arXiv:2507.02032v2 Announce Type: replace-cross
Abstract: One of the forthcoming major challenges in particle physics is the experimental determination of the Higgs trilinear self-coupling. While efforts have largely focused on on-shell double- and single-Higgs production in proton-proton collisions, off-shell Higgs production has also been proposed as a valuable complementary probe. In this article, we design a hybrid neural simulation-based inference (NSBI) approach to construct a likelihood of the Higgs signal incorporating modifications from the Standard Model effective field theory (SMEFT), relevant background processes, and quantum interference effects. It leverages the training efficiency of matrix-element-enhanced techniques, which are vital for robust SMEFT applications, while also incorporating the practical advantages of classification-based methods for effective background estimates. We demonstrate that our NSBI approach achieves sensitivity close to the theoretical optimum and provide expected constraints for the high-luminosity upgrade of the Large Hadron Collider. While we primarily concentrate on the Higgs trilinear self-coupling, we also consider constraints on other SMEFT operators that affect off-shell Higgs production.
Science Journals
arXiv:2605.15603v1 Announce Type: new
Abstract: Model-based reinforcement learning (RL) offers a compelling approach to offline RL by enabling value learning on imagined on-policy trajectories. However, it often suffers from compounding errors due to repeated model inference on self-generated states. While geometric horizon models (GHM) alleviate this issue through direct prediction over a discounted infinite-horizon future, they remain challenged in accurately modeling distant future states. To this end, we introduce universal horizon models (UHM), a generalization of GHM that directly predicts future states under arbitrary horizons. Leveraging this flexibility, we propose a scalable value learning method that employs a winsorized horizon distribution to stabilize training by capping excessively large horizons. Experimental results on 100 challenging OGBench tasks demonstrate that the proposed method outperforms competitive baselines, particularly on tasks with highly suboptimal datasets and those requiring long-horizon reasoning. Project page: https://rllab-snu.github.io/projects/UHM/
arXiv:2507.08762v3 Announce Type: replace
Abstract: We are interested in the relative
conditioning of the problem $y_0\mapsto \mathrm{e}^{tA}y_0$, i.e., the
relative conditioning of the action of the matrix exponential $\mathrm{e}%
^{tA}$ on a vector with respect to perturbations of this vector. The present paper is a qualitative study of the long-time behavior of this
conditioning. In other words, we are interested in studying the propagation to the solution $y(t)$ of perturbations of the initial value for a linear ordinary differential equation $y^\prime(t)=Ay(t)$, by measuring these perturbations with relative errors. We introduce three condition numbers: the first considers a specific initial value and a specific direction of perturbation; the second considers a specific initial value and the worst case by varying the direction of perturbation; and the third considers the worst case by varying both the initial value
and the direction of perturbation. The long-time behaviors of
these three condition numbers are studied.
arXiv:2605.13788v2 Announce Type: replace
Abstract: Active learning for machine-learning interatomic potentials (MLIPs) must address several challenges to be practical: scaling to large candidate pools, leveraging energy-force supervision, and maintaining robustness when candidate pools are biased relative to the target distribution. In this work, we jointly address these challenges. We first introduce a linearly scaling acquisition framework based on chunked feature-space posterior-variance shortlisting. By avoiding materialisation of the candidate and train set kernels, this approach enables screening of ~200k structures within hours and applies broadly to acquisition strategies that score candidates based on molecular similarity metrics. We then extend the Neural Tangent Kernel (NTK) to a force-aware setting via mixed parameter-coordinate derivatives, yielding a force NTK and a joint energy-force NTK that provide natural similarity metrics for vector-field prediction. We demonstrate the effectiveness of the joint energy-force NTK on the OC20 dataset, where force-aware acquisition is crucial: it achieves the lowest energy and force MAE and RMSE across all metrics and distribution splits. Across T1x, PMechDB, and RGD benchmarks, our force NTK methods remain competitive with established baselines while being significantly more efficient than committee-based approaches. Under a controlled candidate-pool shift case study on T1x, acquisition based on pretrained MLIP embeddings and NTKs remains robust, whereas committee-based methods exhibit higher variance. Overall, these results show that a single pretrained MLIP can enable scalable, force-aware, and distribution-robust active learning for foundation-model fine-tuning.
