We investigate a mean-field approach to a quantum brownian particleinteracting with a quantum thermal bath at temperature $T$, and subjected to anon-linear potential. An exact, partially classical description of quantumbrownian motion is proposed, which uses negative probabilities in itsintermediate steps. It is shown that properties of the quantum particle can bemapped to those of two classical brownian particles in a common potential,where one of them interacts with the quantum bath, whereas another oneinteracts with a classical bath at zero temperature. Due to damping the systemallows a unique and non-singular classical limit at $\hbar \to 0$. For high $T$the stationary state becomes explicitly classical. The low-temperature case isstudied through an effective Fokker-Planck equation. Non-trivial purely quantumcorrelation effects between the two particles are found.
展开▼
机译：我们研究了一种在温度为$ T $时与量子热浴相互作用的量子布朗粒子的均场方法，并受到了非线性电势的影响。提出了一个精确的，部分经典的量子布朗运动描述，该描述在中间步骤中使用了负概率。结果表明，量子粒子的性质可以与两个经典布朗粒子的性质处于同一电位，其中一个与量子浴相互作用，而另一个与零温度下的经典浴相互作用。由于阻尼，系统允许在$ \ hbar \至0 $处具有唯一且非奇异的经典限制。对于较高的$ T $，静止状态显然变得很经典。通过有效的Fokker-Planck方程研究低温情况。发现了两个粒子之间的非平凡的纯量子相关效应。
展开▼
