arXiv subjects

Andrés Montoya-Castillo

Publications and source records attributed to Andrés Montoya-Castillo.

At least 19 recordsLinked to original sources

arXiv2026

UGME: A python package for non-Markovian protein folding dynamics

Biomolecular processes, including protein folding, protein-protein association, and protein-DNA recognition, often occur on timescales beyond what individual atomistic molecular dynamics (MD) simulations can reach. To access these longer-timescale dynamics, practitioners commonly combine many parallelized, short trajectories into reduced kinetic models, such as Markov state models (MSMs), that describe how the biomolecules interconvert between a handful of biomolecular configurations (e.g., folded and unfolded states of a protein). Central to MSM construction is the assumption that, at sufficiently long time lags, these projected dynamics become memoryless, such that the future evolution of the system depends only on its current state. Yet, projecting high-dimensional biomolecular dynamics onto a small set of states necessarily discards information about unresolved degrees of freedom, including solvent reorganization, side-chain rearrangements, and intermediate configurations. Because these unresolved motions can continue to influence subsequent dynamics, the resulting dynamics retain memory that is absent from a Markovian description. Here, we present ugme, a modular, open-source Python package for constructing and validating generalized master equations (GME) models that explicitly account for these non-Markovian (memory) effects.

physics.chem-ph↗

arXiv2026

Streamlining Analysis and Design of Two-Dimensional Electronic Spectroscopy using Machine Learning

Two-dimensional electronic spectroscopy (2DES) offers unique insights into the coupling between electronic and nuclear motion and dynamics, making it a key technique in diverse fields, including materials science and biology. Obtaining 2DES data requires a series of measurements that involve multiple pulses to construct the full picture -- a time-consuming task that often necessitates working with limited or noisy data. Here we introduce a machine-learning based framework that aims to maximize the data that can be extracted from 2DES experiments and provides guidance towards the selection of additional experiments. We design a Gaussian mixture model to learn the underlying spectral density of a system, allowing the extraction of reorganization energies and the extrapolation of the 2DES spectra to other time delays beyond those measured, and demonstrate how our framework can be used to select additional measurements to further improve the accuracy. We show that our approach yields accurate results on a variety of systems, including simulations ranging from photoactive yellow protein in the gas phase to Nile red in benzene to the anionic green fluorescent protein chromophore in water, and experiments on Nile blue in ethanol. Our work provides an efficient route to extract maximum insights from 2DES while incurring minimal experimental costs.

physics.chem-ph↗

arXiv2026

Hidden Gauge Freedom in Complex-Pole Hierarchical Equations of Motion

While complex-pole hierarchical equations of motion (HEOM) have dramatically expanded the reach of numerically exact quantum dynamics simulations of open quantum systems, they suffer from numerical instabilities rooted in the non-Hermitian structure of their Liouvillian. Yet, the origin of this structure remains obscure. Here, we report a previously unknown gauge freedom in complex-pole HEOM: a continuous family of analytically equivalent Liouvillians, all encoding the same bath correlation function, whose numerical properties vary dramatically. This gauge controls both the eigenspectrum and non-normality of the hierarchy generator, revealing spectral divergence and non-normal error amplification as two distinct instability mechanisms. By optimizing this gauge, we introduce GO--HEOM, which eliminates divergences in strongly coupled Brownian oscillator environments and extends numerically exact simulations of sub-Ohmic dynamics -- including through the delocalized-to-localized quantum phase transition -- to previously inaccessible coupling strengths. Because this gauge transformation is independent of the bath-correlation decomposition scheme, our GO--HEOM becomes a general, broadly compatible strategy for accessing numerically exact quantum dynamics of open quantum systems over arbitrary coupling and highly non-Markovian regimes.

physics.chem-ph↗

arXiv2026

How to improve the accuracy of semiclassical and quasiclassical dynamics with and without generalized quantum master equations

