Spontaneous emission of radiation from a discrete sine-Gordon kink.
Spontaneous emission of radiation from a discrete sine-Gordon kink.
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DOI：
10.1103/physrevb.40.2284
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发表时间：
1989-08
期刊：
影响因子：
--
通讯作者：
Boesch;Willis;El-Batanouny
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文献类型：
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作者：
Boesch;Willis;El-Batanouny
我们使用集体变量方法来研究离散正弦戈登扭结的声子辐射发射。我们发现，非线性 Peierls-Nabarro 势阱中的扭结、俘获和振荡不仅可以平稳地辐射声子，而且当振荡频率达到某些临界值时，会发出大量突然的声子辐射爆发。我们表明，每当扭结振荡频率的谐波穿过较低声子带边缘并因此开始与声子谱的高态密度区域中的声子模式共振时，就会发生爆发。我们表明，解释捕获情况下的辐射爆发和扭结运动的机制也解释了辐射未捕获扭结的行为。我们将集体变量/ital X/引入到一般离散扭结系统中，它是扭结中心的位置，并且使用我们最近开发的投影算子方法推导了精确的运动方程，对于/ital任何/扭结尺寸有效，对于/ital X/，以及耦合场变量，它们动态地修饰扭结并描述辐射。运动方程对于任何允许单扭结解的离散非线性 Klein-Gordon 波动方程都有效。我们将运动方程应用于离散正弦戈登系统，并与仿真获得了极好的一致性。我们还评论了将离散性视为扰动的问题。« less
We use a collective-variable approach to study the emission of phonon radiation from a discrete sine-Gordon kink. We find that a kink, trapped and oscillating in the nonlinear Peierls-Nabarro potential well not only radiates phonons smoothly but emits large and sudden bursts of phonon radiation when the frequency of oscillation reaches certain critical values. We show that the bursts occur whenever a harmonic of the kink's oscillation frequency crosses the lower phonon band edge and thus begins to resonate with phonon modes in the high-density-of-states region of the phonon spectrum. We show that the mechanism that explains the radiation bursts and kink motion in the trapped case also accounts for the behavior of a radiating untrapped kink. We introduce into a general discrete kink system the collective variable /ital X/, which is the position of the center of the kink, and we derive, using a projection-operator approach we have recently developed, the exact equations of motion, valid for /ital any/ kink size, for /ital X/, and coupled field variables, which dynamically dress the kink and describe the radiation. The equations of motion are valid for any discrete nonlinear Klein-Gordon wave equation that admits a single kink solution. We apply themore » equations of motion to the discrete sine-Gordon system and obtain excellent agreement with simulation. We also comment on the problems of treating discreteness as a perturbation.« less