Quantum Boundary Driven Transport Demonstrates Current Statistics With Engineered Gain And Loss Channels

The behaviour of quantum particles in engineered systems represents a significant frontier in modern physics, and recent advances focus on understanding how particles move through complex channels within these systems. Katha Ganguly and Bijay Kumar Agarwalla, both from the Indian Institute of Science Education and Research Pune, investigate the fundamental statistics of particle transport in a specifically designed quantum lattice. Their work addresses a gap in current knowledge by analysing the full counting statistics of current when the system incorporates both correlated gain and loss of particles, a process that fundamentally alters how particles flow. The researchers demonstrate that incorporating correlated gain and loss channels leads to striking non-reciprocal behaviour, dramatically impacting both the average particle current and its fluctuations, and revealing the crucial role of engineered dissipation in these boundary-driven systems.

Quantum Transport, Open Systems and Fluctuations

This compilation of research explores the fascinating world of quantum transport, open quantum systems, and the role of fluctuations in these systems. Scientists investigate how quantum particles move through materials and devices, particularly when these systems interact with their environment, crucial for comprehending decoherence, dissipation, and behaviour far from equilibrium. Research focuses on characterizing not just average currents and energies, but also the full distribution of these quantities, revealing insights into noise and the limits of measurement, employing full counting statistics to provide a detailed picture of particle and energy flow. Researchers also explore thermal rectification, the quantum analogue of a thermal diode, aiming to create materials that conduct heat preferentially in one direction, requiring the introduction of nonlinearities and asymmetries into the system.

Many studies focus on systems driven out of equilibrium, revealing phenomena not observed in stable conditions, utilizing the Keldysh formalism and path integrals to tackle these complex scenarios. Furthermore, scientists actively investigate reservoir engineering, manipulating the environment surrounding a quantum system to control its behaviour. This body of work encompasses theoretical foundations, computational techniques, and applications to nanoscale devices. Studies delve into fluctuation theorems and counting statistics, establishing the theoretical framework for understanding fluctuations and their connection to thermodynamics.

Researchers also examine scattering matrices and general transport principles, laying the groundwork for understanding particle movement through materials. Investigations into thermal rectification explore nonlinear heat transport and asymmetry in nanoscale devices, while scientists explore the effects of actively manipulating the environment and the impact of localized loss on quantum systems. This research highlights the potential for combining active environmental control with detailed statistical analysis of currents and energies. Scientists are investigating how engineered dissipation can enhance or suppress thermal rectification and exploring the interplay between external driving, fluctuations, and thermodynamics in open quantum systems. Extending the Keldysh formalism to more complex systems, such as those with interacting particles or disorder, remains a key area of investigation, providing a valuable resource for researchers seeking to understand and control quantum systems, paving the way for advancements in quantum technologies and materials science.

Correlated Gain and Loss Control Particle Current

Scientists are developing new methods for controlling particle flow in quantum systems by carefully engineering dissipation. This research focuses on boundary-driven lattices where gain and loss channels are strategically designed to influence particle current. Researchers developed a theoretical framework to analyze the full counting statistics of current, a challenging task with limited prior investigation, centering on a free fermionic lattice where they engineered correlated gain and loss channels to control particle flow and observe resulting non-equilibrium phenomena. To achieve this, the team devised a method for calculating the cumulant generating function of the steady-state particle current, a key quantity for understanding current fluctuations.

They also explored a simplified scenario where the correlated gain-loss channels are approximated as local channels, allowing for the determination of average current and its fluctuations under these conditions. A central aspect of the research involved establishing conditions for current statistical symmetry, creating a balanced gain-loss scenario where the system exhibits predictable behaviour at both ends of the lattice. Crucially, the study reveals a striking difference between correlated and local gain-loss channels: nonreciprocity, dramatically impacting both the average current and its fluctuations, demonstrating the importance of engineered dissipation in boundary-driven systems. This theoretical framework provides a foundation for understanding and potentially controlling quantum systems with engineered dissipation, opening avenues for future research in quantum technologies and materials science.

Current Fluctuations in Driven Fermionic Lattices

This work presents a detailed analysis of particle current in a boundary-driven free fermionic lattice, focusing on the impact of engineered gain and loss channels. Scientists developed a method to calculate the full counting statistics of current, revealing how these channels influence particle flow and fluctuations within the system, establishing a framework for understanding non-equilibrium phenomena in quantum lattices with potential applications in quantum technologies. The team first derived expressions for the moment generating function of the integrated particle current, initially considering only boundary drives without correlated dissipation. Using path integral formalism and a coherent basis, they obtained a compact analytical expression for the generating function, detailing the contributions from the system’s Hamiltonian and boundary conditions.

This allowed for precise calculation of current statistics in the absence of bulk dissipation. Subsequently, the study extended to incorporate correlated gain and loss channels throughout the lattice, modeling these channels using superposition of adjacent local operators, introducing correlations between neighboring sites. The research demonstrates that these correlated dissipators significantly impact both the average current and its fluctuations, exhibiting non-reciprocity in the system. Measurements confirm that the introduction of correlated gain and loss alters the current statistics at the boundaries, creating asymmetry in particle flow.

The team devised conditions for achieving symmetric balanced gain and loss, where current statistics coincide at both ends of the lattice. Experiments reveal that the degree of non-reciprocity is directly linked to the strength of the correlated dissipation, with stronger correlations leading to more pronounced asymmetry in current flow. This breakthrough delivers a comprehensive understanding of how engineered dissipators influence particle transport in boundary-driven systems, providing insights for designing novel quantum devices and exploring out-of-equilibrium phenomena.

Engineered Dissipation Drives Current Asymmetry in Lattices

This work details a significant advance in understanding how engineered dissipation affects quantum systems, specifically focusing on the flow of particles within a boundary-driven lattice. Researchers analytically derived the cumulant generating function, a key tool for describing particle current statistics, in a system with carefully designed gain and loss channels. Initial analysis, mirroring established results, confirmed the validity of the approach by reproducing the well-known Levitov-Lesovik formula when no gain or loss was present. Introducing engineered dissipation revealed that particle current statistics generally differ at opposing boundaries of the lattice, unless a balanced gain-loss scenario, restoring symmetry, is achieved.

A particularly striking finding is the demonstration of nonreciprocity when correlated gain and loss are implemented, leading to a diode-like effect where current flows more easily in one direction than another. This behaviour is absent when only local gain and loss are present, highlighting the importance of the specific design of the dissipative channels. The team acknowledges that their approach, based on the Feynman path integral, could be extended to investigate systems with different types of dissipation, such as those involving dephasing mechanisms within the lattice itself. Future research may explore applying this framework to more complex boundary-driven systems, furthering the development of quantum technologies reliant on precise control of particle flow.

👉 More information
🗞 Full counting statistics for boundary driven transport in presence of correlated gain and loss channels
🧠 ArXiv: https://arxiv.org/abs/2511.12539