arXiv subjects

Amartya Bose

Publications and source records attributed to Amartya Bose.

At least 19 recordsLinked to original sources

arXiv2026

Quantum-Classical Hierarchical Equations of Motion

We develop a quantum-classical hierarchical equations of motion (QC-HEOM) approach for simulating non-Markovian open quantum systems. The method combines the ensemble-averaged classical path reference of the quantum-classical path integral formalism with a hierarchy of auxiliary quantum influence functionals. By incorporating thermal fluctuations through an ensemble average over reference trajectories, the hierarchy is required to represent only the residual quantum memory associated with the imaginary part of the bath response function. Consequently, unlike conventional hierarchical equations of motion, QC-HEOM does not require Matsubara or Padé expansions of the thermal kernel and exhibits only weak temperature dependence of the hierarchy size. Furthermore, because thermal fluctuations are supplied through reference classical trajectories, the framework naturally extends beyond harmonic baths and enables the incorporation of anharmonic and molecular environments through externally generated trajectories. We derive the formalism and demonstrate its exactness for a harmonic bath. Applications to an asymmetric spin-boson model and the seven-site Fenna--Matthews--Olson complex illustrate the accuracy of QC-HEOM. It reproduces benchmark quasi-adiabatic path integral and hierarchical equations of motion results while requiring substantially fewer auxiliary objects, particularly at low temperatures. These results establish QC-HEOM as an efficient framework for treating residual quantum memory in quantum-classical descriptions of open-system dynamics. The separation of thermal fluctuations from residual quantum memory through the use of Wigner trajectories provides an approximate route toward hierarchical treatments of complex anharmonic environments that are inaccessible to conventional HEOM approaches.

quant-ph↗

arXiv2026

Variational Adaptive Gaussian Decomposition: Scalable Quadrature-Free Time-Sliced Thawed Gaussian Dynamics

Time-slicing has emerged as a strategy for incorporating semiclassical propagation into real-time path integral formulation and recovering full quantum dynamics. A central step is the decomposition of a time-evolved wave function into a superposition of Gaussian wave packets (GWPs). Here we introduce a quadrature-free variational framework for GWP decomposition, reformulating it as an optimization problem in which the GWP parameters are chosen to maximize the overlap with the time-evolving wave function. An autoencoderdecoder neural network is used for this optimization, with the representation being adaptively reoptimized during propagation. Each wave packet in this decomposition represents a localized patch of the underlying semiclassical manifold, while retaining full correlations between all degrees of freedom. This variational adaptive Gaussian decomposition (VAGD) approach yields a compact Gaussian expansion, providing a scalable route to time-sliced semiclassical quantum dynamics. While general, applying VAGD to facilitate time-slicing of thawed Gaussian dynamics allows a route to improving the semiclassical treatment to the full quantum mechanical result in a systematic manner.

quant-ph↗

arXiv2026

Path Integral Lindblad Dynamics in Presence of Time-Dependent Fields

The path integral Lindblad dynamics (PILD) method [A. Bose, J. Phys. Chem. Lett. 15(12), 3363-3368 (2024)] had been introduced as a way of incorporating the impact of certain empirical processes like pumps and drains on the dynamics of quantum systems interacting with thermal environments. The method being based on the time-translational invariance of the Nakajima-Zwanzig memory kernel, however, was not able to account for time-dependent external fields. In this communication, we give an alternate, simpler formulation of PILD, that allows us to go beyond this limitation. It does not require the evaluation of the non-Markovian memory kernel directly, and consequently can be applied to Floquet systems as well.

quant-ph↗

arXiv2025

Routes of Transport in the Path Integral Lindblad Dynamics through State-to-State Analysis

