The first passage time in quantum dynamics

Dynamic RIS-assisted THz quantum networks: Joint optimization of entanglement generation and fidelity under channel impairments

Fractional quantum dynamics in dissipative chemical systems: Memory-driven Schrödinger models for anomalous quantum transport

Multifractal mesoscopic fluctuations in the quantum dynamics of a spatially modulated chain

State-to-state quantum dynamics study on the Cl + H2 (v = 0–1, j = 2) reaction: stereodynamical control and vibrational excitation

Emergent dynamical quantum phase transition in a Z3 symmetric chiral clock model

This work integrates the physics-informed neural network (PINN) approach into the neural quantum state framework to simulate open quantum system dynamics and to circumvent the computationally expensive time-dependent variational principle required in conventional variational methods. The proposed PINN-DQME method employs time-encoded neural networks within a time-domain decomposition strategy to represent the evolution governed by the dissipaton-embedded quantum master equation (DQME). We implement and validate this approach in the single-impurity Anderson model, benchmarking the PINN-DQME results against the numerically exact hierarchical equations of motion. The PINN-DQME method demonstrates high accuracy in simulating quantum dissipative dynamics at high temperatures, where non-Markovian effects are weak. However, for strongly non-Markovian dynamics at low temperatures, it encounters challenges with error accumulation during time propagation, highlighting an area for future refinement in applying PINNs to complex quantum dynamical settings.

Proton-coupled electron transfers (PCETs) are elementary steps in electrocatalysis. However, accurate calculations of PCET rates remain challenging, especially considering nuclear quantum effects (NQEs) under a constant potential condition. Statistical sampling of reaction paths is an ideal approach for rate calculations; however, it is always limited by the rare-event issue. Here, we develop an electrochemistry-driven quantum dynamics approach enabling realistic enhanced paths sampling under constant potentials without a priori defined reaction coordinates. We apply the method in modeling the Volmer step of the hydrogen evolution reaction and demonstrate that the NQEs exhibit more than 1 order of magnitude impact on the computed rate constant, indicating an essential role of NQEs in electrochemistry.

The exploration of non-Hermitian quantum systems, particularly those governed by parity-time ([Formula: see text])-symmetry, has revealed a rich landscape of unconventional phase transitions and localization phenomena. Spin chains with quasiperiodic potentials and competing Heisenberg interactions provide a versatile framework for probing these effects. In this study, we investigate the dynamical and spectral signatures of [Formula: see text]-symmetry breaking and localization-delocalization transitions in spin chains subjected to a non-Hermitian Aubry-André potential and tunable Heisenberg couplings across nearest ([Formula: see text]) and next-nearest neighbors ([Formula: see text]). Our analysis reveals that increasing [Formula: see text] monotonically shifts the critical point [Formula: see text], while [Formula: see text] induces a non-linear response, generating a distinct minimum in [Formula: see text]. Notably, [Formula: see text] leads to the emergence of partially imaginary eigenvalues beyond [Formula: see text], decoupling the onset of [Formula: see text]-symmetry breaking from the localization transition. Using inverse and normalized participation ratios, we identify three distinct phases: extended, localized, and an intermediate hybrid regime characterized by a mobility edge. To capture the dynamical fingerprints of these phases, we employ time-dependent density distribution, long-time survival probability [Formula: see text], analysis. Extended phases exhibit ballistic spreading and algebraic decay, while localized regimes show spatial confinement and exponential decay. These observables serve as robust indicators of non-Hermitian phase transitions, offering insights beyond static spectral measures. Overall, our findings underscore the critical role of dynamical metrics in characterizing phase structure in non-Hermitian spin systems. As interest in non-equilibrium quantum dynamics continues to grow, such models provide a compelling platform for understanding the interplay between [Formula: see text]-symmetry, localization, and quantum coherence in complex many-body systems.

Nonadiabatic effects play a key role in the photophysics and photochemistry of molecular systems, yet their efficient inclusion in quantum molecular dynamics simulations remains challenging, due to the need to construct accurate representations of the molecular Hamiltonian within the manifold of relevant electronic states. Here, we present the PyVCHAM library, which builds on the established multimode vibronic-coupling framework, enhanced by modern machine learning techniques for efficient parameter optimization. The code interfaces with electronic structure packages to generate potential energy surfaces, enabling the parametrization of diabatic Hamiltonians for quantum dynamics calculations. Leveraging the optimization of specialized loss functions, the use of automatic differentiation to compute their analytical gradient in parameter space, and the availability of a wide range of optimization algorithms, the core engine substantially improves in terms of accuracy, flexibility, and efficiency compared to existing implementations. The PyVCHAM library introduces a standardized format for storing vibronic-coupling Hamiltonians based on the JSON data format. It also introduces the ability to combine an arbitrary number of existing vibronic Hamiltonians into interacting supersystems or aggregates, where the constituents couple through dipole-dipole interactions. Several illustrative examples highlight the program's ability to treat complex, high-dimensional molecular systems that were previously difficult to access.

