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We propose an algorithm that combines the inchworm method and the frozen Gaussian approximation to simulate the Caldeira-Leggett model in which a quantum particle is coupled with thermal harmonic baths. In particular, we are interested in the real-time dynamics of the reduced density operator. In our algorithm, we use frozen Gaussian approximation to approximate the wave function as a wave packet in integral form. The desired reduced density operator is then written as a Dyson series, which is the series expression of path integrals in quantum mechanics of interacting systems. To compute the Dyson series, we further approximate each term in the series using Gaussian wave packets, and then employ the idea of the inchworm method to accelerate the convergence of the series. The inchworm method formulates the series as an integro-differential equation of "full propagators", and rewrites the infinite series on the right-hand side using these full propagators, so that the number of terms in the sum can be significantly reduced, and faster convergence can be achieved. The performance of our algorithm is verified numerically by various experiments., Comment: 22 pages, 6 figures

We develop the time-dependent regularized 13-moment equations for general elastic collision models under the linear regime. Detailed derivation shows the proposed equations have super-Burnett order for small Knudsen numbers, and the moment equations enjoy a symmetric structure. A new modification of Onsager boundary conditions is proposed to ensure stability as well as the removal of undesired boundary layers. Numerical examples of one-dimensional channel flows is conducted to verified our model., Comment: 30 pages, 24 figures

The experiment of exo-ecosystem and the exploration of extraterrestrial habitability aims to explore the adaptation of terrestrial life in space conditions for the manned space program and the future interstellar migration, which shows great scientific significance and public interests. By our knowledge the early life on Earth, archaea and extremophile have the ability to adapt to extreme environmental conditions and can potentially habitat in extraterrestrial environments. Here we proposed a design and framework for the experiment on exo-ecosystem and extraterrestrial habitability. The conceptual approach involves building an ecosystem based on archaea and extremophiles in a simulated extraterrestrial environment, with a focus on assessing the exobiological potential and adaptability of terrestrial life forms in such conditions through controlled experiments. Specifically, we introduce the Chinese Exo-Ecosystem Space Experiment (CHEESE), which investigates the survivability and potential for sustained growth, reproduction, and ecological interactions of methanogens under simulated Mars and Moon environments using the China Space Station (CSS) as a platform. We highlight that the space station provides unique yet relatively comprehensive conditions for simulating extraterrestrial environments. In conclusion, space experiments involving exo-ecosystems could pave the way for long-term human habitation in space, ensuring our ability to sustain colonies and settlements beyond Earth while minimizing our ecological impact on celestial bodies.

Multi-core neuromorphic systems typically use on-chip routers to transmit spikes among cores. These routers require significant memory resources and consume a large part of the overall system's energy budget. A promising alternative approach to using standard CMOS and SRAM-based routers is to exploit the features of memristive crossbar arrays and use them as programmable switch-matrices that route spikes. However, the scaling of these crossbar arrays presents physical challenges, such as "IR drop" on the metal lines due to the parasitic resistance, and leakage current accumulation on multiple active memristors in their "off" state. While reliability challenges of this type have been extensively studied in synchronous systems for compute-in-memory matrix-vector multiplication (MVM) accelerators and storage class memory, little effort has been devoted so far to characterizing the scaling limits of memristor-based crossbar routers. Here, we study the challenges of memristive crossbar arrays, when used as routing channels to transmit spikes in asynchronous Spiking Neural Network (SNN) hardware. We validate our analytical findings with experimental results obtained from a 4K-ReRAM chip which demonstrates its functionality as a routing crossbar. We determine the functionality bounds on the routing due to the IR drop and leak problem, based on theoretical modeling, circuit simulations for a 22nm FDSOI technology, and experimental measurements. This work highlights the limitations of this approach and provides useful guidelines for engineering the memristor device properties in memristive crossbar routers for multi-core asynchronous neuromorphic systems., Comment: 5 pages, 11 figures

We develop the steady-state regularized 13-moment equations in the linear regime for rarefied gas dynamics with general collision models. For small Knudsen numbers, the model is accurate up to the super-Burnett order, and the resulting system of moment equations is shown to have a symmetric structure. We also propose Onsager boundary conditions for the moment equations that guarantees the stability of the equations. The validity of our model is verified by benchmark examples for the one-dimensional channel flows., Comment: 34 pages, 3 figures

