Dissipative extension of the Ghirardi-Rimini-Weber model
Dissipative extension of the Ghirardi-Rimini-Weber model
复制标题
Ghirardi-Rimini-Weber 模型的耗散扩展
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Bassi
中科院分区：
文献类型：
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作者：
A. Smirne;B. Vacchini;A. Bassi
在本文中，我们提出了一个推广的Ghirardi-Rimini-Weber模型的自发坍缩的波函数。通过引入耗散，避免了能量在长时间尺度上的发散，从而影响了原模型。特别是，我们定义的跳跃算子，这取决于系统的动量，并导致指数松弛的能量到一个有限的值。有限的渐近能量自然地与具有有限温度的崩溃噪声相关联，这是我们扩展模型的基本现实特征。值得注意的是，即使在存在低温噪声的情况下，坍缩模型也是有效的。根据所谓的放大机制，跳跃算子的作用仍然使波函数局部化，并且局部化的相关性随着系统的大小而增加，这保证了对微观和宏观系统演化的统一描述。我们详细研究了我们的模型的功能，在希尔伯特空间的轨迹和系统的平均状态的主方程的水平。此外，我们表明，耗散的Ghirardi-Rimini-Weber模型，以及原来的，可以充分的特点是在一个紧凑的方式通过适当的随机微分方程。
In this paper, we present an extension of the Ghirardi-Rimini-Weber model for the spontaneous collapse of the wave function. Through the inclusion of dissipation, we avoid the divergence of the energy on the long-time scale, which affects the original model. In particular, we define jump operators, which depend on the momentum of the system and lead to an exponential relaxation of the energy to a finite value. The finite asymptotic energy is naturally associated to a collapse noise with a finite temperature, which is a basic realistic feature of our extended model. Remarkably, even in the presence of a low-temperature noise, the collapse model is effective. The action of the jump operators still localizes the wave function and the relevance of the localization increases with the size of the system, according to the so-called amplification mechanism, which guarantees a unified description of the evolution of microscopic and macroscopic systems. We study in detail the features of our model, at the level of both the trajectories in the Hilbert space and the master equation for the average state of the system. In addition, we show that the dissipative Ghirardi-Rimini-Weber model, as well as the original one, can be fully characterized in a compact way by means of a proper stochastic differential equation.