Abstract Tunneling ionization in static or slowly varying electric fields is a cornerstone of strong-field physics and provides the entry point for semiclassical descriptions of above-threshold ionization and high-harmonic generation. In conventional quantum mechanics, the Perelomov-Popov-Terent'ev (PPT) theory and its Ammosov-Delone-Krainov (ADK) form yield an ionization rate whose defining feature is an exponential dependence governed by an under-barrier (imaginary-time) action. Here we develop an analytical ADK-like tunneling model within space-fractional quantum mechanics, where the quadratic kinetic energy is replaced by the Riesz fractional Laplacian of order 1 < α ≤ 2. Working in a static electric field in the length gauge, we derive a closed-form tunneling exponent for a triangular exit barrier. The fractional kinetic operator deforms the conventional I 3/2 p scaling to I 1+1/α p and introduces a characteristic sin(π/α) factor encoding the complex-phase structure associated with nonlocal dispersion. We position this benchmark relative to prior tunneling studies in fractional quantum mechanics (primarily scattering through model barriers and fractal potentials) and provide a validation protocol for testing the exponent in time-dependent simulations of the fractional Schrödinger equation under a constant field. The result establishes a transparent reference for static-field ionization in nonlocal quantum dynamics and a baseline for strong-field approaches extensions.

Embedding non-Markovian open quantum dynamics into an enlarged Markovian space offers a powerful route to nonperturbative simulations, where the dynamics of the extended space state can be governed by multiple distinct Markovian equations. We show that these distinct embeddings arise from different unravelings of Gaussian bath self-energies, generating a family of deterministic, time-local equations for the extended system. Using the Brownian-oscillator spectral density as an illustrative example, we clarify the relationships among existing approaches, including the hierarchical equations of motion and the Lindblad-pseudomode formalism, and demonstrate how this framework enables numerically stable and efficient simulations. This work provides both a transparent theoretical foundation for embedding techniques and a flexible platform for developing new methods to simulate non-Markovian quantum dynamics.

The process tensor framework to open quantum systems provides the most general description of multi-time correlations in non-Markovian quantum dynamics. A compressed representation of a process tensor in terms of matrix product operators (MPO) can be used for numerically exact calculations of multi-time correlation functions in systems strongly coupled to a non-Markovian reservoir. We show here that the numerical effort for computing multi-dimensional spectra can be significantly improved using a time-translation invariant MPO representation of the process tensor obtained from the uniform time-evolving matrix product operator (uniTEMPO) method. In particular, this approach provides a spectral representation of the non-Markovian dynamics that gives direct access to correlation functions in Fourier-space, avoiding explicit real-time evolution. We calculate linear and 2D electronic spectra for an example system and discuss the performance and numerical scaling of our simulations.

Simulating the dynamics of molecular excitons in complex nanophotonic environments requires integrating rigorous electromagnetic simulations with accurate treatments of open quantum system dynamics. In this work, we develop MQED-QD (Macroscopic Quantum Electrodynamics for Quantum Dynamics), a robust computational package for simulating exciton dynamics in arbitrary dielectric and plasmonic environments. Based on the MQED framework, the package offers a unified workflow for constructing the dyadic Green's functions from classical electromagnetic solvers, parametrizing quantum master equations, and propagating the time evolution to determine the molecular subsystem's dynamical properties. To demonstrate the package's capabilities, we simulate exciton transport within a one-dimensional molecular chain near a silver nanostructure, including benchmarking against planar surfaces and exploring the influence of silver nanorods. Our results reveal that surface plasmon polaritons on nanorods drastically enhance long-range dipole-dipole interactions, accelerating exciton delocalization and yielding higher participation ratios compared to planar geometries. MQED-QD provides a powerful, open-source package that facilitates the rational design of nanoscale architectures by elucidating accurate molecular exciton dynamics in conjunction with nanophotonics and plasmonics.