arXiv:2507.08752v3 Announce Type: replace
Abstract: We investigate the propagation of initial value perturbations along the solution of a linear ordinary differential equation \( y'(t) = Ay(t) \). This propagation is analyzed using the relative error rather than the absolute error. Our focus is on the long-term behavior of this relative error, which differs significantly from that of the absolute error. The present paper is a practical sequel to the theoretical papers \cite{M1,M2} on the long-time behavior of the relative error: it includes applicative examples and important issues not addressed in \cite{M1,M2}. In addition, the present paper shows that understanding the long-term behavior provides insights into the growth of the relative error over all times, not just at large times. Therefore, it represents a crucial and fundamental aspect of the conditioning of linear ordinary differential equations, with applications in, for example, non-normal dynamics.
arXiv:2605.15933v1 Announce Type: new
Abstract: We first show how the cohomology of some Bernstein-Gelfand-Gelfand (BGG) sequences that are important for the numerical analysis of partial differential equations, can be obtained through the construction of a long exact sequence connecting cohomology groups. Then we explain the extension of this result to the non-injective/surjective case through the systematic use of short exact sequences of complexes and their associated long exact sequences of cohomology groups. Finally an interpretation in terms of spectral sequences is given.
arXiv:2605.13246v2 Announce Type: replace
Abstract: Reference counting bugs in Linux kernel drivers can lead to severe resource mismanagement and security vulnerabilities. We introduce DrvHorn, a novel automated tool to detect these bugs by reducing reference counting verification to an assertion checking problem leveraging the Linux driver interface. Through efficient modeling of the Linux kernel and aggressive program slicing, DrvHorn discovered 545 bugs, of which 424 were previously unknown, across all platform drivers in v6.6 Linux kernel, with a lower false positive rate of 29.9% compared to prior studies. To address the root causes of these newly discovered bugs, we submitted patches to the Linux kernel, and 45 of them were merged.
arXiv:2605.12309v2 Announce Type: replace
Abstract: The development of separate-encoder Unified multimodal models (UMMs) comes with a rapidly growing inference cost due to dense visual token processing. In this paper, we focus on understanding-side visual token reduction for improving the efficiency of separate-encoder UMMs. While this topic has been widely studied for MLLMs, existing methods typically rely on attention scores, text-image similarity and so on, implicitly assuming that the final objective is discriminative reasoning. This assumption does not hold for UMMs, where understanding-side visual tokens must also preserve the model's capabilities for editing images. We propose G$^2$TR, a generation-guided visual token reduction framework for separate-encoder UMMs. Our key insight is that the generation branch provides a task-agnostic signal for identifying understanding-side visual tokens that are not only semantically relevant but also important for latent-space image reconstruction and generation. G$^2$TR estimates token importance from consistency with VAE latent, performs balanced token selection, and merges redundant tokens into retained representatives to reduce information loss. The method is training-free, plug-and-play, and applied only after the understanding encoding stage, making it compatible with existing UMM inference pipelines. Experiments on image understanding and editing benchmarks show that G$^2$TR substantially reduces visual tokens and prefill computation by 1.94x while maintaining both reasoning accuracy and editing quality, outperforming baselines on almost all benchmarks. Code is at: https://github.com/lijunxian111/G2TR.
