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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations

We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Advanced Finite-Volume Numerics and Source Term Assumptions for Kernel and G-Equation Modelling of Propane/Air Flames

Here G-Equation models represent propagating flame fronts with an implicit two-dimensional surface representation (level-set). Level-set methods are fast, as transport source terms for the implicit surface can be solved with finite-volume operators on the finite-volume domain, without having to build the actual surface. However, they include approximations whose practical effects are not properly understood. In this study, we improved the numerics of the FRESCO CFD code’s G-Equation solver and developed a new method to simulate kernel growth using signed distance functions and the analytical sphere-mesh overlap. We analyzed their role for simulating propane/air flames, using three well-established constant-volume configurations: a one-dimensional, freely propagating laminar flame; a disc-shaped, constant-volume swirl combustor; and torch-jet flame development through an orifice from a two-chamber device. We tested the explicit (sub-cycled) vs. implicit formulation for the standard transport operators (advection, diffusion, compressibility). In addition to the accurate flame swept-volume method for chemistry and species source term, we developed a more accurate estimator for the burnt/unburnt split cell composition. Then, we developed a signed-distance-function (SDF) based method which provides a more stable reinitialization of the level-set field at every time-step. We found that simplifying assumptions common to several G-Equation implementations, for straightforward terms such as compressibility and advection, lead to large errors in predicting the propagation of even laminar flames, with deviations up to ~300% in simulated vs. formulated flame speed. Conversely, the enhanced numerics enabled through the SDF field reinitialization and improved chemistry source term improve simulation stability and smooth flame propagation even with significantly larger solver time-steps.

42 ENGINEERING↗
DOE OSTI2022

Global stochastic optimization of stellarator coil configurations

In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project. Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than 0.1% of the cost of previous work, which considered solely local stochastic optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Theory of Plasmonic Hot-Carrier Generation and Relaxation

Hot-carrier (HC) generation from (localized) surface plasmon decay has recently attracted much attention due to its promising applications in physical, chemical, materials, and energy science. However, the detailed mechanisms of plasmonic HC generation, relaxation, and trapping are less studied. In this work, we developed and applied a quantum-mechanical model and coupled master equation method to study the generation of HCs from plasmon decay and their following relaxation processes with different mechanisms treated on equal footing. First, a quantum-mechanical model for HC generation is developed. Its connection to existing semiclassical models and time-dependent density functional theory (TDDFT) is discussed. Second, the relaxation and lifetimes of HCs are investigated in the presence of electron–electron and electron–phonon interactions. A GW-like approximation is introduced to account for the electron–electron scattering. The numerical simulations on the Jellium nanoparticles with a size up to 1.6 nm demonstrate the electron–electron scattering and electron–phonon scattering dominate different time scale in the relaxation dynamics. We also generalize the model to study the extraction of HCs to attached molecules. The quantum yield of extracting HCs for other applications is found to be size-dependent. In general, the smaller size of NP improves the quantum yield, which is in agreement with recent experimental measurements. Even though we demonstrate this newly developed theoretical formalism with Jellium model, the theory applies to any other atomistic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

2D-FFTLog: efficient computation of real-space covariance matrices for galaxy clustering and weak lensing

ABSTRACT Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate, and numerically stable computation of non-Gaussian real-space covariances for both 3D and projected statistics. The 2D-FFTLog algorithm is easily extended to perform real-space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3-like and a Rubin Observatory’s Legacy Survey of Space and Time Year 1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code CosmoCov for computing the real-space covariances with or without the flat-sky approximation is released along with this paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Nondegenerate Noise-Resilient Superconducting Qubit