Semi- and quasi-classical (SC) theories can handle arbitrary interatomic interactions and are thus well-suited to predict quantum dynamics in condensed phases that encode energy and charge transport, spectroscopic responses, and chemical reactivity. However, SC theories can be computationally expensive and inaccurate. When combined with generalized quantum master equations (GQMEs), the resulting SC-GQMEs have been observed to enhance the efficiency and accuracy of SC dynamics. Yet, while the mechanism responsible for improved efficiency is clear, the underlying improved accuracy remains elusive. What is worse, SC-GQMEs can yield unphysical dynamics in challenging parameter regimes -- a shortcoming that might be avoided if the mechanism of accuracy improvement were understood. Here, we uncover this mechanism. We leverage short-time analyses to prove that exact, "left-handed" time-derivatives delay the onset of SC inaccuracy, and show that their numerical integration yields dynamics with improved accuracy, even without the GQME. We find, however, that these derivatives are a double-edged sword: while offering greater short-time accuracy, they become unphysical in challenging parameter regimes. Because short-lived memory kernels can leverage short-time accuracy while circumventing long-time instability, we develop a protocol to unambiguously determine the memory kernel cutoff, even in challenging regimes where previous treatments had failed. Our insights into accuracy improvement and kernel cutoff protocol can be expected to apply to complex systems that go beyond simple models.

physics.chem-ph↗

arXiv2026

Short-lived memory in multidimensional spectra encodes full signal evolution

Ultrafast multidimensional spectroscopies are powerful tools that can access charge and energy flow in complex materials, shifting chemical kinetics, and even many-body interactions in correlated matter. However, current implementations typically involve complex apparatuses and long averaging times. As a result, these methods have been limited to detailed mechanistic investigations of a few samples, precluding the broad characterization of molecular systems and/or the optimization of material ones. For example, converging the statistical noise in 2D spectra becomes exponentially expensive with increasing waiting times, and extended laser exposure heightens the probability of sample degradation. We address this fundamental challenge by developing a new technique, the spectral generalized master equation (GME), that enables one to employ short-waiting time 2D spectra to determine the full evolution of 2D spectra over arbitrary waiting times with high temporal resolution. In addition to reducing the cost of experiments by multiple orders of magnitude, our approach accurately removes statistical noise, reducing the need for time averaging, while circumventing the increasing convergence costs with longer waiting times. We provide a rigorous theoretical footing for the spectral GME and demonstrate its applicability on theoretically generated and experimentally measured 2D electronic and 2D infrared spectra. We anticipate that this advance has the potential to enable the investigation of systems that are too delicate for study with current multidimensional spectroscopies and accelerate the progress of 2D spectroscopy-based microscopies that can offer highly resolved excitation dynamics with spatial resolution over heterogeneous environments.

physics.chem-ph↗

arXiv2026

For molecular polaritons, disorder and phonon timescales control the activation of dark states in the thermodynamic limit

Collective light-matter systems host an extensive manifold of dark states whose role in the emergence of thermodynamic behavior remains poorly understood, especially in the presence of disorder and structured environments. Here, we develop a hybrid matrix product state-hierarchical equations of motion (MPS-HEOM) approach that enables numerically exact simulations of polariton dynamics from a few emitters to the thermodynamic limit under both static and dynamic disorder. This allows us, for the first time, to provide a quantitative and operational answer to the long-standing question of what is the minimum system size required to reach the thermodynamic limit in collective polaritonic systems. By introducing a convergence scale, $N_{T}$, i.e., the number of molecules required for the photonic dynamics to reach the thermodynamic limit, we show that dynamic disorder generally poses a greater computational challenge than static disorder. We attribute this behavior to the suppression of collective light-matter dynamics by disorder, which dynamically activates non-collective degrees of freedom. We further find that $N_{T}$ exhibits a turnover behavior as the bath becomes more Markovian, as the bath timescales regulate bright-to-dark energy transfer and the involvement of dark and gray states. Hence, phonon timescales control both the breakdown of collective behavior and the growth of $N_{T}$. Our results establish the suppression of collective behavior as the key mechanism governing thermodynamic convergence in disordered light-matter systems.

