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Recently, a general theory of non-equilibrium dynamics is developed [1,2] for non
Markovian open quantum systems of bosons (fermions) interacting with a general bosonic
(fermionic) environment. The exact dissipation and fluctuation dynamics of the open
system is explored through an exact master equation, determined by the non-equilibrium
Green’s functions which account for all the information of non Markovian back-action
memory effects. Using this approach, we develop [3] a non-equilibrium theory of quantum
thermodynamics for arbitrary quantum systems in contact with heat reservoirs. This creates
a new paradigm to the topic of quantum thermodynamics for mesoscopic and nanoscale
systems. We address the issue of real-time thermodynamics that is thermodynamic
processes taking place under non-equilibrium situations. This non-equilibrium theory of
quantum thermodynamics unravels (i) the emergence of classical thermodynamics from
quantum dynamics of a single particle system in the weak system-reservoir coupling
regime; (ii) the breakdown of classical thermodynamics in the strong coupling regime,
induced by non-Markovian memory dynamics; and (iii) the occurrence of negative
temperature associated with a dynamical quantum phase transition. The third law of
thermodynamics, allocated in the deep quantum realm, is also proved in our theory.
Through this exact master equation approach, we also examine [4] the exact decoherence
dynamics and non-Markovian noise power spectrum obtained through the Fourier
transform of the exact two time correlation function for a resonator system coupled to an
electromagnetic reservoir characterized by a low frequency 1/f noise at finite temperature.
We also apply this approach to investigate the transient dynamics of photon statistics
through two-time correlation function g2 for optical fields [5]. We find that the transient
correlations at different time yield a smooth transition from antibunching to bunching
photon statistics in the weak system-environment coupling regime. In the strong-coupling
regime, the two-time correlations exhibit bunching antibunching oscillations that persists
both in the transient process and in the steady-state limit. The photon bunching
antibunching oscillations is a manifestation of strong non-Markovian dynamics, where the
system remains in nonequilibrium from its environment. Recently, we also introduce a non
Markovianity measure [6] using two-time correlation functions which shows interesting
short-time and long-time behaviors depending upon the properties of the system and
reservoir. Such a non-Markovianity [1-10] can be directly measured in experiments since
two time correlation functions are experimentally measurable. In the end, we briefly
discuss on our ongoing projects of probing nonclassical electron transport through quantum
nanostructure, quantum optomechanical heat machine-beyond weak coupling, and real
time dynamics of nonequilibrium transport through quantum dot in the Kondo regime.
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[1] Wei-Min Zhang et al., General non-Markovian dynamics of open quantum systems,
Phys. Rev. Lett. 109, 170402 (2012).
https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.109.170402
[2] Wei-Min Zhang et al., Non-equilibrium quantum theory for Nano-devices based on the Feynman-Vernon
influence functional, New J. Phys. 12, 083013 (2010).
http://iopscience.iop.org/article/10.1088/1367-2630/12/8/083013/pdf
[3] Md. Manirul Ali (Corr auth.), Wei-Min Zhang, Nonequilibrium quantum thermodynamics for open
quantum systems, (submitted to Phys. Rev. A) arXiv:1803.04658 (2018).
https://arxiv.org/pdf/1803.04658.pdf
[4] Md. Manirul Ali (Corr auth.), Ping-Yuan Lo, Wei-Min Zhang, Exact decoherence dynamics of 1/f noise,
New J. Phys. 16, 103010 (2014). http://iopscience.iop.org/article/10.1088/1367-2630/16/10/103010/pdf
[5] Md. Manirul Ali (Corr auth.), Wei-Min Zhang, Nonequilibrium transient dynamics of photon statistics,
Phys. Rev. A 95, 033830 (2017). https://journals.aps.org/pra/pdf/10.1103/PhysRevA.95.033830
[6] Md. Manirul Ali (Corr auth.), P. Y. Lo, M. W. Y. Tu, W. M. Zhang, Non-Markovianity measure using
two-time correlation functions, Phys. Rev. A 92, 062306 (2015).
https://journals.aps.org/pra/pdf/10.1103/PhysRevA.92.062306
[7] Md. Manirul Ali, Po-Wen Chen and Hsi-Sheng Goan, Decoherence-free subspace and disentanglement
dynamics for two qubits in a common non-Markovian squeezed reservoir, Phys. Rev. A 82, 022103
(2010). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.82.022103
[8] Po-Wen Chen, Md. Manirul Ali, Shiaw-Huei Chen, Enhanced quantum nonlocality induced by the
memory of thermal-squeezed environment, J. Phys. A: Math. Theor. 49, 395302 (2016).
http://iopscience.iop.org/article/10.1088/1751-8113/49/39/395302/meta
[9] Md. Manirul Ali (Corr auth.), Po-Wen Chen, Probing nonclassicality under dissipation, J. Phys. A:
Math. Theor. 50, 435303 (2017). http://iopscience.iop.org/article/10.1088/1751-8121/aa8bd8
[10] Po-Wen Chen, Md. Manirul Ali (Corr auth.), Investigating Leggett-Garg inequality for a two level
system under decoherence in a non-Markovian dephasing environment, Scientific Reports (Nature
Publishing Group) 4, 6165 (2014). https://www.nature.com/articles/srep06165
[11] C. Radhakrishnan, P. W. Chen, S. Jambulingam, Tim Byrnes, and Md. Manirul Ali (Corr. auth.), Time
dynamics of quantum coherence and m |