We propose a superconducting qubit based on engineering the first and second harmonics of the Josephson energy and phase relation 𝐸 𝐽⁢1 ⁢cos 𝜑 and 𝐸 𝐽⁢2 ⁢cos 2⁢𝜑. By constructing a circuit such that 𝐸 𝐽⁢2 is negative and |𝐸 𝐽⁢1 | ≪ |𝐸 𝐽⁢2 |, we create a periodic potential with two nondegenerate minima. The qubit, which we dub “harmonium,” is formed from the lowest-energy states of each minimum. Bit-flip protection of the qubit arises due to the localization of each qubit state to their respective minima, while phase-flip protection can be understood by considering the circuit within the Born-Oppenheimer approximation. We demonstrate with time-domain simulations that single- and two-qubit gates can be performed in approximately 100 ns. Finally, we compute the qubit coherence times using numerical diagonalization of the complete circuit in conjunction with state-of-the-art noise models. We estimate out-of-manifold heating times on the order of milliseconds, which can be treated as erasure errors using conventional dispersive readout. We estimate pure-dephasing times on the order of many tens of milliseconds, and bit-flip times on the order of seconds.

quantum error correction↗
DOE OSTI2025

Interacting Dirac magnons in the van der Waals ferromagnet CrBr 3

We study the effects of magnon-magnon interactions in the two-dimensional van der Waals ferromagnet CrBr 3 focusing on its honeycomb lattice structure. Motivated by earlier theoretical predictions of temperature-induced spectral shifts and van Hove singularities in the magnon dispersion [S. S. Pershoguba et al., Phys. Rev. X 8, 011010 (2018)], we go beyond the commonly used thermal magnon approximation by applying second-order perturbation theory in a fully numerical framework. Our analysis uncovers significant deviations from previous analysis: in particular, the predicted singularities are absent, consistent with recent inelastic neutron scattering measurements [S. E. Nikitin et al ., Phys. Rev. Lett. 129, 127201 (2022)]. Moreover, we find that the temperature dependence of the renormalized magnon spectrum exhibits a distinct 𝑇 3 behavior for the optical magnon branch, while retaining 𝑇 2 behavior for the acoustic or down magnon band. This feature sheds light on the collective dynamics of Dirac magnons and their interactions. We further compare the honeycomb case with a triangular Bravais lattice, relevant for ferromagnetic monolayer MnBi 2 ⁢Te 4 , and show that both systems lack singular features while displaying quite distinct thermal trends.

Holstein-Primakoff method↗
DOE OSTI2024

Capturing many-body correlation effects with quantum and classical computing

Theoretical descriptions of excited states of molecular systems in high-energy regimes are crucial for supporting and driving many experimental efforts at light source facilities. However, capturing their complicated correlation effects requires formalisms that provide a hierarchical infrastructure of approximations. These approximations lead to an increased overhead in classical computing methods and, therefore, decisions regarding the ranking of approximations and the quality of results must be made on purely numerical grounds. The emergence of quantum computing methods has the potential to change this situation. Here, in this study, we demonstrate the efficiency of the quantum phase estimator (QPE) in identifying core-level states relevant to x-ray photoelectron spectroscopy. We compare and validate the QPE predictions with exact diagonalization and real-time equation-of-motion coupled-cluster formulations, which are some of the most accurate methods for states dominated by collective correlation effects.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

How correlations change the magnetic structure factor of the kagome Hubbard model

The kagome Hubbard model (KHM) is a paradigmatic example of a frustrated two-dimensional model. While its strongly correlated regime, described by a Heisenberg model, is of topical interest due to its enigmatic prospective spin-liquid ground state, the weakly and moderately correlated regimes remain largely unexplored. Motivated by the rapidly growing number of metallic kagome materials (e.g., Mn 3 Sn, Fe 3 Sn 2 , FeSn, Co 3 Sn 2 S 2 , Gd 3 Ru 4 Al 12 , and AV 3 Sb 5 with A = K, Rb, Cs), here we study the respective regimes of the KHM by means of three complementary numerical methods: the dynamical mean-field theory, the dynamical vertex approximation, and determinant quantum Monte Carlo. In contrast to the archetypal square lattice, we find no tendencies toward magnetic ordering, as magnetic correlations remain short-range. Nevertheless, the magnetic correlations undergo a remarkable crossover as the system approaches the metal-to-insulator transition. The Mott transition itself does not affect the magnetic correlations. Our equal-time and dynamical structure factors can be used as a reference for inelastic neutron scattering experiments on the growing family of metallic kagome materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Real-time evolution of Anderson impurity models via tensor network influence functionals

