含时玻色子二次哈密顿量的精确功特征函数
Exact Work Characteristic Functions for Time-Dependent Bosonic Quadratic Hamiltonians
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中文总结 AI 辅助
本文推导了含时二次玻色子哈密顿量系统功特征函数的精确解析式，统一处理非齐次辛群算符，适用于任意自由度和初始态，并给出自由能、Jarzynski等式等公式，分析仿射与辛贡献对功统计的影响。
中文摘要 AI 辅助
我们推导了由一般含时二次哈密顿量支配的封闭多体玻色子系统中功特征函数的精确解析表达式。这是通过采用统一方案实现的，在该方案中，特征函数中出现的所有算符均被视为非齐次辛群（Metaplectic群）的元素。所得表达式涉及单个辛矩阵、单个相空间位移和单个累积相位。它适用于任意自由度数、二次哈密顿量的任意含时依赖性以及系统的任意初始热平衡态。该形式将幺正演化相关的显式时间排序问题转化为相空间中辛路径的确定，由此可以重构相应的驱动哈密顿量。我们还讨论了在量子功的双投影测量方案中推广到任意非平衡初始态的情况。相同的构造产生了Loschmidt回波和混合态总相位。利用导出的特征函数，我们获得了亥姆霍兹自由能、Jarzynski等式、平均功、功方差和非平衡滞后的公式。无位移哈密顿量、突然淬火、恒定Hessian协议和绝热极限作为一般结果的特例出现。作为示例，我们分析了一个由非传统辛路径构建并表现出物理相关极限情况的一维系统。然后我们展示了仿射和纯辛贡献如何影响功统计和不可逆性。
英文摘要
We derive an exact analytical expression for the characteristic function of work in closed many-body bosonic systems governed by general time-dependent quadratic Hamiltonians. This is made possible by adopting a unified prescription in which all operators appearing in the characteristic function are treated as elements of the inhomogeneous Metaplectic group. The esulting expression involves a single symplectic matrix, a single phase-space displacement, and a single accumulated phase. It holds for any number of degrees of freedom, arbitrary time dependence of the quadratic Hamiltonian, and any initial thermal equilibrium state of the system. The formalism trades the explicit time-ordering problem associated with the unitary evolution for the determination of a symplectic path in phase space, from which the corresponding driving Hamiltonian can be reconstructed. We also discuss the generalization to arbitrary nonequilibrium initial states within the two-projective-measurement scheme for quantum work. The same construction yields Loschmidt echoes and mixed-state total phases. Using the derived characteristic function, we obtain formulas for the Helmholtz free energy, the Jarzynski equality, the mean work, the work variance, and the nonequilibrium lag. Undisplaced Hamiltonians, sudden quenches, constant-Hessian protocols, and the adiabatic limit follow as special cases of the general result. As an illustration, we analyze a one-dimensional system constructed from an unconventional symplectic path and exhibiting physically relevant limiting cases. We then show how affine and purely symplectic contributions affect work statistics and irreversibility.
发表机构
- Instituto de Física, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学物理研究所）
- Instituto Politécnico, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学理工学院）
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