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Quasi-Lindblad pseudomode theory for open quantum systems

Physical Review B 2024年第19期110卷 195148-195148页

作者： Gunhee Park (박건희) Zhen Huang Yuanran Zhu Chao Yang Garnet Kin-Lic Chan Lin Lin Division of Engineering and Applied Science California Institute of Technology Pasadena California 91125 USA Department of Mathematics University of California Berkeley California 94720 USA Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Division of Chemistry and Chemical Engineering California Institute of Technology Pasadena California 91125 USA

We introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics, but we further relax the complete positivity requirement in the Lindblad master equation and formulate a quasi-Lindblad pseudomode theory. We show that this quasi-Lindblad pseudomode formulation directly leads to a representation of the bath correlation function in terms of a complex weighted sum of complex exponentials, an expansion that is known to be rapidly convergent in practice and thus leads to a compact set of pseudomodes. The pseudomode representation is not unique and can differ by a gauge choice. When the global dynamics can be simulated exactly, the system dynamics is unique and independent of the specific pseudomode representation. However, the gauge choice may affect the stability of the global dynamics, and we provide an analysis of why and when the global dynamics can retain stability despite losing positivity. We showcase the performance of this formulation across various spectral densities in both bosonic and fermionic problems, finding significant improvements over conventional pseudomode formulations.

关键词： Open quantum systems Open quantum systems & decoherence Strongly correlated systems Anderson impurity model Lindblad equation Non-Markovian processes Nonperturbative methods Spin-boson model

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Deep potentials for materials science

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Materials Futures 2022年第2期1卷 89-115页

作者： Tongqi Wen Linfeng Zhang Han Wang Weinan E David J Srolovitz Department of Mechanical Engineering The University of Hong KongHong KongHong Kong Special Administrative Region of China DP Technology BeijingPeople’s Republic of China AI for Science Institute BeijingPeople’s Republic of China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijingPeople’s Republic of China HEDPS CAPTCollege of EngineeringPeking UniversityBeijingPeople’s Republic of China School of Mathematical Sciences Peking UniversityBeijingPeople’s Republic of China Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJUnited States of America International Digital Economy Academy(IDEA) ShenzhenPeople’s Republic of China

To fill the gap between accurate(and expensive)ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials,a new class of descriptions of atomic interactions has emerged and been widely applied;*** learning potentials(MLPs).One recently developed type of MLP is the deep potential(DP)*** this review,we provide an introduction to DP methods in computational materials *** theory underlying the DP method is presented along with a step-by-step introduction to their development and *** also review materials applications of DPs in a wide range of materials *** DP Library provides a platform for the development of DPs and a database of extant *** discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

关键词： deep potential atomistic simulation machine learning potential neural network

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Fine-tune chiroptical activity in discrete chiral Au nanorods

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Nano Research 2022年第7期15卷 6574-6581页

作者： Guangchao Zheng Sulin Jiao Wei Zhang Shenli Wang Qinghua Zhang Lin Gu Weixiang Ye Junjun Li Xiaochen Ren Zhicheng Zhang Kwok-yin Wong School of Physics and Microelectronics Zhengzhou UniversityZhengzhou 450001China State Key Laboratory of Chemical Biology and Drug Discovery Department of Applied Biology and Chemical TechnologyThe Hong Kong Polytechnic UniversityKowloonHong KongChina Institute of Applied Physics and Computational Mathematics Beijing 100088China School of Food Science and Engineering Henan University of TechnologyZhengzhou 450001China Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China Department of Applied Physics School of ScienceHainan UniversityHaikou 570228China Tianjin Key Laboratory of Molecular Optoelectronic Sciences Department of ChemistrySchool of ScienceTianjin University&Collaborative Innovation Center of Chemical Science and EngineeringTianjin 300072China

Accurate researches on the surface plasmon resonance(SPR)-based applications of chiral plasmonic metal nanoparticles(NPs)still remain a great ***,a series of chiral plasmonic metal NPs,e.g.,chiral Au nanorods(c-Au NRs),c-Au@Ag core–shell,and c-Au@TiO_(2) core–shell NRs,with different chiroptical activities have been *** circular dichroism(PCD)bands of c-Au NRs can be precisely tailored by tuning the longitudinal SPR(LSPR)and amount of Au NRs as ***,a shift of PCD bands within ultraviolet–visible–near infrared ray(UV–vis–NIR)region can also be achieved through the functionalization of a shell of another metal or ***,chirality transfer from c-Au core to Ag shell leads to new PCD bands at the near-UV *** tuning of PCD bands and chirality transfer are confirmed by our developed theoretical *** chiral Au NRs-based chiral plasmonic nanomaterials with tunable chiroptical activities will be helpful to understand the structure-direct PCD and to extend circularly polarized-based applications.