In this work, we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time nonequilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations, which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Approximate 𝑡-Designs in Generic Circuit Architectures

Unitary 𝑡-designs are distributions on the unitary group whose first 𝑡 moments appear maximally random. Previous work has established several upper bounds on the depths at which certain specific random quantum circuit ensembles approximate 𝑡-designs. Here we show that these bounds can be extended to any fixed architecture of Haar-random two-site gates. This is accomplished by relating the spectral gaps of such architectures to those of one-dimensional brickwork architectures. Our bound depends on the details of the architecture only via the typical number of layers needed for a block of the circuit to form a connected graph over the sites. When this quantity is bounded, the circuit forms an approximate 𝑡-design in at most linear depth. We give numerical evidence for a stronger bound that depends only on the number of connected blocks into which the architecture can be divided. We also give an implicit bound for nondeterministic architectures in terms of properties of the corresponding distribution over fixed architectures.

information scrambling↗
DOE OSTI2025

Quantitative Nonlinear Optical Polarimetry with High Spatial Resolution

Nonlinear optical microscopy such as in the optical second-harmonic generation (SHG) modality has become a popular tool today for probing materials in the physical and biological sciences. While imaging and spectroscopy are widely used in the microscopy mode, nonlinear polarimetry, which can shed light on materials’ symmetry and microstructure, is relatively underdeveloped. This is partly because quantitative analytical modeling of the optical SHG response for anisotropic crystals and films largely assumes low-numerical aperture (NA) focusing of light, where the plane-wave approximation is sufficient. Tight focusing provides unique benefits in revealing out-of-plane polarization responses, which cannot be detected by near-plane-wave illumination at normal incidence. Here, we outline a method for quantitatively analyzing SHG polarimetry measurements obtained under high-NA focusing within a microscope geometry. Experiments and simulations of a variety of standard samples, from single crystals to thin films, are in good agreement, including measured and simulated spatial SHG maps of ferroelectric domains. A solution to the inverse problem is demonstrated, where the spatial distribution of an SHG tensor with unknown tensor coefficient magnitudes is determined by experimentally measured polarimetry. The ability to extract the out-of-plane component of the nonlinear polarization in normal incidence is demonstrated, which can be valuable for high-resolution polarimetry of 2D materials, thin films, heterostructures, and uniaxial crystals with a strong out-of-plane response.

36 MATERIALS SCIENCE↗
DOE OSTI2020

NH 4 OH Looping with Membrane CO 2 Absorber and Distributed Stripper for Enhanced Algae Growth

