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Dynamics of open fermionic nano-systems -- a fundamental symmetry and its application to electron transport in interacting quantum dots
Doctoral thesis, 2018

*time-dependently*controlled operations on individual electrons, promising applications in, e.g., metrology and electron-based quantum computing. In particular, fundamental questions of quantum thermodynamics and the practical necessity to recover waste heat from nanocircuits have attracted attention towards

*electronic energy currents*.

The research articles covered by this thesis contribute to this topic by deriving and exploring a fundamental symmetry relation -- the

*fermionic duality*. This duality applies to the quantum master equation of

*any*locally interacting, fermionic open quantum system tunnel-coupled to non-interacting reservoirs. It yields a crosslink between modes and amplitudes corresponding to the evolution rates in the time-dependent decay of the open-system state. This crosslink involves a mapping between the system of interest and a

*dual*system with inverted environment potentials, local energies, and thus especially inverted interactions. The duality thereby explains many, at first sight unintuitive, transport features and significantly improves their analytic accessability. In particular, we can understand why charge- and energy currents through quantum dots with strong local Coulomb repulsion in fact exhibit features of electron-electron

*attraction*, both in the time-dependent decay after a sudden switch and in the stationary limit.

More fundamental insights are obtained by identifying the duality to be rooted in Pauli's exclusion principle and the parity superselection principle. Namely, this implies that the duality is independent of, and hence combinable with many other general symmetries, including particle-hole symmetry, time-reversal symmetry, detailed balance and Onsager reciprocity. Especially the combination with the latter offers a novel perspective on the thermoelectric response of open, locally interacting electronic nanosystems.

fermion parity

voltage switch

quantum dot

open fermionic quantum system

fermionic duality

master equation

non-equilibrium transport

charging energy

inverted energy

transient response

energy-dependent coupling

## Author

### Jens Schulenborg

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

### Schulenborg, J. and Splettstoesser, J. and Wegewijs, M. R.: Duality for open fermion systems: energy-dependent weak coupling and quantum master equations

### Thermoelectrics of Interacting Nanosystems -- Exploiting Superselection Instead of Time-Reversal Symmetry

Entropy,; Vol. 19(2017)

**Journal article**

### Fermion-parity duality and energy relaxation in interacting open systems

Physical Review B: covering condensed matter and materials physics,; Vol. 93(2016)p. 081411-

**Journal article**

### Relaxation of quantum dots in a magnetic field at finite bias - charge, spin and heat currents

Physica Status Solidi (B): Basic Research,; Vol. 254(2017)

**Journal article**

### Detection of the relaxation rates of an interacting quantum dot by a capacitively coupled sensor dot

Physical Review B - Condensed Matter and Materials Physics,; Vol. 89(2014)p. 195305-

**Journal article**

The devices of interest are so-called quantum dots. Such quantum dots are essentially nanoscale "charge boxes" that can absorb, store and emit a very small number of electrons, and hence serve as important building blocks for more complex nanodevices. As is well-known for equal charges brought closely together, electrons in quantum dots often exert a strongly repulsive force onto each other. Surprisingly, the central insight of this work is that their behavior is in many ways much better understood from a hypothetical situation in which they instead attract each other. Despite being a direct consequence of well-known fundamental symmetry principles, this relation has so far been overlooked. Its various applications in this thesis, however, demonstrate that it substantially simplifies the solution to complicated problems of current scientific and technological relevance.

### Areas of Advance

Nanoscience and Nanotechnology (2010-2017)

### Subject Categories

Physical Sciences

Condensed Matter Physics

### ISBN

978-91-7597-781-2

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4462

### Publisher

Chalmers University of Technology

Kollektorn (A423), MC2, Kemivägen 9, Chalmers

Opponent: Prof. Dr. Milena Grifoni, Institute I - Theoretical Physics, Regensburg University, Germany