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By periodically driving the temperature of reservoirs in a quantum heat engine, geometric or Pancharatnam-Berry phase-like (PBp) effects in the thermodynamics can be observed. The PBp can be identified from a generating function (GF) method within an adiabatic quantum Markovian master equation formalism. The GF is shown not to lead to a standard open quantum system's fluctuation theorem in presence of phase-different modulations with an inapplicability in the use of large deviation theory. Effect of quantum coherences in optimizing the flux is nullified due to PBp contributions. The linear coefficient, 1/2, which is universal in the expansion of the efficiency at maximum power in terms of Carnot efficiency no longer holds true in presence of PBp effects.

Cyclic Pancharatnam-Berry (PB) and adiabatic noncyclic geometric (ANG) effects are investigated in a single electron orbital system connected to two metal contacts with externally driven chemical potential and/or temperatures. The PB contribution doesn't affect the density matrix evolution, but has quantitative effect on the statistics (fluctuations) of electron transfer. The ANG contribution, on the other hand, affects the net flux across the junction. Unlike the PB, the ANG contribution is non-zero when two parameters are identically driven. Closed analytical expressions are derived for the ANG contribution to the flux, and the PB contribution to the first two leading order fluctuations. Fluctuations can be modified by manipulating the relative phases of the drivings. Interestingly, we find that the fluctuations of the pumped charge do not satisfy the steady state fluctuation theorem in presence of nonzero geometric contribution, but can be recovered for a vanishing geometric contribution even in presence of the external driving.

We compute electroluminescent signal in a current carrying single molecule junction using a superoperator formalism. Liouville space loop diagrams are used to identify all density matrix pathways that emit photons via the electroluminescence process. A frequency resolved spectrum is expressed in terms of the various Fock space states of the isolated molecule that participate in the creation and subsequent recombination of exciton. Application is made to a multilevel Coulomb blockade model system and to a gold-benzene-1,4-dithiol-gold molecular junction.

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