Tree tensor network state approach for solving hierarchical equations of motions

The hierarchical equations of motion (HEOM) method is a numerically exact open quantum system dynamics approach. The method is rooted in an exponential expansion of the bath correlation function, which in essence strategically reshapes a continuous environment into a set of effective bath modes that allow for more efficient cutoff at finite temperatures. Based on this understanding, one can map the HEOM method into a Schr\"odinger-like equation with a non-Hermitian super Hamiltonian for an extended wavefunction being the tensor product of the central system wave function and the Fock state of these effective bath modes. Recognizing that the system and these effective bath modes form a star-shaped entanglement structure, in this work, we explore the possibility of representing the extended wave function as an efficient tree tensor network state (TTNS), the super Hamiltonian as a tree tensor network operator of the same structure, as well as the application of a time propagation algorithm using the time-dependent variational principle. Our benchmark calculations based on the spin-boson model with a slow-relaxing bath show that, the proposed HEOM+TTNS approach yields consistent results with that of the conventional HEOM method, while the computation is considerably sped up by a factor of a few orders of magnitude. Besides, the simulation with a genuine TTNS is four times faster than a one-dimensional matrix product state decomposition scheme

Systematic coarse-graining of environments for the non-perturbative simulation of open quantum systems

Conducting precise electronic-vibrational dynamics simulations of molecular systems poses significant challenges when dealing with an environment composed of numerous vibrational modes. Here, we introduce novel techniques for the construction of effective phonon spectral densities that capture accurately open system dynamics over a finite time interval of interest. When combined with existing non-perturbative simulation tools, our approach can reduce significantly the computational costs associated with many-body open system dynamics

Heom.jl: An efficient Julia framework for hierarchical equations of motion in open quantum systems

We introduce an open-source software package called "Heom.jl", a Julia framework to integrate the hierarchical equations of motion (HEOM) for the reduced dynamics of a system simultaneously coupled to multiple bosonic and fermionic environments. Heom.jl features a collection of methods to compute bosonic and fermionic spectra, stationary states, and the full dynamics in the extended space of all auxiliary density operators (ADOs). The required handling of the ADOs multi-indexes is achieved through a user-friendly interface. We exemplify the functionalities of the package by analyzing a single impurity interacting with two fermionic reservoirs (Anderson model), and an ultra-strongly coupled charge-cavity system interacting with one bosonic and two fermionic reservoirs. Heom.jl allows for an order of magnitude speedup in the construction of the HEOM Liouvillian superoperator, solving dynamics and stationary states for all ADOs, with respect to the corresponding method in the Quantum Toolbox in Python (QuTiP), upon which this package is founded.Comment: 19 pages, 7 figures, 4 table

An Effective Model for Capturing the Role of Excitonic Interactions in the Wave-Packet Dynamics of DNA Nucleobases

Investigating exciton dynamics within DNA nucleobases is essential for comprehensively understanding how inherent photostability mechanisms function at the molecular level, particularly in the context of life’s resilience to solar radiation. In this paper, we introduce a mathematical model that effectively simulates the photoexcitation and deactivation dynamics of nucleobases within an ultrafast timeframe, particularly focusing on wave-packet dynamics under conditions of strong nonadiabatic coupling. Employing the hierarchy equation of motion, we simulate two-dimensional electronic spectra (2DES) and calibrate our model by comparing it with experimentally obtained spectra. This study also explores the effects of base stacking on the photo-deactivation dynamics in DNA. Our results demonstrate that, while strong excitonic interactions between nucleobases are present, they have a minimal impact on the deactivation dynamics of the wave packet in the electronic excited states. We further observe that the longevity of electronic excited states increases with additional base stacking and pairing, a phenomenon accurately depicted by our excitonic model. This model enables a detailed examination of the wave packet’s motion on electronic excited states and its rapid transition to the ground state. Additionally, using this model, we studied base stacks in DNA hairpins to effectively capture the primary exciton dynamics at a reasonable computational scale. Overall, this work provides a valuable framework for studying exciton dynamics from single nucleobases to complex structures such as DNA hairpins

