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Resonant spectroscopies, which involve intermediate states with finite lifetimes, provide essential insights into collective excitations in quantum materials that are otherwise inaccessible. However, theoretical understanding in this area is often limited by the numerical challenges of solving Kramers-Heisenberg-type response functions for large-scale systems. To address this, we introduce a multishifted biconjugate gradient algorithm that exploits the shared structure of Krylov subspaces across spectra with varying incident energies, effectively reducing the computational complexity to that of linear spectroscopies. Both mathematical proofs and numerical benchmarks confirm that this algorithm substantially accelerates spectral simulations, achieving constant complexity independent of the number of incident energies, while ensuring accuracy and stability. This development provides a scalable, versatile framework for simulating advanced spectroscopies in quantum materials 

We investigate the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the su(2) Lie algebra, representing an environment with a large magnitude of anharmonicity. Based on the previous work by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and by Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we use the time-domain Prony fitting decomposition scheme to the bare–bath time correlation function (TCF) given by the bosonic fluctuation–dissipation theorem to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy have been explored by a variety of numerical results. We envision that this work provides new insights into extending the hierarchical equations of motion and DEOM approach to certain types of anharmonic environments with arbitrary TCF or spectral density. 

Abstract Objective: This study investigates speech decoding from neural signals captured by intracranial electrodes. Most prior works can only work with electrodes on a 2D grid (i.e., Electrocorticographic or ECoG array) and data from a single patient. We aim to design a deep-learning model architecture that can accommodate both surface (ECoG) and depth (stereotactic EEG or sEEG) electrodes. The architecture should allow training on data from multiple participants with large variability in electrode placements. The model should not have subject-specific layers, and the trained model should perform well on participants unseen during training. Approach: We propose a novel transformer-based model architecture named SwinTW that can work with arbitrarily positioned electrodes by leveraging their 3D locations on the cortex rather than their positions on a 2D grid. We train subject-specific models using data from a single participant and multi-subject models exploiting data from multiple participants. Main Results: The subject-specific models using only low-density 8x8 ECoG data achieved high decoding Pearson Correlation Coefficient with ground truth spectrogram (PCC=0.817), over N=43 participants, significantly outperforming our prior convolutional ResNet model and the 3D Swin transformer model. Incorporating additional strip, depth, and grid electrodes available in each participant (N=39) led to further improvement (PCC=0.838). For participants with only sEEG electrodes (N=9), subject-specific models still enjoy comparable performance with an average PCC=0.798. A single multi-subject model trained on ECoG data from 15 participants yielded comparable results (PCC=0.837) as 15 models trained individually for these participants (PCC=0.831). Furthermore, the multi-subject models achieved high performance on unseen participants, with an average PCC=0.765 in leave-one-out cross-validation. Significance: The proposed SwinTW decoder enables future speech decoding approaches to utilize any electrode placement that is clinically optimal or feasible for a particular participant, including using only depth electrodes, which are more routinely implanted in chronic neurosurgical procedures. The success of the single multi-subject model when tested on participants within the training cohort demonstrates that the model architecture is capable of exploiting data from multiple participants with diverse electrode placements. The architecture’s flexibility in training with both single-subject and multi-subject data, as well as grid and non-grid electrodes, ensures its broad applicability. Importantly, the generalizability of the multi-subject models in our study population suggests that a model trained using paired acoustic and neural data from multiple patients can potentially be applied to new patients with speech disability where acoustic-neural training data is not feasible.