We study a one-dimensional Fermi gas in the presence of dissipative coupling to environment through the Lindblad equation. The dissipation involves energy exchange with the environment and favours the relaxation of electrons to excitations. After switching on the dissipation, the system approaches a steady state, which is described by a generalized Gibbs ensemble. The fermionic single particle density matrix resembles deceivingly to that in a hermitian interaction quench. It decays inversely with the distance for short times due to the fermionic correlations in the initial state, which changes into a noninteger power law decay for late times, representing dissipation-induced Luttinger liquid behavior. However, the crossover between the two regions occurs due to dissipation-induced damping, and is unrelated to the propagation of excitations. The velocity of information spreading is set by the dissipative coupling, and differs significantly from the original sound velocity. The thermodynamic entropy grows as -t ln t initially, and saturates to an extensive value. Our results can be tested experimentally in one-dimensional Dirac systems.

中文翻译：

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一维费米气体中的耗散诱导的Luttinger液体相关性。

我们通过Lindblad方程研究了存在与环境耗散耦合的一维费米气体。耗散涉及与环境的能量交换，有利于电子对激发的弛豫。开启耗散后，系统达到稳态，这由广义的吉布斯合奏描述。费米离子的单粒子密度矩阵与埃尔米特相互作用淬灭中的相似。由于在初始状态下的铁离子相关性，它会在短时间内与距离成反比，这会在后期变为非整数幂律衰减，代表耗散引起的Luttinger液体行为。但是，这两个区域之间的交叉是由于耗散引起的阻尼而发生的，并且与激励的传播无关。信息传播的速度是由耗散耦合设置的，与原始声速明显不同。热力学熵最初随着-t ln t增长，并饱和到一个很大的值。我们的结果可以在一维Dirac系统中进行实验测试。