arXiv 1501.033502015-01-14quant-ph

量子耗散希格斯模型

Quantum dissipative Higgs model

Ehsan Amooghorban, Ali Mahdifar

摘要：

通过使用一个连续的振荡器作为一个水库，我们提出了一个经典的和量子力学的处理存在耗散的希格斯模型。在此基础上，采用完全正则化方法，将球表面上的阻尼质点在守恒有心力作用下进行了数值模拟，定义了共轭动量，导出了哈密顿量。得到了正则变量的运动方程和朗之万方程。结果表明，耗散Higgs模型的动力学不仅由服从Kramers-Kronig关系的投影磁化率张量和噪声算符决定，而且还由球空间的曲率决定.由于球面空间到切平面的球心投影，投影磁化率在切平面上表现出各向异性。为了说明耗散对Higgs模型的影响，计算了球上粒子能级之间的跃迁率。可以看出，只有当过渡和水库的振荡器的频率接近共振时，过渡的可观概率才是可能的。

英文摘要：

By using a continuum of oscillators as a reservoir, we present a classical and a quantum-mechanical treatment for the Higgs model in the presence of dissipation. In this base, a fully canonical approach is used to quantize the damped particle on a spherical surface under the action of a conservative central force, the conjugate momentum is defined and the Hamiltonian is derived. The equations of motion for the canonical variables and in turn the Langevin equation are obtained. It is shown that the dynamics of the dissipative Higgs model is not only determined by a projected susceptibility tensor that obeys the Kramers-Kronig relations and a noise operator but also the curvature of the spherical space. Due to the gnomonic projection from the spherical space to the tangent plane, the projected susceptibility displays anisotropic character in the tangent plane. To illuminate the effect of dissipation on the Higgs model, the transition rate between energy levels of the particle on the sphere is calculated. It is seen that appreciable probabilities for transition are possible only if the transition and reservoir's oscillators frequencies to be nearly on resonance.

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