Ultrastrong coupling limit to quantum mean force Gibbs state for anharmonic environment
arXiv:2405.03044 · doi:10.1063/5.0223734
Abstract
The equilibrium state of a quantum system can deviate from the Gibbs state if the system-environment (SE) coupling is not weak. An analytical expression for this mean force Gibbs state (MFGS) is known in the ultrastrong coupling (USC) regime for the Caldeira-Leggett (CL) model that assumes a harmonic environment. Here, we derive analytical expressions for the MFGS in the USC regime for more general SE models. For all the generalized models considered here, we find the USC state to be diagonal in the basis set by the SE interaction, just like in the CL case. While for the generic model considered, the corresponding USC-MFGS is found to alter from the CL-result, we do identify a class of models more general than the CL model for which the CL-USC result remains unchanged. We also provide numerical verification for our results. These results provide key tools for the study of strong coupling quantum thermodynamics and several quantum chemistry and biology problems under more realistic SE models, going beyond the CL model.
14 pages, 4 figures. Published version. Some minor corrections and typos fixed. Comments are welcome
References in corpus (26)
- Environment-Assisted Quantum Transport
- Fluctuation Theorem for Arbitrary Open Quantum Systems
- First and Second Law of Thermodynamics at strong coupling
- Correlation-dependent coherent to incoherent transitions in resonant energy transfer dynamics
- {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
- Strong Coupling Thermodynamics of Open Quantum Systems
- Open quantum system dynamics and the mean force Gibbs state
- Weak and ultrastrong coupling limits of the quantum mean force Gibbs state
- Approach to Quantum Kramers' Equation and Barrier Crossing Dynamics
- Fermionic Stochastic Schrödinger Equation and Master Equation: An Open System Model
- On the Applicability of the Caldeira-Leggett Model to Condensed Phase Vibrational Spectroscopy
- Hamiltonian of mean force for damped quantum systems
- Thermal energies of classical and quantum damped oscillators coupled to reservoirs
- Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force
- Quantum Kramers' equation for energy diffusion and barrier crossing dynamics in the low friction regime
- Quantum phase space function formulation of reactive flux theory
- Steady state thermodynamics of two qubits strongly coupled to bosonic environments
- Phase space dynamics of overdamped quantum systems
- Effective-Hamiltonian theory: An approximation to the equilibrium state of open quantum systems
- Non-Markovian stochastic description of quantum transport in photosynthetic systems
- System-reservoir theory with anharmonic baths: a perturbative approach
- Steady state in ultrastrong coupling regime: perturbative expansion and first orders
- Dephasing dynamics of an impurity coupled to an anharmonic environment
- Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex
- A qubit strongly interacting with a bosonic environment: Geometry of thermal states
- Local Harmonic Approximation to Quantum Mean Force Gibbs State