Departament d'Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain.
J Phys Condens Matter. 2013 Aug 14;25(32):325601. doi: 10.1088/0953-8984/25/32/325601. Epub 2013 Jul 12.
Following Oriols (2007 Phys. Rev. Lett. 98 066803), an algorithm to deal with the exchange interaction in non-separable quantum systems is presented. The algorithm can be applied to fermions or bosons and, by construction, it exactly ensures that any observable is totally independent of the interchange of particles. It is based on the use of conditional Bohmian wave functions which are solutions of single-particle pseudo-Schrödinger equations. The exchange symmetry is directly defined by demanding symmetry properties of the quantum trajectories in the configuration space with a universal algorithm, rather than through a particular exchange-correlation functional introduced into the single-particle pseudo-Schrödinger equation. It requires the computation of N(2) conditional wave functions to deal with N identical particles. For separable Hamiltonians, the algorithm reduces to the standard Slater determinant for fermions (or permanent for bosons). A numerical test for a two-particle system, where exact solutions for non-separable Hamiltonians are computationally accessible, is presented. The numerical viability of the algorithm for quantum electron transport (in a far-from-equilibrium time-dependent open system) is demonstrated by computing the current and fluctuations in a nano-resistor, with exchange and Coulomb interactions among electrons.
继 Oriols（2007 Phys. Rev. Lett. 98 066803）之后，本文提出了一种处理不可分离量子系统中交换相互作用的算法。该算法可应用于费米子或玻色子，并且通过构造，可以完全确保任何可观测量都与粒子的交换无关。它基于使用条件 Bohmian 波函数，这些波函数是单粒子赝 Schrödinger 方程的解。通过使用通用算法直接定义量子轨迹在配置空间中的交换对称性，而不是通过引入单粒子赝 Schrödinger 方程中的特定交换相关泛函来定义交换对称性。它需要计算 N(2)个条件波函数来处理 N 个相同的粒子。对于可分离哈密顿量，该算法简化为费米子的标准 Slater 行列式（或玻色子的永久行列式）。对于可分离哈密顿量，计算上可获得非可分离哈密顿量的精确解，本文对两粒子系统进行了数值测试。通过计算纳米电阻器中的电流和涨落，展示了该算法在量子电子输运（在远离平衡的时变开放系统中）中的数值可行性，其中电子之间存在交换和库仑相互作用。
