scholarly journals Exponentially Complex “Classically Entangled” States in Arrays of One-Dimensional Nonlinear Elastic Waveguides

Materials ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 3553 ◽  
Author(s):  
Deymier ◽  
Runge ◽  
Hasan ◽  
Calderin
Keyword(s):  
Hilbert Space ◽  
Elastic System ◽  
Multiple Time ◽  
One Dimensional ◽  
Wave Guides ◽  
External Driver ◽  
Scale Perturbation ◽  
Nonlinear Elastic ◽  
Exponential Complexity ◽  
Nonseparable States

We demonstrate theoretically, using multiple-time-scale perturbation theory, the existence of nonseparable superpositions of elastic waves in an externally driven elastic system composed of three one-dimensional elastic wave guides coupled via nonlinear forces. The nonseparable states span a Hilbert space with exponential complexity. The amplitudes appearing in the nonseparable superposition of elastic states are complex quantities dependent on the frequency of the external driver. By tuning these complex amplitudes, we can navigate the state’s Hilbert space. This nonlinear elastic system is analogous to a two-partite two-level quantum system.

Parametric instabifity of transverse and Langmuir waves in a plasma

1975 ◽  
Vol 13 (2) ◽  
pp. 317-326 ◽  
Author(s):  
Kai Fong Lee
Keyword(s):  
Growth Rate ◽  
Electromagnetic Field ◽  
Kinetic Model ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Threshold Intensity ◽  
Langmuir Waves ◽  
Scale Perturbation ◽  
The Subject ◽  
Parametric Instabilities

The parametric excitation of transverse and Langmuir waves by an externally-driven electromagnetic field of frequency (ω0 > 2ωp) in a warm and collisional plasma is studied, using the fluid equations. By an application of the multiple- time-scale perturbation method, the threshold intensity and the growth rate above threshold are obtained. The results are compared with those of Goldman (1969) and Prasad (1968), both of whom worked with a kinetic model.The theory of parametric instabilities in plasmas has been the subject of numerous investigations in recent years. Broadly speaking, the instabilities can be grouped into two categories: those for which the excited waves are purely electrostatic (see e.g. DuBois & Goldman 1965, 1967; Silin 1965; Lee & Su 1966; Jackson 1967; Nishikawa 1968; Kaw & Dawson 1969; Tzoar 1969; Sanmartin 1970; McBride 1970; Perkins & Flick 1971; Fejer & Leer 1972a, b; Bezzerides & Weinstock 1972; DuBois & Goldman 1972), and those for which one of the excited waves is electromagnetic (see e.g. Goldman & Dubois 1965; Montgomery & Alexeff 1966; Chen & Lewak 1970; Bodner & Eddleman 1972; Fejer & Leer 1972b; Lee & Kaw 1972; Forslund et al. 1972).

scholarly journals Integrable extended Hubbard models with boundary Kondo impurities

2001 ◽  
Vol 64 (3) ◽  
pp. 445-467
Author(s):  
Anthony J. Bracken ◽  
Xiang-Yu Ge ◽  
Mark D. Gould ◽  
Huan-Qiang Zhou
Keyword(s):  
Hilbert Space ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Magnetic Moments ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Ansatz Method ◽  
One Dimensional ◽  
Hubbard Models ◽  
Kondo Impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z2-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

scholarly journals The effect of time-varying delay damping on the stability of porous elastic system

2021 ◽  
Vol 5 (1) ◽  
pp. 147-161
Author(s):  
Soh Edwin Mukiawa ◽  
Keyword(s):  
Elastic System ◽  
Time Varying ◽  
Viscoelastic System ◽  
One Dimensional ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

In the present work, we study the effect of time varying delay damping on the stability of a one-dimensional porous-viscoelastic system. We also illustrate our findings with some examples. The present work improve and generalize existing results in the literature.

Numerical Analysis for Acoustic Resonance of One-Dimensional Nonlinear Elastic Bar

2011 ◽  
Vol 50 (7) ◽  
pp. 07HB02 ◽  
Author(s):  
Ryuichi Tarumi ◽  
Tomohiro Matsuhisa ◽  
Yoji Shibutani
Keyword(s):  
Numerical Analysis ◽  
Acoustic Resonance ◽  
One Dimensional ◽  
Elastic Bar ◽  
Nonlinear Elastic

scholarly journals Stripe states in photonic honeycomb ribbon

2015 ◽  
Vol 471 (2177) ◽  
pp. 20140765
Author(s):  
Sul-Ah Park ◽  
Young-Woo Son ◽  
Kang-Hun Ahn
Keyword(s):  
Electric Fields ◽  
Strain Field ◽  
High Energy ◽  
Spatial Distributions ◽  
Two Dimensional ◽  
Zero Energy ◽  
One Dimensional ◽  
Wave Guides ◽  
States Experience ◽  
Hexagonal Crystals

We reveal new stripe states in deformed hexagonal array of photonic wave guides when the array is terminated to have a ribbon-shaped geometry. Unlike the well-known zero energy edge modes of honeycomb ribbon, the new one-dimensional states are shown to originate from high-energy saddle-shaped photonic bands of the ribbon's two-dimensional counterpart. We find that the strain field deforming the ribbon generates pseudo-electric fields in contrast to pseudo-magnetic fields in other hexagonal crystals. Thus, the stripe states experience Bloch oscillation without any actual electric field so that the spatial distributions of stripes have a singular dependence on the strength of the field. The resulting stripe states are located inside the bulk and their positions depend on their energies.

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