关键词： chiral Au nanorods(c-Au NRs) surface plasmon resonance optical activity chirality transfer

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Unified Variational Approach Description of Ground-State Phases of the Two-Dimensional Electron Gas

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Physical Review Letters 2024年第26期133卷 266504-266504页

作者： Conor Smith Yixiao Chen (陈一潇) Ryan Levy Yubo Yang (杨煜波) Miguel A. Morales Shiwei Zhang Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Department of Electrical and Computer Engineering University of New Mexico Albuquerque New Mexico 87131 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different Ansätze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs=37±1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations.

关键词： Wave functions

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Learning algorithms for mean field optimal control

arXiv

引用

arXiv 2025年

作者： Soner, H. Mete Teichmann, Josef Yan, Qinxin Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08540 United States Department of Mathematics ETH Zürich Switzerland Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an N-particle system and leverage the exchangeability of the particles to obtain substantial computational efficiency. In addition to several numerical examples, a convergence analysis is provided. We also developed a universal approximation theorem on Wasserstein *** Codes 35Q89, 35D40, 49L25, 60G99 © 2025, CC BY-NC-ND.

关键词： Optimal control systems

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New insight into pyrrolic-N site effect towards the first NIR window absorption of pyrrolic-N-rich carbon dots

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Nano Research 2023年第4期16卷 6001-6009页

作者： Fitri Aulia Permatasari Reza Umami Citra Deliana Dewi Sundari Tirta Rona Mayangsari Atthar Luqman Ivansyah Fahdzi Muttaqien Takashi Ogi Ferry Iskandar Department of Physics Faculty Mathematics and Natural SciencesInstitut Teknologi BandungJalan Ganesha 10BandungWest Java 40132Indonesia Collaboration Research Center for Advanced Energy Materials National Research and Innovation Agency-Institut Teknologi BandungJalan Ganesha 10BandungWest Java 40132Indonesia Department of Chemistry Faculty of Mathematics and Natural SciencesInstitut Teknologi BandungJl.Ganesha 10BandungWest Java 40132Indonesia Department of Chemistry Education UIN Sunan Gunung Djati BandungJl.CimincrangBandungWest Java 40292Indonesia Department of Chemistry Universitas PertaminaJakarta 12220Indonesia Master Program in Computational Science Faculty of Mathematics and Natural SciencesInstitut Teknologi BandungJl.Ganesha 10BandungWest Java 40132Indonesia Instrumentation and Computational Physics Research Group Faculty of Mathematics and Natural SciencesInstitut Teknologi BandungJl.Ganesha 10Bandung 40132Indonesia Research Center for Nanoscience and Nanotechnology Institut Teknologi BandungJalan Ganesha 10BandungWest Java 40132Indonesia Chemical Engineering Program Department of Advanced Science and EngineeringGraduate School of Advanced Science and EngineeringHiroshima UniversityHigashi-Hiroshima 739-8527Japan

Controlled C-N configurations,i.e.,pyrrolic-N,pyridinic-N,and graphitic-N,are promising strategies to tailor the carbon dots’(CDs)optical properties into the first near infrared(NIR)window(650-900 nm),a responsive range for biomedical ***,a deep understanding of the role of the C-N configuration in the CDs’properties is still challenging and thoughtprovoking owing to their complex ***,an underlying pyrrolic-N concentration and position effect on the pyrrolic-N-rich CDs’absorption was comprehensively elucidated based on the integrated experimental and computational *** assynthesized pyrrolic-N-rich CDs exhibit a first NIR window absorption centered at 650 nm with high photothermal ***-N concentrations from 1.4%to 11.3%and positions(edge and mid-site)were systematically investigated.A mid-site pyrrolic-N was subsequently generated after the pyrrolic-N concentration more than 10%.Edge-site pyrrolic-N induces a frontier orbital hybridization,reducing bandgap energy,while mid-site pyrrolic-N plays a critical role in inducing a first NIR window absorption owing to their high charge ***,pyrrolic-N-rich CDs inherit a bowl-like topological feature,elevating the CDs’layer thickness as much as 0.71 *** study shed light on the design and optimization of pyrrolic-N on CDs for the first NIR window responsive materials in any biomedical application.

关键词： absorption carbon dots charge transfer first near infrared(NIR)window frontier orbital hybridization mid-site pyrrolic-N

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GLOBAL SOLUTIONS TO THE SUPERCOOLED STEFAN PROBLEM WITH BLOW-UPS: REGULARITY AND UNIQUENESS

Probability and Mathematical Physics

引用

Probability and Mathematical Physics 2022年第1期3卷 171-213页

作者： Delarue, François Nadtochiy, Sergey Shkolnikov, Mykhaylo Laboratoire J.A.Dieudonné Université de Nice Sophia-Antipolis UMR CNRS-UNS No. 7351 Nice France Department of Applied Mathematics Illinois Institute of Technology Rettaliata Engineering Center Chicago IL United States ORFE Department Bendheim Center for Finance Program in Applied and Computational Mathematics Princeton University Princeton NJ United States

We consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows us to define global solutions, even in the presence of blow-ups of the freezing rate. We provide a complete description of such solutions, by relating the temperature distribution in the liquid to the regularity of the ice growth process. The latter is shown to transition between (i) continuous differentiability, (ii) Hölder continuity, and (iii) discontinuity. In particular, in the second regime we rediscover the square root behavior of the growth process pointed out by Stefan in his seminal 1889 paper for the ordinary Stefan problem. In our second main theorem, we establish the uniqueness of the global solutions, a first result of this kind in the context of growth processes with singular self-excitation when blow-ups are present. © 2022 Mathematical Sciences Publishers.

