arXiv subjects

Yoshitaka Tanimura

Publications and source records attributed to Yoshitaka Tanimura.

At least 19 recordsLinked to original sources

arXiv2026

sbml4md: A computational platform for System-Bath Modeling via Molecular Dynamics powered by Machine Learning

We introduce sbml4md, a newly developed algorithm implemented as a software package to extract parameters of multimode anharmonic Brownian (MAB) models from molecular dynamics (MD) trajectories for simulating nonlinear vibrational spectra of intramolecular modes of molecular liquids. By leveraging machine learning (ML) techniques to capture vibrational anharmonicity, intermolecular couplings, and bath correlation functions for each mode, sbml4md obviates empirical fitting and enables the modeling of environments with spatial and temporal heterogeneity. This work provides a set of parameters specifically tailored for the Hierarchical Equations of Motion (HEOM) framework, enabling numerically "exact" simulations of nonlinear vibrational spectra. Building upon our previous implementation for intramolecular vibrational modes [Park, Jo, and Tanimura, J. Chem. Phys. 163, 214104 (2025)], the present code enhances optimization efficiency by explicitly accounting for intermolecular vibrational contributions. This extension enables sbml4md to broaden the applicability of HEOM-based dynamical modeling by seamlessly integrating classical MD approaches, thereby providing a flexible and scalable framework for simulating both linear and nonlinear spectra under realistic conditions with minimal empirical input. The accompanying ML code, written in Python, is provided as supporting material.

physics.chem-ph↗

arXiv2026

Isotope Effects in 2D correlation infrared Spectra of Water: HEOM Analysis of Molecular Dynamics-Based Machine Learning Models

We model, simulate, and analyze the intramolecular modes of liquid H2O and D2O to elucidate how energy excitation, relaxation, and vibrational dephasing interplay through anharmonic mode-mode coupling. Our analysis employs two-dimensional (2D) correlation spectra, a representative observable in nonlinear infrared vibrational spectroscopy. Accurate reproduction of these 2D spectral profiles requires not only a precise dynamical description of intramolecular vibrations but also an appropriate treatment of thermal environmental effects arising from strong interactions with surrounding molecules, which act as thermal baths. Capturing the essential features of the 2D spectra further demands a non-Markovian, non-perturbative, and nonlinear description of the interactions between intramolecular modes and their baths. To this end, we adopt a hierarchical equations of motion (HEOM) framework to compute the 2D spectra. By comparing the resulting spectra of H2O and D2O, we explore the underlying mechanisms governing their complex energy and phase relaxation dynamics.

physics.chem-ph↗

arXiv2026

HEOM-Based Numerical Framework for Quantum Simulation of Two-Dimensional Vibrational Spectra in Molecular Liquids (HEOM-2DVS)

The multi-mode anharmonic Brownian motion model provides a universal framework for simulating molecular vibrations in condensed phases. When vibrational energy surpasses thermal excitation, quantum effects become significant, necessitating a rigorous treatment of system-bath entanglement. The hierarchical equations of motion (HEOM) provide a powerful methodology for simulating such open quantum systems. In this context, two-dimensional vibrational spectroscopy (2DVS) constitutes a powerful probe for elucidating the complex dynamics of molecular processes, both experimentally and theoretically. This work introduces a computational implementation, HEOM-2DVS, for treating non-Markovian open quantum dynamics that encompass energy relaxation, dephasing, thermal excitation, and related processes arising from non-perturbative and nonlinear interactions between selected vibrational modes and their thermal environments. To validate the theoretical framework, we computed 2D correlation infrared spectra for three coupled intramolecular vibrational modes of water. The HEOM-2DVS program developed for both CPU and graphics processing unit (GPU) is provided as supplementary material.

physics.chem-ph↗

arXiv2026

Open Quantum Dynamics Theory for Coulomb Potentials: Hierarchical Equations of Motion for Atomic Orbitals (AO-HEOM)

We investigate the quantum dynamics of Coulomb potential systems in thermal baths. We study these systems within the framework of open quantum dynamics theory, focusing on preserving the rotational symmetry of the entire system, including the baths. Thus, we employ a three-dimensional rotationally invariant system-bath (3D-RISB) model to derive numerically ``exact'' hierarchical equations of motion for atomic orbitals (AO-HEOM) that enable a non-perturbative and non-Markovian treatment of system-bath interactions at finite temperatures. To assess the formalism, we calculated the linear absorption spectrum of an atomic system under isotropic thermal environment, with systematic variation of system-bath coupling strength and temperature.

