Dissipative collapse models with nonwhite noises

We study the generalization of the previous collapse model known as quantum mechanics with universal position localizations (QMUPL), which accounts for both memory and dissipative effects. After deriving the nonlocal action describing the system's dynamics, we solve the equation of motion for a quantum harmonic oscillator via the path integral formalism. We give the explicit expression for the Green's function of the process. We focus on the case of an exponential correlation function and we analyze in detail the behavior Gaussian wave functions. In particular, we study the collapse process, comparing the results with those of related models.

Figure 1

Time evolution of $\sigma \left(t\right)$ for a 1-kg particle with initial spread ${\sigma }_0={10}^{-7}$ m, for different values of $\mu$ (in m${}^2$). Smaller values of $\mu$ imply stronger collapse. On this scale, the plot for $\mu =0$ coincides with that for $\mu ={10}^{-32}$. Time is measured in seconds; distance, in meters.

Figure 2

Dependence of $\sigma \left(t\right)$ on $\gamma$, for a fixed time $t=2\times {10}^5$ s. Initial values are $m=1$ kg, ${\sigma }_0={10}^{-7}$ m, and $\mu =5\times {10}^{-19}$ m${}^2$. The bigger $\gamma$ is, the stronger the collapse, except for some values of $\gamma$. Time is measured in seconds; distance, in meters.