arXiv:2605.14344v2 Announce Type: replace
Abstract: Generative modeling has emerged as a promising approach for crystal structure discovery. However, existing LLM-based generative models struggle with low-level atomic precision, while diffusion-based methods fall short in integrating high-level scientific knowledge. As a result, generated structures are often invalid, unstable, or do not possess desirable properties. To address this gap, we propose CrystalReasoner (CrysReas), an end-to-end LLM framework that generates crystal structures from natural language instructions through reasoning and alignment. CrysReas introduces physical priors as thinking tokens, which include crystallographic symmetry, local coordination environments and predicted physical properties before generating atomic coordinates. This bridges the gap between natural language and 3D structures. CrysReas then employs reinforcement learning (RL) with a multi-objective, dense reward function to align generation with physical validity, chemical consistency, and thermodynamic stability. For property-conditioned tasks, we design task-specific reward functions and train specialized models for discrete constraints (e.g., space group) and continuous properties (e.g., elasticity, thermal expansion). Empirical results demonstrate that compared to prior works and baselines without thinking traces or RL, CrysReas obtains better performance on diverse metrics, triples S.U.N. ratio, and achieves better performance for property conditioned generation. CrysReas also exhibits adaptive reasoning, increasing reasoning lengths as the number of atoms increases. Our work demonstrates the potential of leveraging thinking traces and RL for generating valid, stable, and property-conditioned crystal structures.
arXiv:2605.03258v2 Announce Type: replace
Abstract: Large language models often fail at simple counting tasks, even when items to count are in the prompt. We investigate whether this failure occurs because transformers do not represent counts internally, or because they cannot convert representations to the correct output tokens. Across three model families: Pythia, Qwen3, and Mistral, ranging from 0.4B to 14B parameters, we find evidence for the second explanation. Linear probes recover the correct count from intermediate layers with $R^2>0.99$, showing that the information is present. However, the internal directions that encode counts are nearly orthogonal to digit-token output-head rows ($|\cos| \leq 0.032$). In other words, the model stores the count in a form that the digit logits do not naturally read out. We localize this failure with two interventions. Updating only the digit rows of the output head (36,864 parameters) substantially improves constrained digit prediction (60.7--100.0% on four tasks), but it does not fix unconstrained generation (0%); we do not claim that digit-row repair fixes open-ended text. By contrast, small LoRA on attention Q/V (7.67M parameters) improves upstream routing and achieves 83.1%$\pm$7.2% in true greedy autoregressive generation (deployable fix). Logit-lens at layer 35 (entity counting; correct-digit rank): (i) median over 3 seeds drops from order-$10^4$ to 1; (ii) seed 42 shows $54{,}332 \to 838$ (median top-1 while one seed stays far below). Norm, logit-lens, and cross-task analyses generalize the bottleneck to counting, addition, and list length; nulls on MMLU and GSM8K and limited DROP transfer. These results identify counting failure as a geometric readout bottleneck, not an internal-representation failure: the model knows the count but the output pathway is misaligned with tokens needed to express it.
arXiv:2505.03307v3 Announce Type: replace-cross
Abstract: Simulating Clifford and near-Clifford circuits using the extended stabilizer formalism has become increasingly popular, particularly in quantum error correction. Compared to the state-vector approach, the extended stabilizer formalism can solve the same problems with fewer computational resources, as it operates on stabilizers rather than full state vectors. Most existing studies on near-Clifford circuits focus on balancing the trade-off between the number of ancilla qubits and simulation accuracy, often overlooking performance considerations. Furthermore, in the presence of high-rank stabilizers, performance is limited by the sequential property of the stabilizer formalism. In this work, we introduce a parallelized version of the extended stabilizer formalism, enabling efficient execution on multi-core devices such as GPU. Experimental results demonstrate that, in certain scenarios, our Python-based implementation outperforms state-of-the-art simulators such as Qiskit and Pennylane.
