Integrals for lower bounds to the exact energy

Exact path-integral evaluation of locally interacting systems: The subtlety of operator ordering

We discuss how one calculates the coherent path integrals for locally interacting systems, where some inconsistencies with exact results have been reported previously. It is shown that the operator ordering subtlety that is hidden in the local interaction term modifies the Hubbard-Stratonovich transformation in the continuous time formulation, and it helps reproduce known results by the operator method. We also demonstrate that many-body effects in the strong interaction limit can be well characterized by the free-particle theory that is subject to annealed random potentials and dynamical gaug…

维格纳表示可精确推导原子干涉仪相位，路径积分方法则不能

Wigner representation enables the exact derivation of the atom interferometer phase, unlike the path integral approach

针对非惯性参考系中原子干涉仪相位推导问题，本文利用维格纳表示下的原子密度矩阵方程得到精确表达式（含多种力项），并在小旋转角和短探测时间极限下推导出归因于平台运动的三个新项。

Forster resonance energy transfer, absorption and emission spectra in multichromophoric systems: III. Exact stochastic path integral evaluation

A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators one can also immediately compute energy transfer rates using the multi-chromophoric Forster resonant energy transfer formalism. Benchmark calculatio…

Path Integral Molecular Dynamics for Exact Quantum Statistics of Multi-Electronic-State Systems

An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD) [J. Chem. Phys. 145, 024103 (2016); 147, 034109 (2017)] for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD, and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative…

被监控量子比特的纯化：精确路径积分解法

Purification of a monitored qubit: exact path-integral solution

研究连续时间监控下单量子比特纯化动力学，通过碰撞模型框架描述密度矩阵的条件演化，推导出纯度参数的朗之万方程，并利用路径积分法求解，揭示纯化过程中从扩散主导到测量主导的动态相变。

Exact Classical Effective Potential

A quantum spin system can be modelled by an equivalent classical system, with an effective Hamiltonian obtained by integrating all non-zero frequency modes out of the path integral. The effective Hamiltonian H_eff(S_i) derived from the coherent-state integral is highly singular: the quasiprobability density exp(-beta H_eff), a Wigner function, imposes quantisation through derivatives of delta functions. This quasiprobability is the distribution of the time-averaged lower symbol of the spin in the coherent-state integral. We relate the quantum Monte Carlo minus-sign problem to the non-positivit…

含流体时钟的量子宇宙学中半线上的精确路径积分与算符排序模糊性的若干方面

Exact path integrals on half-line in quantum cosmology with a fluid clock and aspects of operator ordering ambiguity

本研究在含理想流体时钟的D+1维平坦均匀宇宙学模型中开展精确半线路径积分量子化，通过保留经典的时移重标度和广义协变对称性，明确了D>2时量子哈密顿量的唯一算符排序方案，并证明D=1时该对称性破缺导致排序模糊。

量子 Hamilton-Jacobi 理论、谱路径积分与精确 WKB 分析

Quantum Hamilton-Jacobi Theory, Spectral Path Integrals and Exact-WKB Analysis

本文利用量子 Hamilton-Jacobi 理论提出谱路径积分 $\ ilde Z(E)$，将相空间路径积分转化为量子特征函数确定与量子周期格点求和，推广了 Gutzwiller 求和。

Efficient Real-Time Path Integrals for Non-Markovian Spin-Boson Models

Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is…

Exact Solution for a Two-Level Atom in Radiation Fields and the Freeman Resonances

Using techniques of complex analysis in an algebraic approach, we solve the wave equation for a two-level atom interacting with a monochromatic light field exactly. A closed-form expression for the quasi-energies is obtained, which shows that the Bloch-Siegert shift is always finite, regardless of whether the original or the shifted level spacing is an integral multiple of the driving frequency, $ω$. We also find that the wave functions, though finite when the original level spacing is an integral multiple of $ω$, become divergent when the intensity-dependent shifted energy spacing is an integ…