physics.chem-ph↗

arXiv2026

Data-driven, non-Markovian modelling of weather in the presence of non-stationary, non-Gaussian, and heteroskedastic climate dynamics

While the generalized Langevin equation (GLE) is a powerful tool to understand the behavior of complex dissipative systems, driving by external fields renders standard GLE construction workflows invalid. Filtering approaches that separate fluctuations from the non-equilibrium response can sometimes circumvent the need for a non-equilibrium formalism when the residual fluctuations are homoskedastic, stationary, and preferably Gaussian. Here, we introduce the temperature time series from Boulder, Colorado, as representative of the more general and complex case where the filtered time series remains non-Gaussian, non-stationary, and heteroskedastic. With this example, we develop a protocol to build an accurate and efficient low-dimensional description of the weather fluctuations. Our protocol classifies the weather data based on the position in the annual cycle, and introduces local homoskedasticity as a metric to identify seasons of likely stationarity. Within these seasons, we build pseudo-equilibrium models. Leveraging state-based generalized master equation modelling as an alternative to the GLE, we resolve difficulties like non-Gaussianity and position dependence of the memory (friction) kernel. Our data-driven approach accurately reproduces the evolving fluctuations of the Boulder temperature time series, illustrating the feasibility of our method as a general tool to describe driven, dissipative systems.

cond-mat.stat-mech↗

arXiv2025

Coherent and Dynamic Small Polaron Delocalization in CuFeO$_{2}$

Small polarons remain a significant bottleneck in the realization of efficient devices using transition metal oxides. Routes to engineer small polaron coupling to electronic states and lattice modes to control carrier localization remain unclear. Here, we measure the formation of small polarons in CuFeO$_{2}$ using transient extreme ultraviolet reflection spectroscopy and compare it to theoretical predictions in realistically parameterized Holstein models, demonstrating that polaron localization depends on its coupling to the high-frequency versus low-frequency components of the phonon bath. We measure that small polaron formation occurs on a comparable ~100 fs timescale to other Fe(III) compounds. After formation, a dynamic delocalization of the small polaron occurs through a coherent lattice expansion between Fe-O layers and charge-sharing with surrounding Fe(IV) states. Our simulations of polaron formation dynamics reveal that two major factors dictate polaron formation timescales: phonon density and reorganization energy distributions between acoustic and optical modes, matching experimental findings. Our work provides a detailed, real-time observation of how electronic-structural coupling in a polaron-host material can be leveraged to suppress polaronic effects for various applications.

cond-mat.mtrl-sci↗

arXiv2025

Numerically exact quantum dynamics with tensor networks: Predicting the decoherence of interacting spin systems

Predicting the quantum dynamics of promising solid-state and molecular quantum technology candidates remains a formidable challenge. Yet, accessing these dynamics is key to understanding and controlling decoherence mechanisms -- a prerequisite for designing better qubits, sensors, and memories. We leverage a matrix product state representation to introduce a numerically exact and scalable method to achieve this goal. We demonstrate that our method accurately predicts coherence and population dynamics of spin networks across a wide range of parameter regimes, encompassing nuclear spin sensors and qubits in solid-state semiconductors and molecular magnets. Our method further predicts spin dynamics under the influence of repeated light pulses, which are commonly used to mitigate decoherence and perform quantum sensing experiments. Our method thus provides reliable results for moderately-sized spin platforms spanning molecular magnets and solid-state spins that can guide the development of approximate but efficient quantum dynamics methods and enable principled inquiry into decoherence mechanisms.

physics.chem-ph↗

arXiv2025

Fast, accurate, and error-resilient variational quantum noise spectroscopy

Detecting and characterizing decoherence-inducing noise sources is critical for developing robust quantum technologies and deploying quantum sensors operating at molecular scales. However, current noise spectroscopies rely on severe approximations that sacrifice accuracy and precision. We propose a novel approach to overcome these limitations. It self-consistently extracts noise spectra that characterize the interactions between a quantum sensor and its environment from commonly performed dynamical decoupling-based coherence measurements. Our approach adopts minimal assumptions and is resilient to measurement errors. We quantify confidence intervals and sensitivity measures to identify experiments that improve spectral reconstruction. We employ our method to reconstruct the noise spectrum of a nitrogen-vacancy sensor in diamond, resolving previously undetected nuclear species at the diamond surface and revealing that previous measurements had overestimated the strength of low-frequency noise by an order of magnitude. Our method uncovers previously hidden structure with unprecedented accuracy, setting the stage for precision noise spectroscopy-based quantum metrology.

