Thermodynamic free-energy spectrum theory for open quantum systems

Generalized system-bath entanglement theorem for Gaussian environments

The entanglement between system and bath often plays a pivotal role in complex systems spanning multiple orders of magnitude. A system-bath entanglement theorem was previously established for Gaussian environments in J. Chem. Phys. 152, 034102 (2020) regarding linear response functions. This theorem connects the entangled responses to the local system and bare bath properties. In this work, we generalize it to correlation functions. Key steps in derivations involve using the generalized Langevin dynamics for hybridizing bath modes and the Bogoliubov transformation that maps the original finite-temperature reservoir to an effective zero-temperature vacuum by employing an auxiliary bath. The generalized theorem allows us to evaluate the system-bath entangled correlations and the bath mode correlations in the total composite space, as long as we know the bare-bath statistical properties and obtain the reduced system correlations. To demonstrate the cross-scale entanglements, we utilize the generalized theorem to calculate the solvation free energy of an electron transfer system with intramolecular vibrational modes.

Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory vs core-system hierarchy construction

In this paper, we present a comprehensive account of quantum dissipation theories with the quadratic environment couplings. The theoretical development includes the Brownian solvation mode embedded hierarchical quantum master equations, a core-system hierarchy construction that verifies the extended dissipaton equation of motion (DEOM) formalism [R. X. Xu et al., J. Chem. Phys. 148, 114103 (2018)]. Developed are also the quadratic imaginary-time DEOM for equilibrium and the λ(t)-DEOM for nonequilibrium thermodynamics problems. Both the celebrated Jarzynski equality and Crooks relation are accurately reproduced, which, in turn, confirms the rigorousness of the extended DEOM theories. While the extended DEOM is more numerically efficient, the core-system hierarchy quantum master equation is favorable for "visualizing" the correlated solvation dynamics.

Nonequilibrium work distributions in quantum impurity system-bath mixing processes

The fluctuation theorem, where the central quantity is the work distribution, is an important characterization of nonequilibrium thermodynamics. In this work, based on the dissipaton-equation-of-motion theory, we develop an exact method to evaluate the work distributions in quantum impurity system-bath mixing processes, in the presence of non-Markovian and strong couplings. Our results not only precisely reproduce the Jarzynski equality and Crooks relation, but also reveal rich information on large deviation. The numerical demonstrations are carried out with a spin-boson model system.

A statistical quasi-particles thermofield theory with Gaussian environments: System-bath entanglement theorem for nonequilibrium correlation functions

For open quantum systems, environmental dissipative effect can be represented by statistical quasi-particles, namely dissipatons. We exploit this fact to establish the dissipaton thermofield theory. The resulting generalized Langevin dynamics of absorptive and emissive thermofield operators are effectively noise-resolved. The system-bath entanglement theorem is then readily followed between a important class of nonequilibrium steady-state correlation functions. All these relations are validated numerically. A simple corollary is the transport current expression, which exactly recovers the result obtained from the nonequilibrium Green's function formalism.

Imaginary-time hierarchical equations of motion for thermodynamic variables

The partition function (PF) plays a key role in the calculation of quantum thermodynamic properties of a system that interacts with a heat bath. The imaginary-time hierarchical equations of motion (imHEOM) approach was developed to evaluate in a rigorous manner the PF of a system strongly coupled to a non-Markovian bath. In this paper, we present a numerically efficient scheme to evaluate the imHEOM utilizing the β-differentiated imHEOM (BD-imHEOM) that are obtained by differentiating the elements of the imHEOM with respect to the inverse temperature. This approach allows us to evaluate the system, system-bath interaction, and heat-bath parts of the PF efficiently. Moreover, we employ a polyharmonic decomposition method to construct a concise hierarchical structure with better convergence, thus reducing the cost of numerical integrations. We demonstrate the proposed approach by compute thermodynamic quantities of a spin-boson system and a 2 × 2 antiferromagnetic triangular spin lattice system with an Ohmic spectral distribution.

Nonequilibrium Kondo regime current noise spectrum of quantum dot systems with the single impurity Anderson model

We investigate the nonequilibrium current noise spectrum of single impurity Anderson model quantum dot systems on the basis of the accurate dissipation equation of motion evaluations. By comparing between the equilibrium and nonequilibrium cases and between the non-Kondo and Kondo regimes, we identify the current noise spectrum of the nonequilibrium Kondo features that actually appear in the entire region of ω ∈ [-eV, eV]. It is well known that the primary Kondo characteristics at ω = ±eV = ±(μ_L - μ_R) display asymmetrical upturns and remarkable peaks in S(ω) and dS(ω)/dω, respectively. These features are originated from the Rabi interference of the transport current dynamics, with the Kondo oscillation frequency of |eV|. Moreover, we also identify the minor but very distinguishable inflections, crossing over from ω = -eV to ω = +eV. This uncovered feature would be related to the interference between two Kondo resonance channels.