arXiv:2511.18719v4 Announce Type: replace
Abstract: Reinforcement learning (RL) has become a powerful tool for post-training visual generative models, with Group Relative Policy Optimization (GRPO) increasingly used to align generators with human preferences. However, existing GRPO pipelines rely on a single scalar reward per sample, treating each image or video as a holistic entity and ignoring the rich spatial and temporal structure of visual content. This coarse supervision hinders the correction of localized artifacts and the modeling of fine-grained perceptual cues. We introduce Visual Preference Policy Optimization (ViPO), a GRPO variant that lifts scalar feedback into structured, pixel-level advantages. ViPO employs a Perceptual Structuring Module that uses pretrained vision backbones to construct spatially and temporally aware advantage maps, redistributing optimization pressure toward perceptually important regions while preserving the stability of standard GRPO. Across both image and video benchmarks, ViPO consistently outperforms vanilla GRPO, improving in-domain alignment with human-preference rewards and enhancing generalization on out-of-domain evaluations. The method is architecture-agnostic, lightweight, and fully compatible with existing GRPO training pipelines, providing a more expressive and informative learning signal for visual generation.
arXiv:2501.19128v5 Announce Type: replace
Abstract: In many real-world scenarios, reward signal for agents are exceedingly sparse, making it challenging to learn an effective reward function for reward shaping. To address this issue, the proposed approach in this paper performs reward shaping not only by utilizing non-zero-reward transitions but also by employing the \emph{Semi-Supervised Learning} (SSL) technique combined with a novel data augmentation to learn trajectory space representations from the majority of transitions, {i.e}., zero-reward transitions, thereby improving the efficacy of reward shaping. Experimental results in Atari and robotic manipulation demonstrate that our method outperforms supervised-based approaches in reward inference, leading to higher agent scores. Notably, in more sparse-reward environments, our method achieves up to twice the peak scores compared to supervised baselines. The proposed double entropy data augmentation enhances performance, showcasing a 15.8\% increase in best score over other augmentation methods
arXiv:2503.00794v2 Announce Type: replace
Abstract: Accurate gait event detection is crucial for gait analysis, rehabilitation, and assistive technology, particularly in exoskeleton control, where precise identification of stance and swing phases is essential. This study evaluated the performance of seven kinematics-based methods and a Long Short-Term Memory (LSTM) model for detecting heel strike and toe-off events across 4363 gait cycles from 588 able-bodied subjects. The results indicated that while the Zeni et al. method achieved the highest accuracy among kinematics-based approaches, other methods exhibited systematic biases or required dataset-specific tuning. The LSTM model performed comparably to Zeni et al., providing a data-driven alternative without systematic bias. These findings highlight the potential of deep learning-based approaches for gait event detection while emphasizing the need for further validation in clinical populations and across diverse gait conditions. Future research will explore the generalizability of these methods in pathological populations, such as individuals with post-stroke conditions and knee osteoarthritis, as well as their robustness across varied gait conditions and data collection settings to enhance their applicability in rehabilitation and exoskeleton control.
arXiv:2605.15734v1 Announce Type: new
Abstract: The use of large language models to assess user states in conversational and adaptive systems is based on the assumption that the metrics used for such assessment are stable and interpretable at the level of individual scores. This paper empirically tests this assumption, focusing on the psychometric reliability of artificial intelligence (AI) measures of user states.
This study employed replication evaluation procedures to assess the repeatability of a broad set of metrics across three different bimodal large language models (GPT-4o audio, Gemini 2.0 Flash, Gemini 2.5 Flash). Analyses include both individual score reliability and aggregated reliability, allowing us to distinguish metrics potentially useful for real-time adaptation from those that retain their value only in aggregated analyses.
The results demonstrate that metric reliability cannot be considered a default property in interpretive domains. The lack of stability at the level of individual scores precludes the interpretation of such scores as indicators of user state in real-time adaptive systems, even if these metrics demonstrate stability after aggregation. At the same time, the study indicates that individually unstable metrics can retain analytical utility in post-hoc studies, identifying rules governing interactions and their relationships with user experience parameters such as satisfaction, trust, and engagement.
