**Submitted:**

**G. Wang and Z. Cai**,*Real-time simulation of open quantum spin chains with inchworm method.***Z. Cai, B. Lin, and M. Lin**,*A positive and moment-preserving Fourier spectral method.***M.R.A. Abdelmalik, Z. Cai, and T. Pichard**,*Moment methods for the 3D radiative transfer equation based on φ-divergences.***Z. Cai, M. Torrilhon, and S. Yang**,*Linear regularized 13-moment equations with Onsager boundary conditions for general gas molecules.***G. Wang and Z. Cai**,*Tree-Based Implementation of the small matrix path integral for system-bath dynamics.***Z. Cai, D. Fang, and J. Lu**,*Asymptotic analysis of diabatic surface hopping algorithm in the adiabatic and non-adiabatic limits.*

**Published:**

**Z. Cai, G. Wang, and S. Yang**,*The bold-thin-bold diagrammatic Monte Carlo method for open quantum systems**,*SIAM Journal on Scientific Computing, 45(4): A1812–A1843, 2023.**Z. Cai, J. Lu, and S. Yang**,*Numerical analysis for inchworm Monte Carlo method: Sign problem and error growth**,*Mathematics of Computation, 92(341): 1141–1209, 2023.**Z. Cai, J. Hu, Y. Kuang, and B. Lin**,*An entropic method for discrete systems with Gibbs entropy**,*SIAM Journal on Numerical Analysis, 60(4): 2345–2371, 2022.**G. Wang and Z. Cai**,*Differential equation based path integral for system-bath dynamics,*SIAM Journal on Scientific Computing, 44(3): B771–B804, 2022.**Z. Cai, J. Lu, and S. Yang**,*Fast algorithms of bath calculations in simulations of quantum system-bath dynamics,*Computer Physics Communications, 278: 108417, 2022.**Z. Cai and Y. Wang**,*Numerical solver for the Boltzmann equation with self-adaptive collision operators*, SIAM Journal on Scientific Computing, 44(2): B275–B309, 2022.**Z. Cai, Y. Kuang, and H. K. Tan**,*Regularization of the complex Langevin method*, Physical Review D, 105: 014508, 2022.**H. Zhan, Z. Cai, and G. Hu**,*The Wigner function of ground state and one-dimensional numerics**,*Journal of Computational Physics, 449: 110780, 2022*.***Z. Cai**,*Moment method as a numerical solver: Challenge from shock structure problems**,*Journal of Computational Physics, 444: 110593, 2021.**S. Yang, Z. Cai, and J. Lu**,*Inclusion-exclusion principle for open quantum systems with Bosonic bath**,*New Journal of Physics, 23: 063049, 2021.**Z. Cai, X. Dong, and Y. Kuang**,*On the validity of complex Langevin method for path integral computations,*SIAM Journal on Scientific Computing, 43(1): A685–A719, 2021.**J. Cao and Z. Cai**,*Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy*, Numerical Mathematics: Theory, Methods and Applications, 14(1): 71–112, 2021.**Z. Hu, S. Yang, and Z. Cai**,*Flows between parallel plates: Analytical solutions of regularized 13-moment equations for inverse-power-law models*, Physics of Fluids, 32(12): 122027, 2020.**B. Lin, C. Zhuang, Z. Cai, R. Zeng, and W. Bao**,*Accurate and Efficient Calculation of Photoionization in Streamer Discharges Using the Fast Multipole Method*, Plasma Sources Science and Technology, 29(12): 125010, 2020.**Z. Cai, J. Lu, and S. Yang**,*Inchworm Monte Carlo Method for Open Quantum Systems*, Communications in Pure and Applied Mathematics, 73(11): 2430–2472, 2020.**Z. Hu and Z. Cai**,*Burnett Spectral Method for High-Speed Rarefied Gas Flows*, SIAM Journal on Scientific Computing, 42(5): B1193–B1226, 2020.**X. Dong, Z. Cai, and Y. Di**,*Alternating Descent Method for Gauge Cooling of Complex Langevin Simulations*, Physical Review D, 102: 054518, 2020.**Z. Cai and Y. Wang**,*Regularized 13-Moment Equations for Inverse Power Law Models*, Journal of Fluid Mechanics, 894: A12, 2020.**Z. Cai, Y. Di, and X. Dong**,*How does Gauge Cooling Stabilize Complex Langevin?*, Communications in Computational Physics, 27(5): 1344–1377, 2020.**Z. Cai, Y. Fan, and Y. Wang**,*Burnett Spectral Method for the Spatially Homogeneous Boltzmann Equation*, Computers & Fluids, 200: 104456, 2020.**Z. Hu, Z. Cai, and Y. Wang**,*Numerical Simulation of Microflows Using Hermite Spectral Methods*, SIAM Journal on Scientific Computing, 42(1): B105–B134, 2020.