论文标题
波浪函数崩溃的Lévy模型
Lévy Models for Collapse of the Wave Function
论文作者
论文摘要
最近，在量子力学的状态减少的随机模型的发展中取得了很多进展。在这样的模型中，波函数的崩溃是一个物理过程，由非线性随机微分方程概括，该方程将Schrödinger方程概括。本文认为基于能量的随机扩展是Schrödinger方程的。迄今为止在该领域进行的大多数工作都关注模型，在该模型中，驱动量子状态的随机动力学的过程是布朗运动。在这里，布朗框架被扩展到更广泛的模型，其中噪声过程是Lévy类型的，承认固定和独立的增量。此类模型的特性不同于布朗还原模型的特性。特别是，对于Lévy模型，解相关速率取决于能量的整体规模。因此，在Lévy还原模型中，即使能级差距很小，宏观量子系统也会自发地塌陷到本征态。
Recently there has been much progress in the development of stochastic models for state reduction in quantum mechanics. In such models, the collapse of the wave function is a physical process, governed by a nonlinear stochastic differential equation that generalizes the Schrödinger equation. The present paper considers energy-based stochastic extensions of the Schrödinger equation. Most of the work carried out hitherto in this area has been concerned with models where the process driving the stochastic dynamics of the quantum state is Brownian motion. Here, the Brownian framework is broadened to a wider class of models where the noise process is of the Lévy type, admitting stationary and independent increments. The properties of such models are different from those of Brownian reduction models. In particular, for Lévy models the decoherence rate depends on the overall scale of the energy. Thus, in Lévy reduction models, a macroscopic quantum system will spontaneously collapse to an eigenstate even if the energy level gaps are small.
