Thermodynamic free-energy spectrum theory for open quantum systems

Abstract

In this work, we develop the free-energy spectrum theory for thermodynamics of open quantum impurity systems that can be either fermionic or bosonic or combined. We identify two types of thermodynamic free-energy spectral functions for open quantum systems and further consider the thermodynamic limit, which supports the Gaussian–Wick description of hybrid environments. We can then relate the thermodynamic spectral functions to the local impurity properties. These could be experimentally measurable quantities, especially for the cases of quantum dots embedded in solid surfaces. Another type of input is the bare–bath coupling spectral densities, which could be accurately determined with various methods. For illustration, we consider the simplest noninteracting systems, with focus on the strikingly different characteristics between the bosonic and fermionic scenarios.

Nonequilibrium system-bath entanglement theorem versus heat transport

“…Theoretical studies have been mainly carried out in terms of nonequilibrium Green's function (NEGF) methods. [1,2] In this work, we exploit the well-established systembath entanglement theorem (SBET), [3,4] with extension to nonequilibrium transport scenario. Adopted here is the Gauss-Wick's environment ansatz [5,6] that is commonly adopted in various quantum dissipation theories.…”

“…These include the formally exact Feynman-Vernon influence functional theory, [7] and its derivative-equivalence the hierarchical equations of motion (HEOM) formalism. [8][9][10][11][12][13][14] While the existing SBET deals with for response functions only, [3,4] the extended theory is concerned with the nonequilibrium steady-state quantum transport current through molecular junctions. In this context, the extended SBET provides an alternative approach to the NEGF formalism.…”

“…The extension to electron current transport would be straightforward on the basis of the fermionic SBET. [4] The remainder of this paper is organized as follows. In Sec.…”

Temperature-dependence of the subdivision potential in nanothermodynamics

“…It is reasonable to render the difference arises from that the thermodynamic limit is not satisfied for small systems. Thermodynamic integration -Now, we apply the thermodynamic integration for the free energy F , as done in our previous works [11,12]. Consider a λ-augmented form of Eq.…”

“…( 18), we have defined ∆S therm/vN (T ) ≡ S therm/vN (T ; λ = 1) − S therm/vN (T ; λ = 0) and used the equality S vN (T ; λ = 0) = S therm (T ; λ = 0) due to the canonicity in the absence of system-bath interactions. Numerically, all these quantities can be computed via the dissipaton-equation-of-motion method (λ-dynamics formalism or imaginary-time formalism) [11][12][13], which is a second quantization generalization of the well-known hierarachical equations of motion, serving as a rigid approach to the dynamics of a specific system coupled to the Gaussian environments [14][15][16][17]. Example -As an example, we consider a spin-boson model…”