The University of Kentucky Center for Applied Energy (UK CAER) has devised a unique, integrated CO2 capture and utilization technology. CO2 from coal-fired power generation flue gas is first captured at half the operating cost of a typical aqueous CO2 capture system (CCS), distributed in an aqueous stream and then fixed by algae in bioreactors where the algae production is increased by 50% over that with a typical intermittent nutrient feeding system. Lower CCS operating cost is achieved by eliminating the flue gas pretreatment step for cooling and SO2 removal, eliminating steam extraction from the power generation steam cycle for solvent regeneration, and eliminating CO2 compression. Higher algae production is achieved by continuous, just-in-time nutrient feed to the bioreactors directly from a distributed solvent regenerator, which maintains the bioreactor pH for optimum growth. The process starts with a uniquely configured membrane absorber, where the flue gas is indirectly contacted with an ammonium hydroxide (NH4OH) solvent. Dissolved NH3 is attractive for both CO2 capture and as an algae nutrient. For CO2 capture it is inexpensive, has a low regeneration energy, is thermally- and oxidatively-stable and has a viscosity near that of water, which makes is easy to transport. Numerous studies have shown that the scrubbing capacity of NH3 is approximately 0.9-1.2 kg of CO2/kg of NH3, with a CO2 removal efficiency of ~99% and half the solvent regeneration energy than that of 30 wt% MEA[1, 2, 3]. NH3 is attractive as an algae nutrient due to its low cost. The rich NH4OH solvent is pumped to a set of distributed regenerators which are co-located with the algae bioreactors. Solvent pumping, transport and distribution reduces the balance of plant (BOP) cost compared to a typical aqueous CCS related to the flue gas duct and boost fan required to transport the flue gas. The energy required for the distributed solvent regeneration is supplied by solar-thermal panels eliminating the need for steam extraction from the power generation steam cycle. After solvent regeneration, the product stream contains both the CO2 captured from the flue gas and volatized NH3 from the solvent. This product stream is fed directly to the bioreactors, eliminating the need for compression of the CO2 stream. The relative amounts of CO2 and NH3 in the product stream are adjusted and controlled by a controlling the regeneration conditions (pressure and temperature). The continuous feed of the right ratio of nutrients overcomes the typical inhibition of algae growth resulting from frequent pH swings in the bioreactor due to unbalanced (intermittent) feeding systems for CO2 and N. Also, because the regenerators will operate at pressure and be located in close proximity to the bioreactors, there is no worry about pressure drop when sparging the gas into the algae. Sparging produces small bubbles which is beneficial for mass transfer efficiency. One known challenge when using an NH4OH solvent is high NH3 emission. Hydrophobic membranes are used for CO2 capture using an aqueous NH3 solution[4, 5] without the direct contact between flue gas and aqueous solution. Additionally, UK CAER CO2 capture and utilization process manages NH3 slip in three extra measures. First, NH3 slip is minimized by working with minimal species partial pressure, which is proportional to the concentration in the liquid. Hence, lowering the capture solvent concentration will lower the NH3 partial pressure. Second, UK CAER’s previous work has demonstrated that the addition of Zn2+ into NH3 solutions to chelate the NH3 can reduce NH3 volatility. Third, the configuration of the membrane CO2 absorber utilizes condensed water from the flue gas to continually wash the gas-side of the membrane to reduce fouling and recapture NH3 slip. Additional details about the UK CAER unique, integrated CO2 capture and utilization technology will be presented along with technology development plans. Diao, N., Q. Li, and Z. Fang. 2004. Heat transfer in ground heat exchangers with groundwater advection. International Journal of Thermal Sciences. 43: 1203-1211, He, Q., M. Chen, L. Meng, K. Liu, and W. Pan. 2004. Study on Carbon Dioxide Removal from Flue Gas by Absorption of Aqueous Ammonia. Western Kentucky University. Yeh, A.C., and H. Bai. 1999. Comparison of ammonia and monoethanolamine solvents to reduce CO2 greenhouse gas emissions. The Science of the Total Environment. 228: 121-133, Villeneuve, K., D. Roizard, J.C. Remigy, M. Iacono, and S. Rode. 2018. CO2 capture by aqueous ammonia with hollow fiber membrane contactors: Gas phase reactions and performance stability. Separation and Purification Technology, 199: 189-197, Toro Molina, C., and C. Bouallou. 2016. Carbon dioxide absorption by ammonia intensified with membrane contactors. Clean Techn Environ Policy 18, 2133–2146 (2016)

