Lara C. Ortmanns, Maarten R. Wegewijs, Janine Splettstoesser
SciPost Phys. 14, 095 (2023) ·
published 4 May 2023
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· pdf
We analyze the time-dependent solution of master equations
by exploiting fermionic duality,
a dissipative symmetry applicable to a large class of open systems
describing quantum transport.
Whereas previous studies mostly exploited duality relations
after partially solving the evolution equations,
we here systematically exploit the invariance under the fermionic duality mapping
from the very beginning when setting up these equations.
Moreover, we extend
the resulting simplifications -so far applied to the local state evolution-
to non-local observables such as transport currents.
We showcase the exploitation of fermionic duality for a quantum dot with strong interaction -covering both the repulsive and attractive case-
proximized by contact with a large-gap superconductor
which is weakly probed by charge and heat currents
into a wide-band normal-metal electrode.
We derive the complete time-dependent analytical solution of this problem
involving non-equilibrium Cooper pair transport, Andreev bound states and strong interaction.
Additionally exploiting detailed balance
we show that even for this relatively complex problem
the evolution towards the stationary state can be understood analytically
in terms of the stationary state of the system itself
via its relation to the stationary state of a dual system
with inverted Coulomb interaction, superconducting pairing and applied voltages.