The main contribution of this work, besides quantifying the severity of the problem (only 31 of 213 metrics met the criteria), is the proposal of a replicable evaluation framework, enabling measurable evaluations of metric applicability. This approach supports more responsible AI design of adaptive systems, in which the interpretation of results requires explicit validation of reliability and monitoring for violations over time.
arXiv:2604.04310v2 Announce Type: replace
Abstract: In robot control, planning, and learning, there is a need for rigid-body dynamics libraries that are highly performant, easy to use, and compatible with CPUs and accelerators. While existing libraries often excel at either low-latency CPU execution or high-throughput GPU workloads, few provide a unified framework that targets multiple architectures without compromising performance or ease-of-use. To address this, we introduce frax, a JAX-based library for robot kinematics and dynamics, providing a high-performance, pure-Python interface across CPU, GPU, and TPU. Via a fully-vectorized approach to robot dynamics, frax enables efficient real-time control and parallelization, while supporting automatic differentiation for optimization-based methods. On CPU, frax achieves low-microsecond computation times suitable for kilohertz control rates, outperforming common libraries in Python and approaching optimized C++ implementations. On GPU, the same code scales to thousands of instances, reaching upwards of 100 million dynamics evaluations per second. We validate performance on a Franka Panda manipulator and a Unitree G1 humanoid, and release frax as an open-source library.
arXiv:2603.29617v2 Announce Type: replace-cross
Abstract: Understanding how the brain processes linguistic constructions is a central challenge in cognitive neuroscience and linguistics. Recent computational studies show that artificial neural language models spontaneously develop differentiated representations of Argument Structure Constructions (ASCs), generating predictions about when and how construction-level information emerges during processing. The present study tests these predictions in human neural activity using electroencephalography (EEG). Ten native English speakers listened to 200 synthetically generated sentences across four construction types (transitive, ditransitive, caused-motion, resultative) while neural responses were recorded. Analyses using time-frequency methods, feature extraction, and machine learning classification revealed construction-specific neural signatures emerging primarily at sentence-final positions, where argument structure becomes fully disambiguated, and most prominently in the alpha band. Pairwise classification showed reliable differentiation, especially between ditransitive and resultative constructions, while other pairs overlapped. Crucially, the temporal emergence and similarity structure of these effects mirror patterns in recurrent and transformer-based language models, where constructional representations arise during integrative processing stages. These findings support the view that linguistic constructions are neurally encoded as distinct form-meaning mappings, in line with Construction Grammar, and suggest convergence between biological and artificial systems on similar representational solutions. More broadly, this convergence is consistent with the idea that learning systems discover stable regions within an underlying representational landscape - recently termed a Platonic representational space - that constrains the emergence of efficient linguistic abstractions.
arXiv:2605.12253v2 Announce Type: replace-cross
Abstract: An \emph{outer-string representation} of a graph $G$ is an intersection representation of $G$ where vertices are represented by curves (strings) inside the unit disk and each curve has exactly one endpoint on the boundary of the unit disk (the anchor of the curve). Additionally, if each two curves are allowed to cross at most once, we call this an \emph{outer-$1$-string representation} of $G$. If we impose a cyclic ordering on the vertices of $G$ and require the cyclic order of the anchors to respect this cyclic order, such a representation is called a \emph{constrained outer-string representation}. In this paper, we present two results about graphs admitting outer-string representations.
Firstly, we show that for a bipartite graph $G$ (and, more generally, for any $\{C_3,C_5\}$-free graph $G$) with a given cyclic order of vertices, we can decide in polynomial time whether $G$ admits a constrained outer-string representation. Our algorithm follows from a characterization by a single forbidden configuration, similar to that of Biedl et al. [GD 2024] for chordal graphs. Secondly, we answer an open question from the same authors and show that determining whether a given graph admits an outer-1-string representation is NP-hard. More generally, we show that it is NP-hard to determine if a given graph $G$ admits an outer-$k$-string representation for any fixed $k\ge1$.