quant-ph↗

arXiv2024

Nonequilibrium relaxation exponentially delays the onset of quantum diffusion

Predicting the exact many-body quantum dynamics of polarons in materials with strong carrier-phonon interactions presents a fundamental challenge, often necessitating one to adopt approximations that sacrifice the ability to predict the transition from nonequilibrium relaxation to thermodynamic equilibrium. Here, we exploit a recent breakthrough that generalizes the concept of memory beyond its conventional temporal meaning to also encompass space. Specifically, we leverage our discovery that the dynamics of observables in systems with local couplings satisfy Green's functions with kernels that are local in time and space. This enables us to employ the dynamics of small lattices over short times to predict the dynamics of thermodynamically large lattices over arbitrarily long timescales while circumventing the deleterious impacts of finite-size effects. We thus interrogate the \textit{exact} nonequilibrium formation and migration of polarons in one- (1D) and two-dimensional (2D) systems, revealing that their motion approaches diffusive transport only asymptotically in time and system size. We also compare transport in 1D and 2D systems to investigate the effect of dimension in polaron migration physics, illustrating how energy variations can cause localization -- a phenomenon observable via current microscopy experiments.

physics.chem-ph↗

arXiv2024

A pedagogical tour of the Fourier transform with applications to NMR and IR spectroscopy

The Fourier Transform (FT) is a fundamental tool that permeates modern science and technology. While chemistry undergraduates encounter the FT as early as second year, their courses often only mention it in passing because computers frequently perform it automatically behind the scenes. Although this automation enables students to focus on `the chemistry', students miss out on an opportunity to understand and use one of the most powerful tools in the scientific arsenal capable of revealing how time-dependent signals encode chemical structure. Although many educational resources introduce chemists to the FT, they often require familiarity with sophisticated mathematical and computational concepts. Here, we present a series of three self-contained, Python-based laboratory activities for undergraduates to understand the FT and apply it to analyze audio signals, an infrared (IR) spectroscopy interferogram, and a nuclear magnetic resonance (NMR) free induction decay (FID). In these activities, students observe how the FT reveals and quantifies the contribution of each frequency present in a temporal signal and how decay timescales dictate signal broadening. Our activities empower students with the tools to transform their own temporal datasets (e.g., FID) to a frequency spectrum. To ensure accessibility of the activities and lower the barrier to implementation, we utilize Google Colab's open-source, cloud-based platform to run Jupyter notebooks. We also offer a pre-laboratory activity that introduces students to the basics of Python and the Colab platform, and reviews the math and programming skills needed to complete the lab activities. These lab activities help students build a qualitative, quantitative, and practical understanding of the FT.

physics.ed-ph↗

arXiv2024

Space-local memory in generalized master equations: Reaching the thermodynamic limit for the cost of a small lattice simulation

The exact quantum dynamics of lattice models can be computationally intensive, especially when aiming for large system sizes and extended simulation times necessary to converge transport coefficients. By leveraging finite memory times to access long-time dynamics using only short-time data, generalized master equations (GMEs) can offer a route to simulating the dynamics of lattice problems efficiently. However, such simulations are limited to small lattices whose dynamics exhibit finite-size artifacts that contaminate transport coefficient predictions. To address this problem, we introduce a novel approach that exploits finite memory in time \textit{and} space to efficiently predict the many-body dynamics of dissipative lattice problems involving short-range interactions. This advance enables one to leverage the short-time dynamics of small lattices to simulate arbitrarily large systems over long times. We demonstrate the strengths of this method by focusing on nonequilibrium polaron relaxation and transport in the dispersive Holstein model, successfully simulating lattice dynamics in one and two dimensions free from finite-size effects, reducing the computational expense of such simulations by multiple orders of magnitude. Our method is broadly applicable and provides an accurate and efficient means to investigate nonequilibrium relaxation with microscopic resolution over mesoscopic length and time scales that are relevant to experiment.