关键词： blow-ups free boundary problem heat equation interacting particle systems mean-field interaction physical solutions probabilistic reformulation self-excitation supercooled Stefan problem zero set

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A Stochastic Approximate Expectation-Maximization for Structure Determination Directly from Cryo-EM Micrographs

arXiv

引用

arXiv 2023年

作者： Kreymer, Shay Singer, Amit Bendory, Tamir The School of Electrical Engineering Tel Aviv University Tel Aviv Israel The Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

A single-particle cryo-electron microscopy (cryoEM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional molecular structure at unknown locations, taken under unknown viewing directions. All existing cryo-EM algorithmic pipelines first locate and extract the projection images, and then reconstruct the structure from the extracted images. However, if the molecular structure is small, the signal-to-noise ratio (SNR) of the data is very low, and thus accurate detection of projection images within the micrograph is challenging. Consequently, all standard techniques fail in low-SNR regimes. To recover molecular structures from measurements of low SNR, and in particular small molecular structures, we devise a stochastic approximate expectation-maximization algorithm to estimate the three-dimensional structure directly from the micrograph, bypassing locating the projection images. We corroborate our computational scheme with numerical experiments, and present successful structure recoveries from simulated noisy measurements. © 2023, CC BY.

关键词： Molecular structure

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Multicontinuum Modeling of Time-Fractional Diffusion-Wave Equation in Heterogeneous Media

arXiv

引用

arXiv 2025年

作者： Bai, Huiran Ammosov, Dmitry Yang, Yin Xie, Wei Kobaisi, Mohammed Al School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan Xiangtan411105 China Chemical and Petroleum Engineering Department Khalifa University of Science and Technology Abu Dhabi127788 United Arab Emirates

This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature. Therefore, in this paper, we derive a multicontinuum time-fractional diffusion-wave model using the multicontinuum homogenization method. For this purpose, we formulate constraint cell problems considering various homogenized effects. These cell problems are implemented in oversampled regions to avoid boundary effects. By solving the cell problems, we obtain multicontinuum expansions of fine-scale solutions. Then, using these multicontinuum expansions and supposing the smoothness of the macroscopic variables, we rigorously derive the corresponding multicontinuum model. Finally, we present numerical results for two-dimensional model problems with different time-fractional derivatives to verify the accuracy of our proposed *** Codes 35B27 (Primary) 26A33, 65M60 (Secondary) Copyright © 2025, The Authors. All rights reserved.

关键词： Wave equations

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CVIT: CONTINUOUS VISION TRANSFORMER FOR OPERATOR LEARNING

arXiv

引用

arXiv 2024年

作者： Wang, Sifan Seidman, Jacob H. Sankaran, Shyam Wang, Hanwen Pappas, George J. Perdikaris, Paris Institution for Foundation of Data Science Yale University United States Graduate Program in Applied Mathematics and Computational Science University of Pennsylvania United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania United States Department of Electrical and Systems Engineering University of Pennsylvania United States

Operator learning, which aims to approximate maps between infinite-dimensional function spaces, is an important area in scientific machine learning with applications across various physical domains. Here we introduce the Continuous Vision Transformer (CViT), a novel neural operator architecture that leverages advances in computer vision to address challenges in learning complex physical systems. CViT combines a vision transformer encoder, a novel grid-based coordinate embedding, and a query-wise cross-attention mechanism to effectively capture multi-scale dependencies. This design allows for flexible output representations and consistent evaluation at arbitrary resolutions. We demonstrate CViT’s effectiveness across a diverse range of partial differential equation (PDE) systems, including fluid dynamics, climate modeling, and reaction-diffusion processes. Our comprehensive experiments show that CViT achieves state-of-the-art performance on multiple benchmarks, often surpassing larger foundation models, even without extensive pretraining and roll-out fine-tuning. Taken together, CViT exhibits robust handling of discontinuous solutions, multi-scale features, and intricate spatio-temporal dynamics. Our contributions can be viewed as a significant step towards adapting advanced computer vision architectures for building more flexible and accurate machine learning models in the physical sciences. All data and code are publicly available at https://***/PredictiveIntelligenceLab/cvit. © 2024, CC BY-NC-SA.

关键词： Computer vision

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