Non-markovian Dynamics in Nonstationary Gaussian Baths Achieves Efficiency Via Extended Hierarchy of Pure States

Understanding how systems interact with their environment is fundamental to physics and chemistry, yet accurately modelling these interactions remains a significant challenge, particularly when the environment itself is changing over time. Vladislav Sukharnikov, along with Stasis Chuchurka from Universität Hamburg and Frank Schlawin from the Max Planck Institute for the Structure and Dynamics of Matter and Universität Hamburg, now present a refined approach to simulating these ‘open’ systems. Their work builds upon existing methods, extending them to handle environments that are not static, but evolve dynamically, a situation common in many real-world scenarios. The team demonstrates that their improved technique, which accurately captures the complex interplay between a system and its fluctuating surroundings, offers greater efficiency and accuracy than current methods, opening new avenues for research into areas such as light-matter interactions and the behaviour of driven materials.

Open Quantum Systems and Dynamics Theory

This compilation represents a comprehensive bibliography focused on open quantum systems, quantum dynamics, and related computational methods. The references cover a broad range of research areas, centering on the theory and simulation of quantum systems interacting with their environment, including phenomena like dissipation, decoherence, and dephasing. Researchers explore various numerical techniques for simulating these systems, including hierarchical equations of motion and quasi-adiabatic propagator path integrals. The bibliography also encompasses studies of quantum optics and light-matter interaction, particularly stimulated Raman scattering.

Several papers address non-Markovian dynamics, where a system’s future behavior depends on its entire past history, and explore methods for quantum control and mitigating decoherence. Applications extend to condensed matter physics, including exciton dynamics and energy transfer in materials, and even quantum information processing. Prominent researchers in this field include F. Schlawin, W. T.

Simulating Open Quantum Systems with Dynamic Baths

Scientists have advanced the hierarchy of pure states (HOPS) approach to simulate open quantum systems interacting with dynamic, nonstationary environments. This work addresses a critical challenge in accurately modeling systems coupled to environments that are not in a standard thermal state, a situation increasingly relevant in emerging research areas like quantum materials and nonlinear phononics. The team extended the conventional decomposition of bath correlation functions to explicitly incorporate time-dependent forms, allowing for a more realistic representation of dynamic environments. To demonstrate the method’s performance, researchers focused on examples of nonstationary squeezed reservoirs, generated through uniform squeezing and parametric amplification.

Rigorous benchmarking against hierarchies of master equations reveals that HOPS achieves superior efficiency when the hierarchy is truncated, requiring fewer computational resources for accurate simulations. This improvement is particularly significant when dealing with complex, non-Markovian dynamics. The team also implemented a pseudomode representation, simplifying the formalism when each contribution to the bath correlation function corresponds to an independent physical environment, further enhancing efficiency in strongly non-Markovian regimes. This research highlights HOPS as a versatile and powerful tool for simulating open quantum systems in dynamic environments, with potential applications ranging from squeezed light-matter interactions to driven materials and dissipative phase transitions.

Time-Dependent Baths Enable Efficient Quantum Simulations

Scientists have advanced the hierarchy of pure states (HOPS) approach to simulate open quantum systems interacting with dynamic, nonstationary environments. This work addresses the need for accurately modeling systems driven far from equilibrium, such as those found in emerging quantum materials research where external stimuli manipulate material properties. The team constructed a novel formulation allowing for time-dependent bath correlation functions, a key advancement enabling the study of systems where the surrounding environment is constantly changing. Experiments reveal that this new HOPS method achieves superior efficiency compared to established techniques like hierarchies of master equations, particularly when truncating the hierarchy to manage computational complexity.

Benchmarking demonstrates that HOPS outperforms these alternative methods in accurately representing the system’s evolution. Furthermore, the team discovered that when each component of the bath correlation function corresponds to a distinct physical environment, a simplified “pseudomode” representation significantly enhances computational efficiency, especially in strongly non-Markovian regimes where memory effects are prominent. The researchers successfully applied this generalized HOPS formulation to examples of nonstationary squeezed reservoirs, generated through uniform squeezing and parametric amplification.

Dynamic Baths Enable Faster Quantum Simulations

This work presents an advanced hierarchy of pure states method, extending its capabilities to simulate open quantum systems interacting with dynamic, nonstationary environments. Researchers successfully adapted the standard approach by allowing for time-dependent decompositions of bath correlation functions, thereby broadening the method’s applicability beyond systems with constant environmental properties. Demonstrations using squeezed reservoirs confirm that this generalized method converges more rapidly than existing techniques when the hierarchy is truncated, indicating improved efficiency in complex simulations. The team also developed a simplification strategy, termed a pseudomode representation, which proves particularly effective when each contribution to the bath correlation function corresponds to an independent physical environment, especially in strongly non-Markovian scenarios. While the current formulation assumes Gaussian environments and linear coupling, the authors outline a pathway to extend the method to encompass a wider range of Gaussian environments and incorporate finite temperature effects. They acknowledge that constructing the hierarchy directly for certain environments can introduce unwanted dependencies on parameters like temperature and squeezing, but demonstrate a procedure to circumvent this limitation by introducing an effective zero-temperature environment with a modified operator.