**B. Lin, C. Zhuang, Z. Cai, R. Zeng, and W. Bao**,*An Efficient and Accurate MPI-based Parallel Simulator for Streamer Discharges in Three Dimensions*, Journal of Computational Physics, 401: 109026, 2020.**Z. Cai and M. Torrilhon**,*On the Holway-Weiss Debate: Convergence of the Grad-Moment-Expansion in Kinetic Gas Theory*, Physics of Fluids, 31: 126105, 2019.**Y. Wang and Z. Cai**,*Approximation of the Boltzmann Collision Operator Based on Hermite Spectral Method*, Journal of Computational Physics, 397: 108815, 2019.**Z. Cai and Y. Wang**,*Suppression of Recurrence in the Hermite-Spectral Method for Transport Equations*, SIAM Journal on Numerical Analysis, 56(5), 3144–3168, 2019.**Z. Cai, Y. Fan, and L. Ying**,*An Entropic Fourier Method for the Boltzmann Equation*, SIAM Journal on Scientific Computing, 40(5), A2858–A2882, 2018.**Z. Cai and J. Lu**,*A Surface Hopping Gaussian Beam Method for High-Dimensional Transport Systems*, SIAM Journal on Scientific Computing, 40(5), B1277–B1301, 2018.**Z. Cai and J. Lu**,*A Quantum Kinetic Monte Carlo Method for Quantum Many-body Spin Dynamics*, SIAM Journal on Scientific Computing, 40: B706–B722, 2018.**Z. Cai and M. Torrilhon**,*Numerical Simulation of Microflows Using Moment Methods with Linearized Collision Operator*, Journal of Scientific Computing, 74: 336–374, 2018.**Z. Cai, Y. Fan, Z. Hu, R. Li, and H. Wang**,*The Development and Application of the Moment Method in the Gas Kinetic Theory*, Scientia Sinica Informationis, 46: 1465–1488, 2016.**Z. Cai, Y. Fan, and R. Li**,*A Framework on Moment Model Reduction for Kinetic Equation*, SIAM Journal on Applied Mathematics, 75: 2001–2023, 2015.**Z. Cai and M. Torrilhon**,*Approximation of the Linearized Boltzmann Collision Operator for Hard-Sphere and Inverse-Power-Law Models*, Journal of Computational Physics, 295: 617–643, 2015.**Z. Cai and R. Li**,*The NRxx Method for Polyatomic Gases*, Journal of Computational Physics, 267: 63–91, 2014.**Z. Cai, Y. Fan and R. Li**,*Globally Hyperbolic Regularization of Grad’s Moment System*, Communications in Pure and Applied Mathematics, 67: 464–518, 2014.**Z. Cai, Y. Fan, and R. Li**,*On Hyperbolicity of 13-Moment System*, Kinetic and Related Models, 7(3): 415–432, 2014.**Z. Cai, Y. Fan, R. Li, and Z. Qiao**,*Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision*, Communications in Computational Physics, 15(5): 1368–1406, 2014.**Z. Cai, Y. Fan, R. Li, T. Lu, and W. Yao**,*Quantum Hydrodynamic Model of Density Functional Theory*, Journal of Mathematical Chemistry, 51(7): 1747–1771, 2013.**Z. Cai, R. Li, and Z. Qiao**,*Globally Hyperbolic Regularized Moment Method with Applications to Microflow Simulation*, Computers & Fluids, 81: 95–109, 2013.**Z. Cai, R. Li, and Y. Wang**,*Solving Vlasov Equations Using NRxx Method*, SIAM Journal on Scientific Computing, 35(6): A2807–A2831, 2013.**Z. Cai, Y. Fan, and R. Li**,*Globally Hyperbolic Regularization of Grad’s Moment System in One Dimensional Space*, Communications in Mathematical Sciences, 11(2): 547–571, 2013.**Z. Cai, Y. Fan, R. Li, T. Lu, and Y. Wang**,*Quantum Hydrodynamic Model by Moment Closure of Wigner Equation*, Journal of Mathematical Physics, 53(10): 103503, 2012.**Z. Cai, R. Li, and Z. Qiao**,*NRxx Simulation of Microflows with Shakhov Model, SIAM Journal on Scientific Computing*, 34(1): A339–A369, 2012.**Z. Cai, R. Li, and Y. Wang**,*An Efficient NRxx Method for Boltzmann-BGK**Equation*, Journal of Scientific Computing, 50(1): 103–119, 2012.**Z. Cai, R. Li, and Y. Wang**,*Numerical Regularized Moment Method for High**Mach Number Flow*, Communications in Computational Physics, 11(5): 1415–1438, 2012.**Z. Cai and R. Li**,*Numerical Regularized Moment Method of Arbitrary Order for**Boltzmann-BGK Equation*, SIAM Journal on Scientific Computing, 32(5): 2875–2907, 2010.**Z. Cai and R. Li**,*An h-Adaptive Mesh Method for Boltzmann-BGK/Hydrodynamics**Coupling*, Journal of Computational Physics, 229(5): 1661–1680, 2010.