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Register a new userStatistical Generalization of Regenerative Bosonic and Fermionic Stirling Cycles
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We have constructed an unified framework for generalizing the finite-time thermodynamic behavior of statistically distinct bosonic and fermionic Stirling cycles with regenerative characteristics. In our formalism, working fluid consisting of particles obeying Fermi-Dirac and Bose-Einstein statistics are treated under equal footing and modelled as a collection of non-interacting harmonic and fermionic oscillators. In terms of frequency and population of the two oscillators, we have provided an interesting generalization for the definitions of heat and work that are valid for classical as well as non-classical working fluids. Based on a generic setting under finite time relaxation dynamics, novel results on low and high temperature heat transfer rates are derived. Characterized by equal power, efficiency, entropy production, cycle time and coefficient of performance, thermodynamic equivalence between two types of Stirling cycles is established in the low temperature ``quantum regime.
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We consider the application of the original Meyer-Miller (MM) Hamiltonian to mapping fermionic quantum dynamics to classical equations of motion. Non-interacting fermionic and bosonic systems share the same one-body density dynamics when evolving from the same initial many-body state. The MM classical mapping is exact for non-interacting bosons, and therefore it yields the exact time-dependent one-body density for non-interacting fermions as well. Starting from this observation, the MM mapping is compared to different mappings specific for fermionic systems, namely the spin mapping (SM) with and without including a Jordan-Wigner transformation, and the Li-Miller mapping (LMM). For non-interacting systems, the inclusion of fermionic anti-symmetry through the Jordan-Wigner transform does not lead to any improvement in the performance of the mappings and instead it worsens the classical description. For an interacting impurity model and for models of excitonic energy transfer, the MM and LMM mappings perform similarly, and in some cases the former outperforms the latter when compared to a full quantum description. The classical mappings are able to capture interference effects, both constructive and destructive, that originate from equivalent energy transfer pathways in the models.
The hierarchical equations of motion (HEOM) method is a powerful numerical approach to solve the dynamics and steady-state of a quantum system coupled to a non-Markovian and non-perturbative environment. Originally developed in the context of physical chemistry, it has also been extended and applied to problems in solid-state physics, optics, single-molecule electronics, and biological physics. Here we present a numerical library in Python, integrated with the powerful QuTiP platform, which implements the HEOM for both bosonic and fermionic environments. We demonstrate its utility with a series of examples. For the bosonic case, we present examples for fitting arbitrary spectral densities, modelling a Fenna-Matthews-Olsen photosynthetic complex, and simulating dynamical decoupling of a spin from its environment. For the fermionic case, we present an integrable single-impurity example, used as a benchmark of the code, and a more complex example of an impurity strongly coupled to a single vibronic mode, with applications in single-molecule electronics.
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