Analyzing routes of transport for open quantum systems with non-equilibrium initial conditions is extremely challenging. The state-to-state approach [A. Bose, and P.L. Walters, J. Chem. Theory Comput. 2023, 19, 15, 4828-4836] has proven to be a useful method for understanding transport mechanisms in quantum systems interacting with dissipative thermal baths, and has been recently extended to non-Hermitian systems to account for empirical loss. These non-Hermitian descriptions are, however, not capable of describing empirical processes of more general nature, including but not limited to a variety of pumping processes. We extend the state-to-state analysis to account for Lindbladian descriptions of generic dissipative, pumping and decohering processes acting on a system which is exchanging energy with a thermal bath. This Lindblad state-to-state method can elucidate routes of transport in systems coupled to a bath and additionally acted upon by Lindblad jump operators. The method is demonstrated using examples of excitonic aggregates subject to incoherent pumping and draining processes. Using this new state-to-state formalism, we demonstrate the establishment of steady-state excitonic currents across molecular aggregates, yielding a different first-principles approach to quantifying the same.

quant-ph↗

arXiv2025

Excitonic description of singlet fission beyond dimer model : a matrix product state approach

The importance of singlet fission as a fundamental process with a variety of implications in energy harvesting cannot be overstated. The challenge is in characterizing the energy states of these large singlet fission molecular aggregates that participate in the process. Large dimensionality and essential multi-configuration nature of the electronic states of interest combine to make accurate ab initio calculations prohibitively difficult. We present a spin-resolved tight-binding excitonic model for singlet fission that can be parameterized based on ab initio calculations on monomers and dimers of molecules, and is highly suitable for the study of aggregates using tensor network methods such as the density matrix renormalization group. This tensor network coarse-grained model is demonstrated specifically on the pentacene crystal, where we evaluate the spectra and density of states. We show the natural emergence of bands of states in some cases, and characterize them. Through an analysis of entanglement entropy of the eigenstates, we gain crucial insight into the extent of their multireference character. This method is useful in understanding not just the structure of these extended aggregates, but also being the cornerstone for incorporation of vibronic features and simulation of the singlet fission dynamics.

physics.chem-ph↗

arXiv2025

A Non-Hermitian State-to-State Analysis of Transport in Aggregates with Multiple Endpoints

Efficiency of quantum transport through aggregates with multiple end-points or traps proves to be an emergent and a highly non-equilibrium phenomenon. We present a numerically exact approach for computing the emergent time scale and amount of extraction specific to particular traps leveraging a non-Hermitian generalization of the recently introduced state-to-state transport analysis [Bose and Walters, J. Chem. Theory Comput. 2023, 19, 15, 4828-4836]. This method is able to simultaneously account for the coupling between various sites, the many-body effects brought in by the vibrations and environment held at a non-zero temperature, and the local extraction processes described by non-Hermitian terms in the Hamiltonian. In fact, our non-Hermitian state-to-state analysis goes beyond merely providing an emergent loss time-scale. It can parse the entire dynamics into the constituent internal transport pathways and loss to environment. We demonstrate this method using examples of an exciton transport in a lossy polaritonic cavity. The loss at the cavity and the extraction of the exciton from a terminal molecule provide competing mechanisms that our method helps to unravel, revealing extremely interesting non-intuitive physics. This non-Hermitian state-to-state analysis technique contributes an important link in understanding and elucidating the routes of transport in open quantum systems.

quant-ph↗

arXiv2025

Adaptive Kink Filtration: Achieving Asymptotic Size-Independence of Path Integral Simulations Utilizing the Locality of Interactions

Recent method developments involving path integral simulations have come a long way in making these techniques practical for studying condensed phase non-equilibrium phenomena. One of the main difficulties that still needs to be surmounted is the scaling of the algorithms with the system dimensionality. The majority of recent techniques have only changed the order of this scaling (going from exponential to possibly a very high ordered polynomial) and not eased the dependence on the system size. In this current work, we introduce an adaptive kink filtration technique for path generation approach that leverages the locality of the interactions present in the system and the consequent sparsity of the propagator matrix to remove the asymptotic size dependence of the simulations for the propagation of reduced density matrices. This enables the simulation of larger systems at a significantly reduced cost. This technique can be used both for simulation of non-equilibrium dynamics and for equilibrium correlation functions, and is demonstrated here using examples from both -- simulating the excitonic dynamics in bacteriochlorophyll chains and their absorption and emission spectra. We show that the cost becomes constant with the dimensionality of the system. The only place where a system size-dependence still remains is the calculation of the dynamical maps or propagators which are important for the transfer tensor method. The cost of calculating this solvent-renormalized propagator is the same as the cost of propagating all the elements of the reduced density matrix, which scales as the square of the size. This adaptive kink-filtration technique promises to be instrumental in extending the affordability of path integral simulations for very large systems.

