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arXiv 1609.07249quant-phcond-mat.stat-mech
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耗散二次开放系统的解:第一部分:玻色子

Solutions for dissipative quadratic open systems: part I - bosons

Chu Guo, Dario Poletti

摘要:

这是一个工作,在两个部分中,我们将展示如何解决一个大类的Lindblad主方程的非相互作用粒子的$L$网站。在第一部分,我们集中在玻色子粒子。我们展示了如何减少问题的对角化的$L \times L$非厄米矩阵。特别是,对于均匀链的边界耗散驱动,矩阵是三对角加边的Toeplitz矩阵,其可以解析地求解正常主模式及其松弛率(rapidities)。在无法找到解析解的情况下,我们的方法仍然可以提供数值计算的加速。我们用这种数值方法研究了具有合成规范场的边界驱动玻色梯中非平衡相变时的弛豫能隙。最后,我们展示了如何构建非平衡稳态。

英文摘要:

This is a work in two parts in which we show how to solve a large class of Lindblad master equations for non-interacting particles on $L$ sites. In part I we concentrate on bosonic particles. We show how to reduce the problem to diagonalizing an $L \times L$ non-Hermitian matrix. In particular, for boundary dissipative driving of a uniform chain, the matrix is a tridiagonal bordered Toeplitz matrix which can be solved analytically for the normal master modes and their relaxation rates (rapidities). In the regimes in which an analytical solution cannot be found, our approach can still provide a speed-up in the numerical evaluation. We use this numerical method to study the relaxation gap at non-equilibrium phase transitions in a boundary driven bosonic ladder with synthetic gauge fields. We conclude by showing how to construct the non-equilibrium steady state.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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