quant-ph↗

arXiv2025

MO-HEOM: Extending Hierarchical Equations of Motion to Molecular Orbital Space

Studies of quantum thermal effects on molecular excitation dynamics have often relied on oversimplified models, such as energy eigenstates or low-dimensional potentials, which fail to capture the complexity of real chemical systems. In reality, molecules are spatially extended and embedded in anisotropic environments, where molecular orbitals (MOs) play a central role in determining quantum behavior. To advance beyond these limitations, we propose a three-dimensional rotationally invariant system-bath (3D-RISB) model within the MO framework, with explicit inclusion of intramolecular vibrational motion. From this MO foundation, we derive numerically ``exact'' hierarchical equations of motion (MO-HEOM). As a demonstration, we analyze hydrogen molecules and hydrogen molecular ions with vibrational degrees of freedom, revealing their linear absorption spectra.

physics.chem-ph↗

arXiv2025

System-Bath Modeling in Vibrational Spectroscopy via Molecular Dynamics: A Machine Learning Framework for Hierarchical Equations of Motion (HEOM)

Molecular vibrations in solutions, especially OH stretching and bending in water, drive ultrafast energy relaxation and dephasing in chemical and biological systems. We present a machine learning approach for constructing system-bath models of intramolecular vibrations in solution, compatible with quantum simulations via the hierarchical equations of motion (HEOM). Using classical molecular dynamics trajectories generated with a force field specifically developed for quantum molecular dynamics, the model captures anharmonic mode coupling and non-Markovian dissipation through spectral distribution functions (SDFs). These features, in turn, enable quantum mechanical treatment of ultrafast energy relaxation, vibrational dephasing, and thermal excitation within the HEOM framework.. The trained model yields physically interpretable parameters, validated against infrared spectra. Notably, combining Brownian oscillator and Drude SDFs -- representing inter- and intramolecular vibrational modes -- significantly improves learning performance and supports rigorous simulation of nonlinear vibrational spectroscopy.

physics.chem-ph↗

arXiv2025

A Multimode Classical Hierarchical Fokker-Planck Equations Approach to Molecular Vibrations: Simulating Two-Dimensional Spectra

The multimode Brownian model with nonlinear system-bath coupling offers a flexible framework for studying both intra- and intermolecular vibrational modes in condensed-phase molecular systems. This approach allows us to calculate linear and nonlinear spectra of molecular vibrations and to examine thermal effects-such as anharmonicity, energy relaxation, and dephasing-as reflected in the spectral peak profiles. In this study, we present a computer program based on classical hierarchical Fokker-Planck equations applied to three vibrational modes of a molecular liquid. The primary objective of developing this code was to simulate the two-dimensional correlation spectrum of the intramolecular modes of liquid water. [R. Hoshino and Y. Tanimura, J. Chem. Phys. 162, 044105 (2025)]. The code has been further refined to optimize grid selection and numerical integration routines for graphics processing units (GPUs). As a demonstration, we apply this setup to simulate three interacting modes representing intermolecular vibrations in water, and calculate the resulting two-dimensional terahertz-Raman signals. The code and example routines are available in the supplementary material.

physics.chem-ph↗

arXiv2025

Quantum hierarchical Fokker-Planck equations with U(1) gauge fields: Application to the Aharonov-Bohm ring

We investigate a three-dimensional subsystem under a time-dependent U(1) gauge field coupled to rotationally invariant environments. To capture the dynamic behavior of the subsystem under thermal excitations and dissipations, it is imperative to treat the bath in a non-Markovian and nonperturbative manner. This is because quantum noise is constrained by the uncertainty principle, which dictates the relationship between the noise correlation time and the amplitude of the energy fluctuation. To this end, we derive the hierarchical equations of motion (HEOM) incorporating the gauge field, enabling a rigorous investigation of the dynamics of the reduced subsystem. Transforming the HEOM into the Wigner representation yields quantum hierarchical Fokker-Planck equations [U(1)-QHFPE] with U(1) gauge fields. These equations incorporate vector fields into the damping operators while preserving both gauge invariance and rotational symmetry. To demonstrate the practical use of the formalism, the effects of a heat bath in the Aharonov-Bohm (AB) ring. Our investigation includes simulations of the equilibrium distribution, linear absorption spectra, and AB currents under thermal conditions. Within a rotationally invariant system-bath (RISB) model, we predict the emergence of a persistent current even in dissipative environments, provided the bath is non-Markovian and the temperature is sufficiently low. We also assessed the validity of the Caldeira-Leggett model in this context.

