Dynamics with Simultaneous Dissipations to Fermionic and Bosonic Reservoirs (2501.18140v1)

Abstract: We introduce a non-phenomenological framework based on the influence functional method to incorporate simultaneous interactions of particles with fermionic and bosonic thermal reservoirs. In the slow-motion limit, the electronic friction kernel becomes Markovian, enabling an analytical expression for the friction coefficient. The framework is applied to a prototypical electrochemical system, where the metal electrode and solvent act as fermionic and bosonic reservoirs, respectively. We investigate quantum vibrational relaxation of hydrogen on metal surfaces, showing that dissipation to electron-hole pairs reduces the relaxation time. Additionally, in solvated proton discharge, electronic friction prolongs charge transfer by delaying proton transitions between potential wells. This study provides new insights into the interplay of solvent and electronic dissipation effects, with direct relevance to electrochemical processes and other systems involving multiple thermal reservoirs.

• The paper proposes a non-phenomenological framework using the influence functional method to model simultaneous dissipative interactions with fermionic and bosonic reservoirs.
• It employs a quasiclassical Langevin equation to capture non-Markovian effects, clarifying dual dissipation roles in vibrational relaxation and proton transfer processes.
• Numerical studies reveal that electronic friction enhances damping for hydrogen vibrational relaxation and prolongs charge transfer in electrochemical applications.

Dynamics with Simultaneous Dissipations to Fermionic and Bosonic Reservoirs

The paper "Dynamics with Simultaneous Dissipations to Fermionic and Bosonic Reservoirs" by Arguelles and Sugino addresses a significant gap in the theoretical treatment of open quantum systems by proposing a novel non-phenomenological framework to model particle interactions with both fermionic and bosonic thermal reservoirs. The influence functional path integral method is utilized to derive a quasiclassical Langevin equation, accommodating non-Markovian effects and allowing analytical expressions within the slow-motion limit. This paper is particularly focused on electrochemical systems where metal electrodes and solvents represent the fermionic and bosonic reservoirs, respectively.

Theoretical Framework

The authors establish a comprehensive canonical formalism using a total Hamiltonian that describes interactions of a particle with dual thermal reservoirs. This model includes contributions from both bosonic and fermionic reservoirs, represented as harmonic oscillators and electron-hole pair interactions, respectively. The influence functional method is invoked to facilitate derivation without phenomenological assumptions, yielding expressions for both the dissipation kernel and its Markovian limit. This theoretical construct permits integration of multifaceted dissipative processes, often neglected due to complex inter-reservoir interactions which are critical when reaction centers are variably distant from electrodes.

Numerical Studies and Applications

The framework was deployed in two paradigmatic cases: quantum vibrational relaxation of hydrogen atoms on metal surfaces and proton discharge in a solvated state on metal electrodes.

1. Vibrational Relaxation of Hydrogen: The paper showcases how electronic friction, induced by electron-hole pair formations, couples with phononic dissipation to accelerate vibrational energy relaxation. Numerical simulations demonstrated that these electronic contributions enhance damping, which is crucial for understanding vibrational dynamics on metal surfaces.
2. Proton Discharge Dynamics: In modeling the Volmer step in electrochemical processes on metal electrodes, the paper investigates the dual dissipation effects. The findings indicate that electronic friction extends the duration of charge transfer processes by imposing an additional drag due to its localization near electronic level crossings. This nuanced interaction suggests implications for reaction kinetics and the modulation of electron chemistries.

Implications and Future Directions

The implications of incorporating simultaneous fermionic and bosonic reservoir interactions extend beyond the domain of electrochemistry. The resulting non-equilibrium dynamics shed light on energy dissipation mechanisms vital for designing advanced materials and processes in chemical and materials science. As the influence functional method facilitates a unified description, these insights could guide further exploration into coupled thermal reservoirs across various physical chemistry applications.

On a theoretical front, this framework enriches the understanding of non-Markovian dynamics in open quantum systems. Future directions might explore its applicability in other complex systems, potentially expanding to cover more intricate interactions, such as those involving soft matter or biomolecular environments, where dual dissipation channels are prominent. Furthermore, extending this methodology to include stochastic simulation techniques will enable more refined predictions of system behaviors under diverse conditions.

In conclusion, this paper provides a robust theoretical foundation for enhanced understanding and modeling capability regarding dual dissipation effects in systems involving fermionic and bosonic reservoirs, thus propelling the discourse in the field towards a more comprehensive treatment of multi-reservoir interactions.