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febrero 19, 2018 @ 2:30 pm - 4:00 pm
In my talk I will present an overview of geometric phases introduced in the study of driven open quantum systems, in particular in relation to pumping effects in quantum dots which can be generated entirely by interaction effects.
I will first show that generally pumping phases arise due to a very concrete gauge freedom in the description of charge transport measurements: the calibration of the external meter that registers the transported charge. I will discuss how an ideal ”noisy meter” with known “noise” can in principle be used to reliably measure transport and show how this directly implies that extra geometric contributions appear in all the statistical moments of the transported charge when driving the open system.
The gauge freedom is usually silently fixed in derivations of master-equation current formulas thereby obscuring the origin of the geometric phases. Remarkably, gauge transformations that vary arbitrarily fast in time are not in conflict with the Markovian approximation, and, in fact, excluding them would break gauge invariance. Moreover, our approach extends to geometric phases for open system governed by general non-Markovian quantum master equations of the Nakajima-Zwanzig type.
Finally, I will show that the measurement process is also the key to resolving apparently conflicting physical claims made in two “schools” of pumping formalisms: by explicitly changing the boundary of the open system from including the meter to excluding it, Berry’s adiabatic phase is transformed into Landsberg’s (leading) nonadiabatic phase. This indicates that a relation between geometry and accessible information in open systems. In striking contrast to closed systems, we find that purely geometric considerations can be in conflict with the physical restriction of the positivity of the quantum state, which translates into a violation of Bochner’s criterion for the statistic of transport.
Reference: T. Pluecker, M. R. Wegewijs, J. Splettstoesser, arxiv 1711.10431 (2018)