arXiv:2212.13347v3 Announce Type: replace
Abstract: We report a diffuse Maxwellian illumination scheme for wide-field retinal laser Doppler holography. Inserting an engineered diffuser in the illumination arm transforms a spatially concentrated near-infrared laser focus into an angularly diversified illumination pattern, thereby reducing local irradiance near the anterior segment while preserving coherent interferometric detection. This configuration allows the eyepiece to be positioned closer to the cornea, increasing the digitally reconstructed retinal field of view without producing a localized corneal hot spot. We compare three illumination geometries: focused non-diffuse illumination, diffuse illumination at the same cornea--eyepiece distance, and diffuse Maxwellian illumination. Diffuse Maxwellian illumination expands the retinal field of view while preserving Doppler contrast in broad and high-frequency fluctuation bands. Light-hazard assessment is limited to the current ophthalmic standards ISO 15004-2:2024 and ANSI Z80.36-2021. Based on measured beam profiles, the recommended operating power at 852 nm is set by the most restrictive relevant exposure condition among the assessed anterior-segment, iris, and retinal limits. These results support diffuse illumination as a practical route toward safer, non-mydriatic, wide-field Doppler holography of the human retina.
arXiv:2504.00663v2 Announce Type: replace
Abstract: Existing hardware-aware NAS (HW-NAS) methods typically assume access to precise information circa the target device, either via analytical approximations of the post-compilation latency model, or through learned latency predictors. Such approximate approaches risk introducing estimation errors that may prove detrimental in risk-sensitive applications. In this work, we propose a two-stage HW-NAS framework, in which we first learn an architecture controller on a distribution of synthetic devices, and then directly deploy the controller on a target device. At test-time, our network controller deploys directly to the target device without relying on any pre-collected information, and only exploits direct interactions. In particular, the pre-training phase on synthetic devices enables the controller to design an architecture for the target device by interacting with it through a small number of high-fidelity latency measurements. To guarantee accessibility of our method, we only train our controller with training-free accuracy proxies, allowing us to scale the meta-training phase without incurring the overhead of full network training. We benchmark on HW-NATS-Bench, demonstrating that our method generalizes to unseen devices and searches for latency-efficient architectures by in-context adaptation using only a few real-world latency evaluations at test-time.
arXiv:2502.04871v2 Announce Type: replace
Abstract: The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved numerically. In this paper, we developed a finite volume element method (FVEM) with the Gauss-Seidel projection method (GSPM) for the micromagnetics simulations. We provide the approximation error in space and depict the energy law when the FVEM is adopted. Owing to the GSPM for time-marching, the discrete system is decoupled component by component, making the computational complexity comparable to that of solving the scalar heat equation implicitly. This significantly accelerates real simulations. We present several numerical experiments to validate the theoretical analysis and the efficiency gain. Additionally, we study the blow-up solution and efficiently simulate the 2D magnetic textures using the proposed method.
arXiv:2605.08401v2 Announce Type: replace
Abstract: Recent advances in large language models (LLMs) have demonstrated remarkable reasoning capabilities, largely stimulated by Reinforcement Learning with Verifiable Rewards (RLVR). However, existing RL algorithms face a fundamental limitation: their exploration remains largely constrained by the inherent capability boundary of the policy model. Although recent methods introduce external expert demonstrations to extend this boundary, they typically rely on complete trajectory-level guidance, which is sample-inefficient, information-sparse, and may confine exploration to a static guidance space. Inspired by the potential of multi-agent systems, we propose $\textbf{AIPO}$, an enhanced reinforcement learning framework that improves LLM reasoning through active multi-agent interaction during exploration. Specifically, AIPO enables the policy model to proactively consult three functional collaborative agents, $\textit{Verify Agent}$, $\textit{Knowledge Agent}$, and $\textit{Reasoning Agent}$, when encountering reasoning bottlenecks, thereby receiving fine-grained and targeted guidance to actively expand its capability boundary during training. We further introduce a tailored importance sampling coefficient together with a clipping strategy to mitigate the off-policy bias and gradient vanishing issues that arise when learning from agent-provided feedback. After training, the policy model performs reasoning independently without relying on collaborative agents. Extensive experiments on diverse reasoning benchmarks, including AIME, MATH500, GPQA-Diamond, and LiveCodeBench, show that AIPO consistently improves reasoning performance, generalizes robustly across different policy models and RLVR algorithms, and effectively expands the reasoning capability boundary of the policy model.
