## Quantum scars

A quantum scar corresponds to enhanced density along an unstable classical periodic orbit (Eric Heller, 1984). In our recent article in Scientific Reports, we have shown that two-dimensional (2D) separable quantum systems perturbed by randomly distributed bumps show a new type of scarring, which is unexpectedly strong and robust. These scars follow the classical orbits of the corresponding unperturbed system (without bumps).

We are currently studying quantum scars in magnetic fields and plan to utilize them also in quantum transport. In the calculation of scars we use our freely available itp2D code that can solve thousands of eigenstates in an arbitrary 2D potential.

FIG: Pentagram-shaped quantum scar appears in a r⁵-type potential as the amplitude (A) of the background distortion (Gaussian bumps) is increased

## Quantum control

We use quantum optimal control theory (OCT) to design optimized external fields such as laser pulses to drive the system from an initial state to a predefined target. We have used OCT for both semiconductor nanostructures (see figure below) and atomic and molecular systems. In the first case, we have proposed a coherent spin switch in a quantum ring which could be applied as a **single-qubit gate** [Phys. Rev. Lett. **98**, 157404 (2007)]. Along these lines we have also designed a **coherent charge switches** using optical fields [Phys. Rev. B **86**, 205308 (2012)] or local voltage gates [Phys. Rev. B **87**, 241303(R) (2013)].

In atomic systems, we have developed and applied OCT, for example, to enhance ionization in H2+ molecules [Europhys. Lett. **87**, 53001 (2009)] and proposed a scheme to suppress ionization by light field control [Phys. Rev. A **86**, 033426 (2012)]. We have also established a control scheme on **high-harmonic generation** [Phys. Rev. A **90**, 053402 (2014)]. More recently, we have developed and applied OCT to the control of photoelectrons and Rydberg states.

FIG: Two proposed schemes to coherently control coupled quantum dots in an optimized manner. The system is either coupled to an optical field (a) or to a gate voltage (b).

## Quantum transport and dynamics

Within quantum transport, we have studied the many-electron Aharonov-Bohm (AB) effect in quantum rings [Phys. Rev. B **81**, 245316 (2010)] as well as in AB interferometers [New. J. Phys. **14**, 053024 (2012)]. In addition, we have examined real-space quantum transport accross chaotic cavities such as stadium-shaped quantum dots [Phys. Rev. E **88**, 022913 (2013)]. In essence, we have found that the magnetoconductance in chaotic quantum dots has fractal properties in a qualitative agreement with experiments. We are currently extending our scheme to examine equilibrium transport through scarred eigenstates (see quantum scars above).

## 2D Materials for Quantum Technologies

2-dimensional and layered materials, such as transition metal dichalcogenides (TMD) provide a promising platform for developing components for novel semiconductor- superconductor hybrid devices, such as sensors, switches, qubits and logical components in nanometer-scale electronics. Especially edges and interfaces lead to tunable electronic properties, which can be utilized in, e.g, control of spin polarized currents or proximity induced superconductivity in semimetallic or semiconducting heterostructures. In modeling appropriate materials, we utilize Nambu-Gorkov Green’s function approach in materials specific tight-binding basis, which allow controlled inclusion of, e.g., Hamiltonian matrix elements for spin-orbit

coupling or superconducting pairing, as well as coupling to bosonic modes in form of self-energies in Dyson’s equation.

Among our recent studies, we have modeled proximity induced superconductivity in monolayer MoS2 on Pb [ACS Nano 2020], which project was lead by prof. Maria Iavarone at Temple University. Among the earlier highlights are as study of edge states of Ag/Si(111) reconstructed surfaces [Applied Physics Letters 2019], modeling superconductivity in metal decorated graphene [Journal of Physics 2017], electrically tunable spin-polarized tunneling channels in silicene sheets [APL 2014] and modeling interplay between strain and doping in high-temperature superconductors [Nano Letters2014].

## Artificial graphene

Artificial graphene is a recently realized man-made nanosystem that exhibits graphene-like physics in a tunable setup. The system can be created by, e.g., positioning molecules in a triangular lattice on a metal surface, or by patterning quantum dots in a honeycomb configuration.

In our recent studies we have examined electron-electron interactions in semiconductor artificial graphene [Phys. Rev. Lett. **108**, 246803 (2012)]. We have also examined the emergence of Dirac physics in finite flakes of artificial graphene [Phys. Rev. B **89**, 235433 (2014)]. Our first-principles simulations on molecular graphene have revealed co-existing band structures arising from both the honeycomb lattice as well as the Kagome lattice. These results were published in Nano Letters in 2016.

## Density-functional theories

Density-functional theory (DFT) has been the most successful approach for first-principles studies in quantum chemistry. Its practical bottleneck is the exchange-correlation functional, for which we develop accurate and computationally efficient approximations. We focus on both three-dimensional functionals in view of atoms and molecules (see, e.g., J. Chem. Phys. **132**, 044112 (2010)) and two-dimensional approximations in view of quantum dots, wires, and rings (see, e.g., Phys. Rev. B **80**, 165112 (2009)). We have also studied the theoretical constraints and bounds for the indirect Coulomb interaction (Phys. Rev. Lett. **102**, 206406 (2009)).

More recently, we have focused on time-dependent DFT (TDDFT) and examined its capability to capture strong-field effects in atoms and molecules. In the soft X-ray regime of laser pulses produced with free-electron lasers, TDDFT seems to be a valid approach to describe multielectron ionization as demonstrated in Phys. Rev. A **90**, 033412 (2014).

## Time-series analysis the heartbeat and heart cell signals

TO BE UPDATED!

## The physics of drumming

What is the similarity between a romanesco broccoli and drumming? Well, the common feature is fractality: in the case of broccoli the geometry is self-similar with repeating patterns at smaller and smaller scales. In drumming, fractals appear in human fluctuations from a “perfect” metronome-type pulse. Fractal fluctuations play a role behind the musical groove, and they seem to be present in famous recording of virtuoso drummers as shown in our paper, PLoS ONE 10(6): e0127902 (2015).

Our study has attracted quite a bit of attention with, e.g., a feature story in the Science Magazine and a very nice video on the Sixty Symbols Youtube Channel – thanks to Prof. Philip Moriarty! We are currently extended our drumming research on a variety of interesting issues … stay tuned!