Přenos excitační energie ve fotosyntetických reakčních centrech

Fotosyntetická reakční centra mají pro fotosyntetizující organismy kruciální roli. Právě zde totiž dochází k tzv. separaci náboje, kdy je energie excitovaného stavu elektronu využita na ionizaci molekul a uvolněný elektron se pak podílí na ustanovení transmembránového elektrochemického gradientu H+ iontů využívaného ATP syntázami. Světlosběrné komplexy absorbují energii dopadajících fotonů a s vysokou účinností blížící se jedné ji přenášejí právě do reakčních center. Efektivita tohoto přenosu budí zájem vědců již mnoho dekád a rozvoj experimentálních metod umožnil značné porozumění jeho původu. Získané poznatky, v kombinaci s kvantově mechanickými přístupy, lze navíc využít i na ryze teoretický výzkum zahrnující detailní počítačové simulace. Vlastnosti celých molekulární komplexů tak mohou být určeny s vysokou přesností a nezávisle na experimentech. Text této práce přestavuje úvod do teoretického studia fotosyntézy a shrnuje vývoj odvětví za poslední dvě dekády. Popsané hlavní teoretické přístupy a modely jsou dále prezentovány na příkladu reakčních center purpurové fotosyntetizující bakterie Rhodobacter sphaeroides, která představuje důležitý modelový organismus. Na tomto příkladě jsou také srovnány experimentálně i teoreticky získané hodnoty časů přenosu excitační energie.The photosynthetic reaction centres have uppermost importance in photosynthesis. They represent the actual place where the energy carried by photons is turned into charge-separated states which then enable to establish the electrochemical H+ transmembrane gradient used by ATP synthases. The photosynthetic light- harvesting complexes gather the energy of light radiation and direct it in the form of electronic excitation energy into the reaction centres. The efficiency of this process is exceptionally high, close to unity, what is capturing the interest of researchers for decades. The development of experimental techniques has led to better understanding of this process down to atomic scale. Nowadays, this insight along with the theoretical basis stemming from quantum mechanics can be used to perform accurate computer simulations which can determine properties of the whole molecular aggregates independently of experiments. This thesis provides an introduction into the field of theoretical photosynthesis research, and it summarises the progress made in past two decades. The detailed theoretical approaches are being put into perspective of the reaction centres of photosynthetic purple bacterium Rhodobacter sphaeroides which is a valuable model organism. Both experimental and theoretical results of...Department of Experimental Plant BiologyKatedra experimentální biologie rostlinFaculty of SciencePřírodovědecká fakult

An Exciton Dynamics Model of Bryopsis corticulans Light-Harvesting Complex II

Bryopsis corticulans is a marine green macroalga adapted to the intertidal environment. It possesses siphonaxanthin-binding light-harvesting complexes of photosystem II (LHCII) with spectroscopic properties markedly different from the LHCII in plants. By applying a phenomenological fitting procedure to the two-dimensional electronic spectra of the LHCII from B. corticulans measured at 77 K, we can extract information about the excitonic states and energy-transfer processes. The fitting method results in well-converged parameters, including excitonic energy levels with their respective transition dipole moments, spectral widths, energy-transfer rates, and coupling properties. The 2D spectra simulated from the fitted parameters concur very well with the experimental data, showing the robustness of the fitting method. An excitonic energy-transfer scheme can be constructed from the fitting parameters. It shows the rapid energy transfer from chlorophylls (Chls) b to a at subpicosecond time scales and a long-lived state in the Chl b region at around 659 nm. Three weakly connected terminal states are resolved at 671, 675, and 677 nm. The lowest state is higher in energy than that in plant LHCII, which is probably because of the fewer number of Chls a in a B. corticulans LHCII monomer. Modeling based on existing Hamiltonians for the plant LHCII structure with two Chls a switched to Chls b suggests several possible Chl a-b replacements in comparison with those of plant LHCII. The adaptive changes result in a slower energy equilibration in the complex, revealed by the longer relaxation times of several exciton states compared to those of plant LHCII. The strength of our phenomenological fitting method for obtaining excitonic energy levels and energy-transfer network is put to the test in systems such as B. corticulans LHCII, where prior knowledge on exact assignment and spatial locations of pigments are lacking

Fingerprint and universal Markovian closure of structured bosonic environments

We exploit the properties of chain mapping transformations of bosonic environments to identify a finite collection of modes able to capture the characteristic features, or fingerprint, of the environment. Moreover we show that the countable infinity of residual bath modes can be replaced by a universal Markovian closure, namely a small collection of damped modes undergoing a Lindblad-type dynamics whose parametrization is independent of the spectral density under consideration. We show that the Markovian closure provides a quadratic speed-up with respect to standard chain mapping techniques and makes the memory requirement independent of the simulation time, while preserving all the information on the fingerprint modes. We illustrate the application of the Markovian closure to the computation of linear spectra but also to non-linear spectral response, a relevant experimentally accessible many body coherence witness for which efficient numerically exact calculations in realistic environments are currently lacking.Comment: 6+23 pages, 3+12 figures. Minor changes. Close to published versio