quant-ph↗

arXiv2025

Quantum Hierarchical Fokker-Planck Equations with U(1) Gauge Fields (U(1)-QHFPE): A Computational Framework for Aharonov-Bohm Effects

We introduce U(1)-QHFPE, a non-Markovian and non-perturbative open quantum dynamics software package for solving quantum Fokker-Planck equations incorporating gauge fields within the Hierarchical Equations of Motion (HEOM) formalism. The framework rigorously preserves gauge invariance and rotational symmetry, enabling accurate simulations of transport phenomena such as the Aharonov-Bohm effect under strong system-bath coupling. In this regime, quantum entanglement between the system and bath emerges naturally. Demonstration programs include calculations of symmetric and antisymmetric correlation functions in Aharonov-Bohm ring geometries, showcasing the code's ability to resolve topological quantum interference in dissipative open systems.

quant-ph↗

arXiv2025

Analysis of intramolecular modes of liquid water in two-dimensional spectroscopy: a classical hierarchical equations of motion approach

Two-dimensional (2D) vibrational spectroscopy is a powerful means of investigating the structure and dynamics of complex molecules in condensed phases. However, even in theory, analysis of 2D spectra resulting from complex inter- and intra-molecular motions using only molecular dynamics methods is not easy. This is because molecular motions comprise complex multiple modes, and peaks broaden and overlap owing to various relaxation processes and inhomogeneous broadening. On the basis of an anharmonic multimode Brownian oscillator model with nonlinear system-bath coupling, we have developed an approach that simulates 2D spectra, taking into account arbitrary modes of intermolecular and intramolecular vibrations simultaneously. Although only two-mode quantum calculations are feasible with this model, owing to high computational costs, here we restrict ourselves to the classical case and perform three-mode calculations. We demonstrate the applicability of our method by calculating 2D correlation infrared spectra of water for symmetric stretching, antisymmetric stretching, and bending modes. The quantum effects of these results are deduced by comparing 2D quantum spectra previously obtained for two intramolecular modes with those obtained using our classical approach under the same physical conditions. The results show that the 2D spectra calculated by separating the stretching modes into symmetric and asymmetric modes provide better descriptions of peak profiles, such as the splitting of cross-peaks.

physics.chem-ph↗

arXiv2024

Hierarchical equations of motion for multiple baths (HEOM-MB) and their application to Carnot cycle

We have developed a computer code for the thermodynamic hierarchical equations of motion derived from a spin subsystem coupled to multiple Drude baths at different temperatures, which are connected to or disconnected from the subsystem as a function of time. The code can simulate the reduced dynamics of the subsystem under isothermal, isentropic, thermostatic, and entropic conditions. The extensive and intensive thermodynamic variables are calculated as physical observables, and Gibbs and Helmholtz energies are evaluated as intensive and extensive work. The energy contribution of the system--bath interaction is evaluated separately from the subsystem using the hierarchical elements of the HEOM. The accuracy of the calculated results for the equilibrium distribution and the two-body correlation functions are assessed by contrasting the results with those obtained from the time-convolution-less Redfield equation. It is shown that the Lindblad master equation is inappropriate for thermodynamic description of a spin--boson system. Non-Markovian effects in thermostatic processes are investigated by sequentially turning on and off the baths at different temperatures with different switching times and system--bath coupling. In addition, the Carnot cycle is simulated under quasi-static conditions. To analyze the work done for the subsystem in the cycle, thermodynamic work diagrams are plotted as functions of intensive and extensive variables. The C++ source codes are provided as supplementary material.

cond-mat.stat-mech↗

arXiv2024

Classical and quantum thermodynamics in a non-equilibrium regime: Application to Stirling engine