physics.chem-ph↗

arXiv2024

Impact of Loss Mechanisms on Linear Spectra of Excitonic and Polaritonic Aggregates

The presence of loss mechanisms governed by empirical time-scales affect the dynamics and spectra of systems in profound ways. However, incorporation of these effects and their interaction with the thermal dissipative environments interacting with the system prove to be challenging. We have recently developed the path integral Lindblad dynamics (PILD) method to combine numerically rigorous path integral simulations with Lindblad dynamics to account for such empirical loss mechanisms. In this work, we utilize the PILD method to study the absorption and circular dichroism spectra of chiral molecular aggregates and excitonic polaritons. We demonstrate that the effect of loss on particular states in both systems can differ not just on the basis of the symmetries of the state but also on the basis of complicated "interactions" of the system and the loss mechanism with the dissipative environments. We present probably the first numerical exploration of the CD spectrum of chiral molecular aggregates confined in a cavity. While the CD spectrum of just the excitonic aggregates itself is not amenable to simplistic understanding like the exciton chirality (EC) rule, the CD spectrum of polaritonic molecules is even more complex. Additionally, the impact of empirical loss on the polaritonic CD spectrum seems to be highly site-dependent. The impact of a lossy cavity is qualitatively different from the impact of a molecule that leaks the excitation. We explore some of those effects in depth leveraging the framework of path integral Lindblad dynamics.

physics.chem-ph↗

arXiv2024

Path integral Lindblad master equation through transfer tensor method & the generalized quantum master equation

Path integrals have, over the years, proven to be an extremely versatile tool for simulating the dynamics of open quantum systems. The initial limitations of applicability of these methods in terms of the size of the system has steadily been overcome through various developments, making numerical explorations of large systems a more-or-less regular feature. However, these simulations necessitate a detailed description of the system-environment interaction through accurate spectral densities, which are often difficult to obtain. Additionally, for several processes, such as spontaneous emission, one only has access to a rough estimation of an empirical timescale, and it is not possible to really define a proper spectral density at all. In this communication, an approach of incorporating such processes within an exact path integral description of other dissipative modes is developed through the Nakajima-Zwanzig master equations. This method will allow for a numerically exact non-perturbative inclusion of the degrees of freedom that are properly described by a bath using path integrals, while incorporating the empirical time scale through the Lindblad master equation. The cost of this approach is dominated by the cost of the path integral method used, and the impact of the Lindbladian terms is effectively obtained for free. This path integral Lindblad dynamics method is demonstrated with the example of electronic excitation transfer in a 4-site model of the Fenna-Matthews-Olson complex with the exciton has a propensity of being "lost" to the charge transfer state at the third chromophore. The impact of different time-scales of abstraction of the exciton is illustrated at no extra cost.

quant-ph↗

arXiv2024

Analysis of Time-Evolution of Gaussian Wavepackets in Non-Hermitian Systems

Simulation and analysis of multidimensional dynamics of a quantum non-Hmeritian system is a challenging problem. Gaussian wavepacket dynamics has proven to be an intuitive semiclassical approach to approximately solving the dynamics of quantum systems. A Gaussian wavepacket approach is proposed for a continuous space extension to the Hatano-Nelson model that enables transparent analysis of the dynamics in terms of complex classical trajectories. We demonstrate certain cases where the configuration space trajectory can be made fully real by transforming the initial conditions to account for the non-Hermiticity appropriately through the momentum coordinates. However, in general the complex phase space is unavoidable. For the cases where the trajectory is real, the effective force can be decomposed into that due to the potential energy surface and that due to the imaginary vector potential. The impact of the vector potential on the trajectory of the wavepacket is directly proportional to both the strength of the vector potential and the width of the wavepacket.