Abstract The time-dependent Schrödinger equation (TDSE) in real space is fundamental to understanding the dynamics of many-electron quantum systems, with applications ranging from quantum chemistry to condensed matter physics and materials science. However, solving the TDSE for complex fermionic systems remains a significant challenge, particularly due to the need to capture the time-evolving many-body correlations, while the antisymmetric nature of fermionic wavefunctions complicates the function space in which these solutions must be represented. We propose a general-purpose neural network framework for solving the real-space TDSE, Fermionic Antisymmetric Spatio-Temporal Network, which treats time as an explicit input alongside spatial coordinates, enabling a unified spatiotemporal representation of complex, antisymmetric wavefunctions for fermionic systems. This approach formulates the TDSE as a global optimization problem, avoiding step-by-step propagation and supporting highly parallelizable training. The method is demonstrated on five benchmark problems: a 1D harmonic oscillator, interacting fermions in a time-dependent harmonic trap, 3D hydrogen orbital dynamics, a laser-driven hydrogen atom, and a laser-driven H$_2$ molecule, achieving excellent agreement with reference solutions across all cases. These results demonstrate the method's accuracy and flexibility within the bound-state manifold across various dimensions and interaction regimes. While the current localized Ansatz inherently restricts the description of extensive ionization and continuum states, the method demonstrates the capability to stably simulate coherent multi-electron dynamics over extended time windows. Our framework offers a highly expressive alternative to traditional basis-dependent or mean-field methods, opening new possibilities for ab initio simulations of time-dependent quantum systems, with applications in quantum dynamics, molecular control, and ultrafast spectroscopy.

We introduce two complementary formulations within memory kernel coupling theory (MKCT) for non-Markovian quantum dynamics: a projection-based method (PMKCT) in the time domain and a continued fraction representation (CF-MKCT) in the frequency domain. The PMKCT operates on the matrix representation of MKCT and enforces asymptotic stability by removing unstable spectral components through orthogonal projection. The CF-MKCT yields a rapidly convergent representation, achieving high accuracy with only N ∼ 8 moments while preserving numerical stability by construction; the inverse Fourier transformation back to the time domain naturally yields a stable solution and converges rapidly with relatively few moments. Together, these two formulations provide a stable, accurate, and versatile framework for simulating non-Markovian quantum dynamics. Benchmark calculations on the spin-boson model with Ohmic spectral densities show excellent agreement with numerically exact results.

Coupling excitons with quantized radiation has been shown to enable coherent ballistic transport at room temperature inside optical cavities. Previous theoretical works employ a simple description of the material, depicting it as a one-dimensional single-layer placed in the middle of an optical cavity, thereby ignoring the spatial variation of the radiation field. In contrast, in most experiments, the optical cavity is filled with organic molecules or multiple layers of two-dimensional materials. Here, we develop an efficient mixed-quantum-classical approach, introducing a bright layer description, that enables the simulation of exciton-polariton quantum dynamics in all three dimensions. Our simulations reveal that, for the same Rabi splitting, a multilayered material extends the quantum coherence lifetime and enhances transport compared to a single-layer material. We find that this enhanced coherence can be traced to a synchronization of phonon fluctuations over multiple layers, wherein the collective light-matter coupling in a multilayered material effectively suppresses the phonon-induced dynamical disorder.

Nonadiabatic effects arising from conical intersections between excited states play a crucial role in the optical properties of a wide range of chromophores and must be accounted for in first-principles modeling of spectral lineshapes. In this work, we investigate the importance of nonadiabatic effects in the absorption spectra of indole and cyanoindole derivatives by contrasting three modeling approaches. In the Gaussian-Condon and Gaussian-non-Condon theory formalisms, the linear response function is computed from excitation energy fluctuations of independent adiabatic excited states sampled along molecular dynamics trajectories, with the latter approach additionally including transition dipole moment fluctuations to account for Herzberg-Teller-type effects. In contrast, the tensor-network-based thermalized time-evolving density-matrix with orthogonal polynomials (T-TEDOPA) approach allows for numerically exact quantum dynamics simulations of explicitly coupled diabatic excited states. We find that only the explicit coupling of the two lowest-lying excited states, La and Lb, within the T-TEDOPA approach yields accurate absorption spectra for all systems, while an adiabatic treatment underestimates spectral contributions from excitations into states with highly mixed electronic character. We further elucidate the role of polar solvent stabilization of the charge-transfer character La state by comparing indole in vacuum and in water, showing that solvent effects significantly shape the ultrafast population transfer between excited states and contribute to differences in the experimental absorption lineshapes. Finally, we discuss the influence of cyano substituent position on the optical properties of cyanoindole derivatives through changes in the energy ordering of La and Lb, their relative transition dipole moments, and the stabilization of the charge-transfer state in a polar solvent.

Interrelation of dipolar spin dynamics and multiple quantum dynamics of a two-spin system with dephasing relaxation.

We investigate a two-component Bose–Einstein condensate as a platform for quantum metrology and characterize the dynamical evolution of the quantum state using two complementary metrics: the quantum Fisher information and the normalized Shannon entropy. With time-dependent control, metrological resources can be prepared and stabilized over a finite time window. These schemes provide a comprehensive assessment of the quantum dynamics of these resources in terms of phase sensitivity and the concentration of the state distribution, thereby offering a theoretical basis for designing robust quantum metrology protocols.