citation statements)

References 23 publications

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“…One could make it a periodic diatomic chain [8] or even an aperiodic diatomic chain [8]. We are providing a list of recent advances made by the method of recurrence relations on others [38][39][40][41][42][43][44]. For related studies on HC by Fokker-Planck dynamics and non-exponential decay, see [7,45,46].…”

Section: Discussionmentioning

confidence: 99%

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Local Dynamics in an Infinite Harmonic Chain

Lee¹

2016

Symmetry

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Section: Discussionmentioning

confidence: 99%

“…In an infinite HC, there are also infinitely many periods. See Equation (40). Thus, the HC has the necessary and possibly sufficient property for chaos.…”

Section: Harmonic Chain and Logistic Mapmentioning

confidence: 99%

Local Dynamics in an Infinite Harmonic Chain

Lee¹

2016

Symmetry

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“…23 A chain composed of classic harmonic oscillators with alternating masses and one mass impurity was studied using the recurrence relations method. 24 The monatomic mass-spring chain with a cubic nonlinearity was studied by the multiple scales analysis of wave–wave interactions. 25 Free wave propagation properties in one-dimensional chains of nonlinear oscillators were investigated by means of nonlinear maps.…”

Section: Introductionmentioning

confidence: 99%

Lateral vibration analysis of monatomic chains considering atomic longitudinal displacement

Liu

Qin

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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The lateral vibration of monatomic chains considering atomic longitudinal displacements is studied by using the string vibration theory. The modes of lateral vibration of monatomic chains are assumed as the modes of string vibration. Based on the string assumption, the equation of string vibration for monatomic chains is established. Coordinates of the vibration atoms can be calculated by utilizing boundary conditions and symmetry conditions of monatomic chains. The natural angular frequencies of transverse vibration of monatomic chains are calculated by the string vibration method. The tension of the quantum limitation is given and the value of limitation can be used to distinguish nanoelectromechanical systems from quantum-electromechanical Systems. Natural angular frequencies and resonant frequencies of the monatomic chain string are associated with the axial tension acting on the string and the length of monatomic chains, and they can be altered by changing the length of the string and the axial tension acting on the string. The nonlinear vibration of single atomic chain can be analyzed using the improved Lindstedt-Poincaré multiscale method. The study found that the stiffness of the carbon monatomic chain can be altered by changing the length of the string and the tension acting on the string.

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“…Several approaches have been used to calculate these quantities, including exact diagonalization [33][34][35] and the method of recurrence relations [8,17,[36][37][38]. The latter has also been applied to electron gases [39], velocity autocorrelation functions of many-body systems [40], and harmonic oscillator chains [41,42].…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the method of recurrence relations produces analytic results for the dynamic correlation functions of interest. There are a few instances where the recurrence relations method produces exact results, such as in the TI and XY models [17], as well as in harmonic oscillator chains [41,42]. It does not require explicit knowledge of the eigenvalues and eigenstates of the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the transverse Ising model with next-nearest-neighbor interactions

et al. 2015

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We study the effects of next-nearest-neighbor (NNN) interactions on the dynamics of the one-dimensional spin-1/2 transverse Ising model in the high-temperature limit. We use exact diagonalization to obtain the time-dependent transverse correlation function and the corresponding spectral density for a tagged spin. Our results for chains of 13 spins with periodic boundary conditions produce results which are valid in the infinite-size limit. In general we find that the NNN coupling produces slower dynamics accompanied by an enhancement of the central mode behavior. Even in the case of a strong transverse field, if the NNN coupling is sufficiently large, then there is a crossover from collective mode to central mode behavior. We also obtain several recurrants for the continued fraction representation of the relaxation function.

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Momentum autocorrelation function of an impurity in a classical oscillator chain with alternating masses— I. General theory

Cited by 20 publications

References 23 publications

Local Dynamics in an Infinite Harmonic Chain

Local Dynamics in an Infinite Harmonic Chain

Lateral vibration analysis of monatomic chains considering atomic longitudinal displacement

Dynamics of the transverse Ising model with next-nearest-neighbor interactions

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