We present two diagrammatic Monte Carlo methods for quantum systems coupled with harmonic baths, whose dynamics are described by integro-differential equations. The first approach can be considered as a reformulation of Dyson series, and the second one, called "bold-thin-bold diagrammatic Monte Carlo", is based on resummation of the diagrams in the Dyson series to accelerate its convergence. The underlying mechanism of the governing equations associated with the two methods lies in the recurrence relation of the path integrals, which is the most costly part in the numerical methods. The proposed algorithms give an extension to the work ["Fast algorithms of bath calculations in simulations of quantum system-bath dynamics", Computer Physics Communications, to appear], where the algorithms are designed based on reusing the previous calculations of bath influence functionals. Compared with the algorithms therein, our methods further include the reuse of system associated functionals and show better performance in terms of computational efficiency and memory cost. We demonstrate the two methods in the framework of spin-boson model, and numerical experiments are carried out to verify the validity of the methods.

We present fast algorithms for the summation of Dyson series and the inchworm Monte Carlo method for quantum systems that are coupled with harmonic baths. The algorithms are based on evolving the integro-differential equations where the most expensive part comes from the computation of bath influence functionals. To accelerate the computation, we design fast algorithms based on reusing the bath influence functionals computed in the previous time steps to reduce the number of calculations. It is proven that the proposed fast algorithms reduce the number of such calculations by a factor of $O(N)$, where $N$ is the total number of time steps. Numerical experiments are carried out to show the efficiency of the method and to verify the theoretical results.

We present two fast algorithms which apply inclusion-exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo (dQMC) and inchworm Monte Carlo method, respectively. In the case of inchworm Monte Carlo, the proposed fast algorithm gives an extension to the work ["Inclusion-exclusion principle for many-body diagrammatics", Phys. Rev. B, 98:115152, 2018] from fermionic to bosonic systems. We prove that the proposed fast algorithms reduce the computational complexity from double factorial to exponential. Numerical experiments are carried out to verify the theoretical results and to compare the efficiency of the methods.

We study the structure of stationary channel flows predicted by the regularized 13-moment equations. Compared with the previous work [P. Taheri et al., Phys. Fluids, 21 (2009), 017102], we focus on gases whose molecules satisfy the general inverse power law. The analytical solutions are obtained for the semi-linear equations, and the structures of Couette, Fourier, and Poiseuille flows are solved by coupling the general solutions with newly derived boundary conditions. The results show excellent agreement with the reference solution in the slip-flow regime. Our results also show that the R13 equations derived from inverse power law models can have better accuracy than the R13 equations of Maxwell molecules with altered viscosity.

We consider the numerical analysis of the inchworm Monte Carlo method, which is proposed recently to tackle the numerical sign problem for open quantum systems. We focus on the growth of the numerical error with respect to the simulation time, for which the inchworm Monte Carlo method shows a flatter curve than the direct application of Monte Carlo method to the classical Dyson series. To better understand the underlying mechanism of the inchworm Monte Carlo method, we distinguish two types of exponential error growth, which are known as the numerical sign problem and the error amplification. The former is due to the fast growth of variance in the stochastic method, which can be observed from the Dyson series, and the latter comes from the evolution of the numerical solution. Our analysis demonstrates that the technique of partial resummation can be considered as a tool to balance these two types of error, and the inchwormMonte Carlo method is a successful case where the numerical sign problem is effectively suppressed by such means. We first demonstrate our idea in the context of ordinary differential equations, and then provide complete analysis for the inchworm Monte Carlo method. Several numerical experiments are carried out to verify our theoretical results., Comment: 58 pages, 8 figures

We investigate in this work a recently proposed diagrammatic quantum Monte Carlo method --- the inchworm Monte Carlo method --- for open quantum systems. We establish its validity rigorously based on resummation of Dyson series. Moreover, we introduce an integro-differential equation formulation for open quantum systems, which illuminates the mathematical structure of the inchworm algorithm. This new formulation leads to an improvement of the inchworm algorithm by introducing classical deterministic time-integration schemes. The numerical method is validated by applications to the spin-boson model.

We consider the a posteriori error estimation for an atomistic-to-continuum cou- pling scheme for a generic one-dimensional many-body next-nearest-neighbour interaction model in 1D. We derive and rigorously prove the efficiency of the residual type estimator. We prove the equivalence between the residual type and the gradient recovery type estima- tor in the continuum region and propose a (novel) hybrid a a posteriori error estimator by combining the two types of estimators. Our numerical experiments illustrate the optimal con- vergence rate of the adaptive algorithms using these estimators whose efficiency factors are also presented.