Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, 14195 Berlin, Germany.
Phys Rev Lett. 2011 May 13;106(19):196402. doi: 10.1103/PhysRevLett.106.196402. Epub 2011 May 11.
We study the problem of energy relaxation in a one-dimensional electron system. The leading thermalization mechanism is due to three-particle collisions. We show that for the case of spinless electrons in a single channel quantum wire the corresponding collision integral can be transformed into an exactly solvable problem. The latter is known as the Schrödinger equation for a quantum particle moving in a Pöschl-Teller potential. The spectrum for the resulting eigenvalue problem allows for bound-state solutions, which can be identified with the zero modes of the collision integral, and a continuum of propagating modes, which are separated by a gap from the bound states. The inverse gap gives the time scale at which counterpropagating electrons thermalize.
我们研究了一维电子系统中的能量弛豫问题。主要的热化机制是由于三体碰撞。我们表明，对于单通道量子线中无自旋电子的情况，相应的碰撞积分可以转化为一个完全可解的问题。后者被称为在 Pöschl-Teller 势中运动的量子粒子的薛定谔方程。由此产生的本征值问题的谱允许有束缚态解，可以与碰撞积分的零模相对应，以及连续的传播模式，它们与束缚态之间存在间隙。反向间隙给出了反向传播电子热化的时间尺度。