physics.chem-ph↗

arXiv2024

Symmetry breaking fluctuations split the porphyrin Q bands

Porphyrins offer a malleable and cost-efficient platform to sculpt bioinspired technologies with tunable charge transfer, energy conversion, and photocatalytic properties. Yet, despite decades of research, the physical mechanisms that determine their electronic spectra remain elusive. Even for metal-free porphyrins, no consensus exists on the origin of the splitting of their $Q$-bands, an energetic region critical in photosynthesis. We leverage our recent statistical treatment of molecular motions in the condensed phase to predict their linear absorption spectra. By bridging exact quantum-dynamical expressions with atomistic simulations, our theory is the first to capture the spectra of representative porphyrins in solution: porphine, tetraphenylporphyrin, and tetraphenylporpholactone. Our work reveals that $Q$-band splitting arises from extreme timescale separation of nuclear motions that turn symmetry-forbidden transitions bright. We exploit these insights to propose and confirm how chemical modifications tune the optical properties of porphyrins, demonstrating the potential for developing design principles to tailor their optoelectronic behavior.

physics.chem-ph↗

arXiv2024

Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions

Multitime quantum correlation functions are central objects in physical science, offering a direct link between experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system's complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.

physics.chem-ph↗

arXiv2024

Mori generalized master equations offer an efficient route to predict and interpret transport

Predicting how a material's microscopic structure and dynamics determine its transport properties remains a fundamental challenge. To alleviate this task's often prohibitive computational expense, we propose a Mori-based generalized quantum master equation (GQME) to predict the frequency-resolved conductivity of small-polaron forming systems described by the dispersive Holstein model. Unlike previous GQME-based approaches to transport that scale with the system size and only give access to the DC conductivity, our method requires only one calculation and yields both the DC and AC mobilities. We further show to easily augment our GQME with numerically accessible derivatives of the current to increase computational efficiency, collectively offering computational cost reductions of up to $90\%$, depending on the transport regime. Finally, we leverage our exact simulations to demonstrate the limited applicability of the celebrated and widely invoked Drude-Smith model in small-polaron forming systems. We instead introduce a cumulant-based analysis of experimentally accessible frequency data to infer the microscopic Hamiltonian parameters. This approach promises to provide valuable insights into material properties and facilitate guided design by linking macroscopic terahertz measurements to the microscopic details of small polaron-forming systems.

physics.chem-ph↗

arXiv2024

Fourier Transform Noise Spectroscopy

Spectral characterization of noise environments that lead to the decoherence of qubits is critical to developing robust quantum technologies. While dynamical decoupling offers one of the most successful approaches to characterize noise spectra, it necessitates applying large sequences of $π$ pulses that increase the complexity and cost of the method. Here, we introduce a noise spectroscopy method that utilizes only the Fourier transform of free induction decay or spin echo measurements, thus removing the need for the application many $π$ pulses. We show that our method faithfully recovers the correct noise spectra for a variety of different environments (including $1/f$-type noise) and outperforms previous dynamical decoupling schemes while significantly reducing their experimental overhead. We also discuss the experimental feasibility of our proposal and demonstrate its robustness in the presence of statistical measurement error. Our method is applicable to a wide range of quantum platforms and provides a simpler path toward a more accurate spectral characterization of quantum devices, thus offering possibilities for tailored decoherence mitigation.

quant-ph↗

arXiv2023

Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra

Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer-tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of the data can be arbitrarily coarsened, especially along the $t_2$ axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands $\mathcal{O}(10^3)$ fewer data points. We are further able to decompose the spectra into 1-, 2-, and 3-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.

physics.chem-ph↗