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This article aims at providing a self-contained introduction to theoretical modeling of gate-induced carrier density in graphene sheets. For this, relevant theories are introduced, namely, classical capacitance model (CCM), self-consistent…
We present a factor graph formulation and particle-based sum-product algorithm for robust localization and tracking in multipath-prone environments. The proposed sequential algorithm jointly estimates the mobile agent's position together…
We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between…
Two long-standing problems in the construction of coherent state path integrals, the unwarranted assumption of path continuity and the ambiguous definition of the Hamiltonian symbol, are rigorously solved. To this end the fully controlled…
Quantum transport properties of disordered graphene with structural defects (Stone-Wales and divacancies) are investigated using a realistic {\pi}-{\pi}* tight-binding model elaborated from ab initio calculations. Mean free paths and…
In autonomous driving, accurately interpreting the movements of other road users and leveraging this knowledge to forecast future trajectories is crucial. This is typically achieved through the integration of map data and tracked…
We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
Graph states are a key resource for measurement-based quantum computation and quantum networking, but state-preparation costs limit their practical use. Graph states related by local complement (LC) operations are equivalent up to…
We theoretically study magnetic ground states of doped zigzag graphene nanoribbons and the emergence of topological domain walls. Using the Hartree-Fock mean-field approach and an effective continuum model, we demonstrated that the carrier…
We provide a method for the generation of effective continuum Hamiltonians that goes beyond the well known k.p method in being equally effective in both high, and low (or no) symmetry situations. Our approach is based on a surprising exact…
Counter-diabatic driving protocols were proposed as a means to do fast changes in the Hamiltonian without exciting transitions. Such driving in principle allows one to realize arbitrarily fast annealing protocols or implement fast…
We consider the role of non-localities in speed-density data used to fit fundamental diagrams from vehicle trajectories. We demonstrate that the use of anticipated densities results in a clear classification of speed-density data into…
For an $n$-vertex graph $G$, let $z(G;k)$ denote the number of zero forcing sets of size $k$. A conjecture of Boyer et al. asserts that the path $P_n$ maximizes these numbers coefficientwise among all $n$-vertex graphs; equivalently, the…
Topological invariants, rigorously defined only in the thermodynamic limit, have been generalized to topological indicators applicable to finite-size disordered systems. However, in many experimentally relevant situations, such as…
Aharonov and Casher showed that Pauli Hamiltonians in two dimensions have gapless zero modes. We study the adiabatic evolution of these modes under the slow motion of $N$ fluxons with fluxes $\Phi_a\in\mathbb{R}$. The positions,…
Topological phases of gapped one-particle Hamiltonians with (anti)-unitary symmetries are classified by strong topological invariants according to the Altland-Zirnbauer table. Those indices are still well-defined in the regime of strong…
The strategy of shortcuts to adiabaticity enables us to realize adiabatic dynamics in finite time. In the counter-diabatic driving approach, an auxiliary Hamiltonian which is called the counter-diabatic Hamiltonian is appended to an…
Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta $\Lambda$ in the Brillouin zone (BZ) with protected degeneracies at $\Lambda$. Commonly TIs are distinguished from trivial…
We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a…