Related papers: Topological bulk-edge effects in quantum graph tra…
Topological states require the presence of extended bulk states, as usually found in the picture of energy bands and topological states bridging the bulk gaps. But in driven systems this can be circumvented, and one can get topological…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
Transport in strongly correlated fermions cannot be understood by fermionic quasiparticles alone. We present a theoretical framework for quantum transport that incorporates strong local correlations of fermion pairs. These contact…
Dissipation is a common occurrence in real-world systems and is generally considered to be detrimental to transport. In this study, we examine the transport properties of a narrow quantum anomalous Hall system with dissipation applied on…
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by…
We present a static framework for analysing quantum routing protocols that we call the \textit{cost-vector formalism}. Here, quantum networks are recast as multi-graphs where edges represent two-qubit entanglement resources that…
Quantized transport is a prominent feature in topological physics, with canonical examples being the quantum Hall effect and adiabatic Thouless pump, which are based on the Chern number, a topological invariant of 2D systems. Going beyond…
Quantum effects play an important role in quantum measurement theory. The set of all quantum effects can be organized into an algebraical structure called effect algebra. In this paper, we study various topologies on the Hilbert space…
The topological pumping [1-3] is revisited from a view point of the bulk-edge correspondence. Shift of the center of mass (CM) as a pumped charge is explicitly given by the Berry connection in time direction. We show that observed pumping…
The exponential speed-up of quantum walks on certain graphs, relative to classical particles diffusing on the same graph, is a striking observation. It has suggested the possibility of new fast quantum algorithms. We point out here that…
Certain topological systems with time-varying Hamiltonian enable quantized and disorder-robust transport of excitations. Here, we introduce the modification of the celebrated Thouless pump when the on-site energies remain fixed, while the…
We explore theoretically how the coupling to cavity vacuum fields affects the electron transport in quantum conductors due to the counter-rotating-wave terms of light-matter interaction. We determine the quantum conductance in terms of the…
The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a randomly chosen momentum belongs to the spectrum of the periodic…
Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often deviates the edge anticrossing even into the bulk, where corner…
A Floquet systems is a periodically driven quantum system. It can be described by a Floquet operator. If this unitary operator has a gap in the spectrum, then one can define associated topological bulk invariants which can either only…
A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be…
We theoretically study the electron transport properties in a ferromagnetic/normal/ferromagnetic tunnel junction, which is deposited on the top of a topological surface. The conductance at the parallel (\textbf{P}) configuration can be much…
Novel classical wave phenomenon analogs of the quantum spin Hall effect are mostly based on the construction of pseudo-spins. Here we show that the non-trivial topology of a system can also be realized using orbital angular momentum through…
Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic,…
We suggest a way of confining quasiparticles by an external potential in a small region of a graphene strip. Transversal electron motion plays a crucial role in this confinement. Properties of thus obtained graphene quantum dots are…