quant-ph↗

arXiv2023

Quantum correlation functions through tensor network path integral

Tensor networks have historically proven to be of great utility in providing compressed representations of wave functions that can be used for calculation of eigenstates. Recently, it has been shown that a variety of these networks can be leveraged to make real time non-equilibrium simulations of dynamics involving the Feynman-Vernon influence functional more efficient. In this work, tensor networks are utilized for calculating equilibrium correlation function for open quantum systems using the path integral methodology. These correlation functions are of fundamental importance in calculations of rates of reactions, simulations of response functions and susceptibilities, spectra of systems, etc. The influence of the solvent on the quantum system is incorporated through an influence functional, whose unconventional structure motivates the design of a new optimal matrix product-like operator that can be applied to the so-called path amplitude matrix product state. This complex time tensor network path integral approach provides an exceptionally efficient representation of the path integral enabling simulations for larger systems strongly interacting with baths and at lower temperatures out to longer time. The design and implementation of this method is discussed along with illustrations from rate theory, symmetrized spin correlation functions, dynamical susceptibility calculations and quantum thermodynamics.

quant-ph↗

arXiv2023

A tensor network representation of path integrals: Implementation and analysis

Tensors with finite correlation afford very compact tensor network representations. A novel tensor network-based decomposition of real-time path integral simulations involving Feynman-Vernon influence functional is introduced. In this tensor network path integral (TNPI) technique, the finite temporarily non-local interactions introduced by the influence functional can be captured very efficiently using matrix product state representation for the path amplitude (PA) tensor. We illustrate this particular TNPI method through various realistic examples, including a charge transfer reaction and an exciton transfer in a dimer. We also show how it is readily applied to systems with greater than two states by simulating a 7-site model of FMO and a molecular wire model. The augmented propagator (AP) TNPI utilizes the symmetries of the problem, leading to accelerated convergence and dramatic reductions of computational effort. We also introduce an approximate method that speeds up propagation beyond the non-local memory length. Furthermore, the structure imposed by the tensor network representation of the PA tensor naturally suggests other factorizations that make simulations for extended systems more efficient. These factorizations would be the subject of future explorations. The flexibility of the AP-TNPI framework makes it a promising new addition to the family of path integral methods for non-equilibrium quantum dynamics.

physics.chem-ph↗

arXiv2023

QuantumDynamics.jl: A modular approach to simulations of dynamics of open quantum systems

Simulation of non-adiabatic dynamics of a quantum system coupled to dissipative environments poses significant challenges. New sophisticated methods are regularly being developed with an eye towards moving to larger systems and more complicated description of solvents. Many of these methods, however, are quite difficult to implement and debug. Furthermore, trying to make the individual algorithms work together through a modular application programming interface (API) can be quite difficult. We present a new, open-source software framework, QuantumDynamics.jl, designed to address these challenges. It provides implementations of a variety of perturbative and non-perturbative methods for simulating the dynamics of these sytems. Most prominently, QuantumDynamics.jl supports hierarchical equations of motion and the family of methods based on path integrals. Effort has been made to ensure maximum compatibility of interface between the various methods. Additionally, QuantumDynamics.jl, being built on a high-level programming language, brings a host of modern features to explorations of systems such as usage of Jupyter notebooks and high level plotting for exploration of systems, possibility of leveraging high-performance machine learning libraries for further development. Thus, while the built-in methods can be used as end-points in themselves, the package provides an integrated platform for experimentation, exploration, and method development.

quant-ph↗

arXiv2023

Impact of solvent on state-to-state population transport in multistate systems using coherences

Understanding the pathways taken by a quantum particle during a transport process is an enormous challenge. There are broadly two different aspects of the problem that affect the route taken. First is obviously the couplings between the various sites, which translates into the intrinsic "strength" of a state-to-state channel. Apart from the inter-state couplings, the solvents affecting the energies of the state, and their relative coupling strengths and time-scales form the second factor. This impact of dissipative media is significantly more difficult to analyze. Building on recently derived relations between coherences and population derivatives, we present an analysis of the transport that allows us to account for both the effects in a rigorous manner. We demonstrate the richness hidden behind the transport even for a relatively simple system, a 4-site coarse-grained model of the Fenna-Matthews-Olson complex. The effect of the local dissipative media is highly non-trivial. We show that while the impact on the total site population may be small, there are dramatic changes to the pathway taken by the transport process. The ability to untangle the dynamics at a greater granularity opens up possibilities in terms of design of novel systems with an eye towards quantum control.