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2023

Quantum Search Approaches to Sampling-Based Motion Planning

In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse environments, we formulate the Quantum Full Path Search Algorithm (q-FPS), which creates a superposition of full random path solutions, manipulates probability amplitudes with Quantum Amplitude Amplification (QAA), and quantum measures a single obstacle free full path solution. For dense unstructured environments, we formulate the Quantum Rapidly Exploring Random Tree algorithm, q-RRT, that creates quantum superpositions of possible parent-child connections, manipulates probability amplitudes with QAA, and quantum measures a single reachable state, which is added to a tree. As performance depends on the number of oracle calls and the probability of measuring good quantum states, we quantify how these errors factor into the probabilistic completeness properties of the algorithm. We then numerically estimate the expected number of database solutions to provide an approximation of the optimal number of oracle calls in the algorithm. We compare the q-RRT algorithm with a classical implementation and verify quadratic run-time speedup in the largest connected component of a 2D dense random lattice. We conclude by evaluating a proposed approach to limit the expected number of database solutions and thus limit the optimal number of oracle calls to a given number.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Effect of dust on rainfall over the Red Sea coast based on WRF-Chem model simulations

Water is the single most important element of life. Rainfall plays an important role in the spatial and temporal distribution of this precious natural resource, and it has a direct impact on agricultural production, daily life activities, and human health. One of the important elements that govern rainfall formation and distribution is atmospheric aerosol, which also affects the Earth's radiation balance and climate. Therefore, understanding how dust compositions and distributions affect the regional rainfall pattern is crucial, particularly in regions with high atmospheric dust loads such as the Middle East. Although aerosol and rainfall research has garnered increasing attention as both an independent and interdisciplinary topic in the last few decades, the details of various direct and indirect pathways by which dust affects rainfall are not yet fully understood. Here, we explored the effects of dust on rainfall formation and distribution as well as the physical mechanisms that govern these phenomena, using high-resolution WRF-Chem simulations (~1.5 km × 1.5 km) configured with an advanced double-moment cloud microphysics scheme coupled with a sectional eight-bin aerosol scheme. Our model-simulated results were realistic, as evaluated from multiple perspectives including vertical profiles of aerosol concentrations, aerosol size distributions, vertical profiles of air temperature, diurnal wind cycles, and spatio-temporal rainfall patterns. Rainfall over the Red Sea coast is mainly caused by warm rain processes, which are typically confined within a height of ~6 km over the Sarawat mountains and exhibit a strong diurnal cycle that peaks in the evening at approximately 18:00 local time under the influence of sea breezes. Numerical experiments indicated that dust could both suppress or enhance rainfall. The effect of dust on rainfall was calculated as total, indirect, and direct effects, based on 10-year August-average daily-accumulated rainfall over the study domain covering the eastern Red Sea coast. For extreme rainfall events (domain-average daily-accumulated rainfall of ≥ 1.33 mm), the net effect of dust on rainfall was positive or enhancement (6.05 %), with the indirect effect (4.54 %) and direct effect (1.51 %) both causing rainfall increase. At a 5 % significance level, the total and indirect effects were statistically significant whereas the direct effect was not. For normal rainfall events (domain-average daily-accumulated rainfall < 1.33 mm), the indirect effect enhanced rainfall (4.76 %) whereas the direct effect suppressed rainfall (-5.78 %), resulting in a negative net suppressing effect (-1.02 %), all of which were statistically significant. We investigated the possible physical mechanisms of the effects and found that the rainfall suppression by dust direct effects was mainly caused by the scattering of solar radiation by dust. The surface cooling induced by dust weakens the sea breeze circulation, which decreases the associated landward moisture transport, ultimately suppressing rainfall. For extreme rainfall events, dust causes net rainfall enhancement through indirect effects as the high dust concentration facilitates raindrops to grow when the water vapor is sufficiently available. Our results have broader scientific and environmental implications. Specifically, although dust is considered a problem from an air quality perspective, our results highlight the important role of dust on sea breeze circulation and associated rainfall over the Red Sea coastal regions. Our results also have implications for cloud seeding and water resource management.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Learning continuous models for continuous physics

Abstract Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