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arXiv:0807.1415 · Nuclear Physics B

Towards a kinetic theory for fermions with quantum coherence

Matti Herranen, Kimmo Kainulainen, Pyry Matti Rahkila

Published Oct 2, 2008• 36 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2008.09.032

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In this work, we construct one-dimensional interacting lattice spinor theories with discretization in momentum space. We focus on strongly interacting Schwinger and Nambu--Jona-Lasinio models and perform ab-initio calculation of their single-particle and two-particle momentum distribution functions at finite temperature. We observe, at low temperature, high-momentum tail in single-particle and two particle distribution which reveals relative momentum in fermion-antifermion boundstates, as well as quasi-free spinor gases behavior at high temperature. The non-vanishing connected four-momentum function reveals the quantum coherence in momentum space under thermal equilibrium of the system and indicate the single particle correlation would remember more microscopic details within a thermal system. Overall, for a high-enough temperature at which the thermal kinetic energy comparable with the interaction, we observe that the two-particle correlation is subdominant compared to the single particle distributions, which indicates the applicability of kinetic theory.
Abstract We study the fluctuations of generic currents in multi-terminal, multi-channel coherent quantum transport settings. In the quantum regime, these fluctuations and the resulting precision differ strongly depending on whether the device is of fermionic or bosonic nature. Using scattering theory, we show that the precision is bounded by constraints set by the entropy production and by the activity in the spirit of thermodynamic or kinetic uncertainty relations, valid for fermionic and bosonic quantum systems also in the absence of time-reversal symmetry. Furthermore, we derive a combined thermodynamic kinetic uncertainty relation, which is tight over a wide range of parameters and can hence predict the reachable precision of a device. Since these constraints can be expressed in terms of observables accessible in transport measurements, such as currents and bandwidth, we foresee that the tight thermodynamic kinetic uncertainty-like bounds are also useful as an inference tool: they can be exploited to estimate entropy production from transport observables, such as the charge current and its noise, which are more easily accessible in experiment.
We demonstrate that quantum coherence can be generated by the interplay of coupling to an incoherent environment and kinetic processes. This joint effect even occurs in a repulsively interacting fermionic system initially prepared in an incoherent Mott insulating state. In this case, coupling a dissipative noise field to the local spin density produces coherent pairs of fermions. The generated pair coherence, while metastable, is long lived and spatially extended. This conceptually surprising approach provides a path towards a better control of quantum many-body correlations.