physics.chem-ph↗

arXiv2023

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex

The dynamics of the excitation energy transfer (EET) in photosynthetic complexes is an interesting question both from the perspective of fundamental understanding and the research in artificial photosynthesis. Challenges persist in numerically simulating these systems both in parameterizing them and following their dynamics over long periods of time. Over the past decade, very accurate spectral densities have been developed to capture spatial inhomogeneties in the Fenna-Matthews-Olson (FMO) complex. We investigate the dynamics of FMO with an exact treatment of various theoretical spectral densities. Because FMO has Hamiltonian elements that connect most of the bacteriochlorophyll sites together, it becomes difficult to rigorously identify the energy transport pathways in the complex. We use the recently introduced ideas of relating coherence to population derivatives to analyze the transport process and reveal some of the pathways.

physics.chem-ph↗

arXiv2022

Tensor Network Path Integral Study of Dynamics in B850 LH2 Ring with Atomistically Derived Vibrations

The recently introduced multisite tensor network path integral (MS-TNPI) allows simulation of extended quantum systems coupled to dissipative media. We use MS-TNPI to simulate the exciton transport and the absorption spectrum of a B850 bacteriochlorophyll (BChl) ring. The MS-TNPI network is extended to account for the ring topology of the B850 system. Accurate molecular dynamics-based description of the molecular vibrations and the protein scaffold is incorporated through the framework of Feynman-Vernon influence functional. To relate the present work with the excitonic picture, an exploration of the absorption spectrum is done by simulating it using approximate and topologically consistent transition dipole moment vectors. Comparison of these numerically exact MS-TNPI absorption spectra are shown with second-order cumulant approximations. The effect of temperature on both the exact and the approximate spectra is also explored.

physics.chem-ph↗

arXiv2022

Effect of Phonons and Impurities on the Quantum Transport in XXZ Spin-Chains

Numerical and analytic results have been used to characterize quantum transport in spin chains, showing the existence of both ballistic and diffusive motion. Experiments have shown that heat transfer is surprisingly always diffusive. The scattering from phonons and impurities have been postulated to be the two factors critical in causing the diffusive transport. In this work, we evaluate the transport process by incorporating a bath of phonons and impurities in order to understand the role played by each of the factors. While methods like time-dependent density matrix renormalization group (tDMRG) can be used to simulate isolated spin chains, the coupling with phonons make simulations significantly more challenging. The recently developed multisite tensor network path integral (MS-TNPI) method builds a framework for simulating the dynamics in extended open quantum systems by combining ideas from tDMRG and Feynman-Vernon influence functional. This MS-TNPI is used to characterize dynamics in open, extended quantum systems. Simulations are done with the commonly used sub-Ohmic, Ohmic and super-Ohmic spectral densities describing the phononic bath. We show that while the transport in presence of impurities eventually becomes diffusive, the exact details are dependent on the specifics of the interactions and amount of impurities. In contrast, the presence of a bath makes the transport diffusive irrespective of the parameters characterizing the bath.

quant-ph↗

arXiv2022

Effect of Temperature Gradient on Quantum Transport

The recently introduced multisite tensor network path integral (MS-TNPI) method [Bose and Walters, J. Chem. Phys., 2022, 156, 24101.] for simulation of quantum dynamics of extended systems has been shown to be effective in studying one-dimensional systems. Quantum transport in these systems are typically studied at a constant temperature. However, temperature seems to be a very obvious parameter that can be spatially changed to control the quantum transport. Here, MS-TNPI is used to study ``non-equilibrium'' effects of an externally imposed temperature gradient on the quantum transport in one-dimensional extended quantum systems.

physics.chem-ph↗