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We propose a quasi-particle description for the hierarchical equations of motion formalism for quantum dissipative dynamics systems. Not only it provides an alternative mathematical means to the existing formalism, the new protocol clarifies also explicitly the physical meanings of the auxiliary density operators and their relations to full statistics on solvation bath variables. Combining with the standard linear response theory, we construct further the hierarchical dynamics formalism for correlated spectrum of system--bath coherence. We evaluate the spectrum matrix for a demonstrative spin-boson system-bath model. While the individual diagonal element of the spectrum matrix describes the system or the solvation bath correlation, the off-diagonal elements characterize the correlation between system and bath solvation dynamics.
We study the coherence trapping of a qubit correlated initially with a non-Markovian bath in a pure dephasing channel. By considering the initial qubit-bath correlation and the bath spectral density, we find that the initial qubit-bath correlation ca
In this work, we establish a so-called system-bath entanglement theorem, for arbitrary systems coupled with Gaussian environments. This theorem connects the entangled system-bath response functions in the total composite space to those of local syste
A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields. An exact hi
We show that the change of the fluctuation spectrum near the quantum critical point (QCP) may result in the continuous change of critical exponents with temperature due to the increase in the effective dimensionality upon approach to QCP. The latter
Understanding non-equilibrium heat transport is crucial for controling heat flow in nano-scale systems. We study thermal energy transfer in a generalized non-equilibrium spin-boson model (NESB) with non-commutative system-bath coupling operators and