Open systems evolve over time interacting with fermionic or bosonic reservoirs representing electrons in electrodes, lattice vibrations or electromagnetic fields. These reservoirs act as energy dissipation channels and sources of fluctuations that affect the dynamics. In electrochemical systems, the dynamics occurs under a moderate non-equilibrium condition influenced by a delicate balance of the multiple reservoirs. A critical property for characterizing such systems is the rate at which energy and charge are exchanged with the reservoirs, which can be investigated in principle using a microscopic-like theory based on the Langevin equation by incorporating the fluctuations and dissipation. The effect of multiple reservoirs, however, has received limited attention.
In this talk, we present a reformulation of the particle dynamics using the influence functional path integral [1] framework, which yields without phenomenological assumptions, a quasiclassical Langevin equation that incorporates non-Markovian effects of bosonic and fermionic reservoirs. As an example of the fermionic reservoir, we consider electrons in a metal electrode, where the dissipation of particle energy occurs via electron-hole pairs excitations giving rise to electronic friction. An explicit expression for the local dissipation kernel (Markovian kernel) is given in the limit of slow particle motion [2] providing a way to calculate the energy transfer rate through stochastic simulations. For demonstration purposes, we applied the framework to prototypical electrochemical systems [3] where a hydrogen (H) atom moves in contact with a metal electrode and solvent modes. We explore the interplay of the reservoirs using two scenarios: (1) quantum vibrational relaxation of a hydrogen (H) confined on a metal surface and (2) solvated electrochemical proton discharge.
[1] R. P. Feynman and F. L. Vernon, Ann. Phys. 24, 118 (1963).
[2] E. F. Arguelles and O. Sugino, J. Chem. Phys. 160, 144102 (2024).
[3] E. F. Arguelles and O. Sugino, in preparation.