arXiv:2605.16113v1 Announce Type: new
Abstract: Large language models (LLMs) have achieved unprecedented success due to their exceptional generative capabilities. However, because they depend on knowledge encapsulated from training corpora, they may produce hallucinations, stereotypes, and socially biased content. In particular, LLMs are prone to prejudiced responses involving race, gender, and age, which are collectively referred to as social biases. Prior studies have used fine-tuning and prompt engineering to mitigate such biases in LLMs, but these methods require additional training resources or domain knowledge to design the framework. Moreover, they may degrade the original capabilities of LLMs and often overlook the need for dynamic debiasing contexts for fairer inference. In this paper, we propose DebiasRAG, a novel tuning-free and dynamic query-specific debiasing framework based on retrieval-augmented generation (RAG). DebiasRAG improves fairness while preserving the intrinsic properties of LLMs, such as representation ability. DebiasRAG consists of three stages: (1) query-specific debiasing candidate generation; (2) context candidate pool construction; and (3) gradient-updated debiasing-guided context piece reranking. First, DebiasRAG leverages self-diagnosed bias contexts relevant to the query through regular retrieval, where the bias contexts are prepared offline by the DebiasRAG provider. Given the query-specific bias contexts, DebiasRAG reversely produces debiasing contexts, which are provided as additional fairness constraints for LLM outputs. Second, a regular RAG retrieval process produces query-related contexts from the regular RAG document database, such as a chunked Wikipedia dataset.
arXiv:2507.16830v5 Announce Type: replace
Abstract: We investigate the fractional time description of a generalized quantum light-matter system modeled by a time-dependent Jaynes-Cummings (JC) interaction, with different coupling types: constant, linear, exponential, and sinusoidal. Two formulations of the time fractional Schr\"odinger equation (TFSE) are examined, with a focus on their impact on population inversion and entanglement. Our findings highlight that the introduction of fractional order introduces memory effects, associated with damped oscillations and asymptotic decay. Furthermore, we find that the time-dependent couplings, combined with distinct fractional formulations, influence how these effects occur, ultimately resulting in high or low entanglement. A key finding of our work is that, under sinusoidal coupling, non-periodic dynamics is preserved for both formulations of the TFSE; however, within a certain range, the fractional order can act as a control mechanism for the non-periodic evolution.
arXiv:2605.15805v1 Announce Type: cross
Abstract: In typical single-molecule force spectroscopy experiments the mechanical unfolding of molecular complexes or biomolecules is studied applying a force ramp to one end of the system while the other end is kept fixed in space. The computational counterpart of this type of experiments can routinely be performed using molecular dynamics simulations with atomistic resolution. However, due to the large difference in time scales often coarse graining procedures are applied in the simulations. Most of the applied techniques do not allow to follow the atomistic details of the relevant conformational transitions due to the structural simplifications used to speed up the simulations. Here, we apply an earlier developed dynamic coarse graining technique based on Markov state modeling to a model peptidic system that does not unfold in a simple two-state manner. Using the donor-acceptor distances of the helical hydrogen bonds as collective variables and performing a dimension reduction technique allows us to construct a Markov model of the unfolding process that correctly represents the microscopic behavior of the system. The chosen example shows that the method can be used to mimick the mechanical unfolding process of systems for which the end-to-end distance does not provide a sufficient order parameter and that do not unfold in a simple cooperative manner.