Entangled system-and-environment dynamics: Phase–space dissipaton theory

Abstract

Dissipaton-equation-of-motion (DEOM) theory [Y. J. Yan, J. Chem. Phys. 140, 054105 (2014)] is an exact and nonperturbative many-particle method for open quantum systems. The existing dissipaton algebra treats also the dynamics of hybrid bath solvation coordinates. The dynamics of conjugate momentums remain to be addressed within the DEOM framework. In this work, we establish this missing ingredient, the dissipaton algebra on solvation momentums, with rigorous validations against necessary and sufficient criteria. The resulted phase-space DEOM theory will serve as a solid ground for further developments of various practical methods toward a broad range of applications. We illustrate this novel dissipaton algebra with the phase-space DEOM-evaluation on heat current fluctuation.

Nonequilibrium system-bath entanglement theorem versus heat transport

“…The existing dissipaton equation of motion theory can be exploited to the direct evaluation on the transport current and the noise spectrum. [19][20][21] The quantity of interest in this section is…”

“…The direct evaluation can be carried out by exploiting the established dissipaton equation of motion (DEOM) theory. [21] In the following, we will establish the extended SBET for the indirect evaluation of Eq. ( 19).…”

A nonequilibrium statistical quasi-particles thermofield theory

“…We will further exploit this theory to establish relations between some important equilibrium or nonequilibrium steady-state correlation functions, between the aribitary system and non-Markovian hybrid environment modes. These universal relations can all be validated, by the exact dissipaton equation of motion (DEOM) approach [18][19][20]. The latter is an accurate and versatile theory, which extends the convention hierarchical equations of motion [21][22][23][24][25][26] to cover not only the reduced system but also the hybrid environment dynamics.…”

“…The latter is an accurate and versatile theory, which extends the convention hierarchical equations of motion [21][22][23][24][25][26] to cover not only the reduced system but also the hybrid environment dynamics. The DEOM theory introduces the concept of dissipaton, together with the dissipaton algebra [18][19][20]. The emerging Lindblad's form of core-system QDTs adopt also certain discrete pseudo-mode system-environment couplings descriptions [27][28][29].…”

“…where ρ T (t; Â) is an augmented total composite density operator that can be either Âρ T (t) or ρ T (t) Â. The generalized diffusion equation established earlier in the DEOM theory [18][19][20] goes now by its absorptive (+) and emissive (−) components. Equations ( 6)-( 9) constitute the main ingredients of DTF formalism in this work.…”