We have developed a thermodynamic theory in the non-equilibrium regime, which we describe as a thermodynamic system-bath model [S. Koyanagi and Y. Tanimura, J. Chem. Phys. \textbf{160}, 234112 (2024)]. Based on the dimensionless (DL) minimum work principle, non-equilibrium thermodynamic potentials are expressed in terms of non-equilibrium extensive and intensive variables in time derivative form. This is made possible by incorporating the entropy production rate into the definitions of non-equilibrium thermodynamic potentials. These potentials can be evaluated from the DL non-equilibrium-to-equilibrium minimum work principle, which is derived from the principle of DL minimum work and is equivalent to the second law of thermodynamics. We thus obtain the non-equilibrium Massieu-Planck potentials as entropic potentials and the non-equilibrium Helmholtz-Gibbs potentials as free energies. Unlike fluctuation theorem and stochastic thermodynamics theory, this theory does not require the assumption of a factorized initial condition and is valid in the full quantum regime where the system and bath are quantum mechanically entangled. Our results are numerically verified by simulating a thermostatic Stirling engine consisting of two isothermal processes and two thermostatic processes using the quantum hierarchical Fokker--Planck equations and the classical Kramers equation derived from the thermodynamic system-bath model. We then show that, from weak to strong system-bath interactions, the thermodynamic process can be analyzed using a non-equilibrium work diagram analogous to the equilibrium one for given time-dependent intensive variables. The results can be used to develop efficient heat machines in non-equilibrium regimes.

cond-mat.stat-mech↗

arXiv2024

Thermodynamic quantum Fokker-Planck equations and their application to thermostatic Stirling engine

We developed a computer code for the thermodynamic quantum Fokker-Planck equations (T-QFPE), derived from a thermodynamic system-bath model. This model consists of an anharmonic subsystem coupled to multiple Ohmic baths at different temperatures, which are connected to or disconnected from the subsystem as a function of time. The code numerically integrates the T-QFPE and their classical expression to simulate isothermal, isentropic, thermostatic, and entropic processes in both quantum and classical cases. The accuracy of the results was verified by comparing the analytical solutions of the Brownian oscillator. Additionally, we illustrated a breakdown of the Markovian Lindblad-master equation in the pure quantum regime. As a demonstration, we simulated a thermostatic Stirling engine employed to develop non-equilibrium thermodynamics [S. Koyanagi and Y. Tanimura, J. Chem. Phys 161, 114113 (2024)] under quasi-static conditions. The quasi-static thermodynamic potentials, described as intensive and extensive variables, were depicted as work diagrams. In the classical case, the work done by the external field is independent of the system-bath coupling strength. In contrast, in the quantum case, the work decreases as the coupling strength increases due to quantum entanglement between the subsystem and bath. The codes were developed for multicore processors using Open multiprocessing (OpenMP) and for graphics processing units (GPU) using the Compute United Device Architecture (CUDA). These codes are provided as supplementary materials.

cond-mat.stat-mech↗

arXiv2024

Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle

We formulate a thermodynamic theory applicable to both classical and quantum systems. These systems are depicted as thermodynamic system-bath models capable of handling isothermal, isentropic, thermostatic, and entropic processes. Our approach is based on the use of a dimensionless thermodynamic potential expressed as a function of the intensive and extensive thermodynamic variables. Using the principles of dimensionless minimum work and dimensionless maximum entropy derived from quasi-static changes of external perturbations and temperature, we obtain the Massieu-Planck potentials as entropic potentials and the Helmholtz-Gibbs potentials as free energy. These potentials can be interconverted through time-dependent Legendre transformations. Our results are verified numerically for an anharmonic Brownian system described in phase space using the low-temperature quantum Fokker-Planck equations in the quantum case and the Kramers equation in the classical case, both developed for the thermodynamic system-bath model. Thus, we clarify the conditions for thermodynamics to be valid even for small systems described by Hamiltonians and establish a basis for extending thermodynamics to non-equilibrium conditions.

cond-mat.stat-mech↗

arXiv2023

Coherent two-dimensional THz magnetic resonance spectroscopies for molecular magnets: Analysis of Dzyaloshinskii-Moriya interaction

