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Optimizing hierarchical equations of motion for quantum dissipation and quantifying quantum bath effects on quantum transfer mechanisms

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10.1063/1.4724193

### Abstract

We present an optimized hierarchical equations of motion theory for quantum dissipation in multiple Brownian oscillators bath environment, followed by a mechanistic study on a model donor-bridge-acceptor system. We show that the optimal hierarchy construction, via the memory-frequency decomposition for any specified Brownian oscillators bath, is generally achievable through a universal pre-screening search. The algorithm goes by identifying the candidates for the best be just some selected Padé spectrum decomposition based schemes, together with *a priori* accuracy control criterions on the sole approximation, the white-noise residue ansatz, involved in the hierarchical construction. Beside the universal screening search, we also analytically identify the best for the case of Drude dissipation and that for the Brownian oscillators environment without strongly underdamped bath vibrations. For the mechanistic study, we quantify the quantum nature of bath influence and further address the issue of localization versus delocalization. Proposed are a reduced system entropymeasure and a state-resolved constructive versus destructive interference measure. Their performances on quantifying the correlated system-environment coherence are exemplified in conjunction with the optimized hierarchical equations of motion evaluation of the model system dynamics, at some representing bath parameters and temperatures. Analysis also reveals the localization to delocalization transition as temperature decreases.

© 2012 American Institute of Physics

Received 22 March 2012
Accepted 17 May 2012
Published online 11 June 2012

Acknowledgments: Support from the National Natural Science Foundation of China (NNSFC) (21033008 and 21073169), the National Basic Research Program of China (2010CB923300 and 2011CB921400), the Fundamental Research Funds for the Central Universities of China (2340000034), and the Hong Kong UGC (AoE/P-04/08-2) is gratefully acknowledged.

Article outline:

I. INTRODUCTION

II. BACKGROUND

A. Hierarchical equations of motion formalism

B. Brownian oscillators bath

C. Three PSD approximants of Bose function

III. OPTIMIZING HEOM WITH ACCURACY CONTROL: GENERAL CONSIDERATIONS

A. The bath decomposition schemes

B. Accuracy control on white noise residue ansatz

C. Search for the best HEOM construction

IV. TWO SPECIAL CASES: ANALYTICAL IDENTIFICATIONS

A. [*N*/*N*] the best for Drude dissipation

B. [*N* + 1/*N*] the best for BO dissipation of *r* _{BO} ⩾ 0.5

V. QUANTIFYING QUANTUM BATH EFFECTS ON QUANTUM TRANSFER MECHANISMS

VI. CONCLUDING REMARKS

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2012-06-11

2014-04-19

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