Department of Physics, University of California, Berkeley, California 94720, USA and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
Phys Rev Lett. 2015 Dec 31;115(26):267201. doi: 10.1103/PhysRevLett.115.267201. Epub 2015 Dec 23.
The rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in an isolated quantum system have an emergent thermodynamical description whenever the energy or particle current commutes with the Hamiltonian. Concrete examples include the energy current in the 1D spinless fermion model with nearest-neighbor interactions (XXZ spin chain), the energy current in Lorentz-invariant theories or the particle current in interacting Bose gases in arbitrary dimension. Even far from equilibrium, these rates are controlled by state functions, which we call "expansion potentials," expressed as integrals of equilibrium Drude weights. This relation between nonequilibrium quantities and linear response implies nonequilibrium Maxwell relations for the Drude weights. We verify our results via density-matrix renormalization group calculations for the XXZ chain.
在孤立量子系统中，当能量或粒子流与哈密顿量对易时，能量和粒子密度以任意大的温度和化学势差趋同的速率具有一种涌现的热力学描述。具体的例子包括具有最近邻相互作用的一维无自旋费米子模型（XXZ 自旋链）中的能量流、洛伦兹不变理论中的能量流或任意维度的相互作用玻色气体中的粒子流。即使远离平衡，这些速率也受到状态函数的控制，我们称之为“膨胀势”，表示为平衡德拜权重的积分。这种非平衡量与线性响应之间的关系意味着德拜权重的非平衡麦克斯韦关系。我们通过 XXZ 链的密度矩阵重整化群计算验证了我们的结果。