To investigate the novel quantum dynamic behaviors of magnetic materials that arise from complex spin-spin interactions, it is necessary to probe the magnetic response at a speed greater than the spin-relaxation and dephasing processes. Recently developed two-dimensional (2D) terahertz magnetic resonance (THz-MR) spectroscopy techniques use the magnetic components of laser pulses, and this allows investigation of the details of the ultrafast dynamics of spin systems. For such investigations, quantum treatment -- not only of the spin system itself but also of the environment surrounding the spin system -- is important. In our method, based on the theory of multidimensional optical spectroscopy, we formulate nonlinear THz-MR spectra using an approach based on the numerically rigorous hierarchical equations of motion. We conduct numerical calculations of both linear (1D) and 2D THz-MR spectra for a linear chiral spin chain. The pitch and direction of chirality (clockwise or anticlockwise) are determined by the strength and sign of the Dzyaloshinskii-Moriya interaction (DMI). We show that not only the strength but also the sign of the DMI can be evaluated through the use of 2D THz-MR spectroscopic measurements, while 1D measurements allow us to determine only the strength.

cond-mat.mes-hall↗

arXiv2023

Discretized hierarchical equations of motion in mixed Liouville--Wigner space for two-dimensional vibrational spectroscopies of liquid water

A model of a bulk water system describing the vibrational motion of intramolecular and intermolecular modes is constructed, enabling analysis of its linear and nonlinear vibrational spectra, as well as the energy transfer processes between the vibrational modes. The model is described as a system of four interacting anharmonic oscillators nonlinearly coupled to their respective heat baths. To perform a rigorous numerical investigation of the non-Markovian and nonperturbative quantum dissipative dynamics of the model, we derive discretized hierarchical equations of motion in mixed Liouville-Wigner space (DHEOM-MLWS), with Lagrange-Hermite mesh discretization being employed in the Liouville space of the intramolecular modes and Lagrange-Hermite mesh discretization and Hermite discretization in the Wigner space of the intermolecular modes. One-dimensional infrared and Raman spectra and two-dimensional terahertz-infrared-visible and infrared-infrared-Raman spectra are computed as demonstrations of the quantum dissipative description provided by our model.

physics.comp-ph↗

arXiv2023

Simulating two-dimensional correlation spectroscopies with third-order infrared and fifth-order infrared--Raman processes of liquid water

To investigate the possibility of measuring the intermolecular and intramolecular anharmonic coupling of balk water, we calculate third-order two-dimensional (2D) infrared (IR) spectra and fifth-order 2D IR-IR-Raman-Raman spectra expressed in terms of four-body correlation functions of optical observables. For this purpose, a multimode Brownian oscillator model of four interacting anharmonic oscillators strongly coupled to their respective heat baths is employed. The nonlinearity of the system-bath interactions is considered to describe thermal relaxation and vibrational dephasing. The linear and nonlinear spectra are then computed in a non-Markovian and nonperturbative regime in a rigorous manner using the discretized hierarchical equations of motion in mixed Liouville-Wigner space (DHEOM-MLWS). The calculated 2D spectra for stretching-bending, bending-librational, stretching-librational, and stretching-translational modes consist of various positive and negative peaks exhibiting essential details of the intermolecular and intramolecular mode-mode interactions under thermal relaxation and dephasing at finite temperature.

cond-mat.soft↗

arXiv2022

Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams

We investigate the efficiency of a quantum Carnot engine based on open quantum dynamics theory. The model includes time-dependent external fields for the subsystems controlling the isothermal and isentropic processes and for the system--bath (SB) interactions controlling the transition between these processes. Numerical simulations are conducted in a nonperturbative and non-Markovian SB coupling regime using the hierarchical equations of motion under these fields at different cycle frequencies. The work applied to the total system and the heat exchanged with the baths are rigorously evaluated. In addition, by regarding quasi-static work as free energy, we compute the quantum thermodynamic variables and analyze the simulation results using thermodynamic work diagrams for the first time. Analysis of these diagrams indicates that, in the strong SB coupling region, the fields for the SB interactions are major sources of work, while in other regions, the field for the subsystem is a source of work. We find that the maximum efficiency is achieved in the quasi-static case and is determined solely by the bath temperatures, regardless of the SB coupling strength, which is a numerical manifestation of Carnot's theorem.

cond-mat.stat-mech↗