Accurately characterizing the properties of semiconductors at atomic resolution is crucial for advancing semiconductor technology. One of the key challenges in quantitatively interpreting Scanning Tunneling Spectroscopy (STS) is the influence of tipinduced band bending (TIBB) during semiconductor measurements. This thesis presents a numerical method that self-consistently solves the one-dimensional Poisson equation to correct for TIBB in adatom-covered semiconductors. The model uses the Block-SOR-Newton method to solve the nonlinear system of equations that arises from the discretization of the Poisson equation. Simulations demonstrate that the model can accurately describe the effect of the STM tip voltage on band bending. However, numerical instabilities were observed for high doping concentrations and surface state energies close to the Fermi level, attributed to overshooting of the Newton method. Potential solutions, such as using a Newton-Krylov method and adaptive grid refinement, were proposed to address these instabilities. Future work includes extending the model to non-equilibrium situations by introducing the full set of semiconductor equations and expanding to three dimensions to account for the STM tip geometry. These advancements would provide a useful tool for correcting STS data, ultimately deepening our understanding of semiconductor physics at the atomic scale.

The DESHIMA 2.0 spectrometer, installed on the ASTE telescope, is designed to enable broadband, high-sensitivity observations in the submillimetre wavelength range. This design allows simultaneous observation across a wide frequency range, making it possible to detect multiple emission lines in a single measurement. This is particularly useful for identifying emission lines from distant galaxies with unknown redshifts, allowing redshift determination in a single observation. This study evaluates the sensitivity and noise limitations of DESHIMA 2.0, addressing whether its on-sky performance aligns with a photon-noise model and lab-measured instrument characteristics.

First, the sensitivity of DESHIMA 2.0, integrated with the ASTE telescope, is assessed under fixed tele- scope conditions by observing the atmospheric signal without nodding the telescope or beam-switching. Observations confirm that the instrument operates near the photon-noise limit, consistent with theoret- ical predictions and laboratory measurements.

Next, a combined ABBA chopping-and-nodding technique, which integrates beam-switching with nod- ding of the telescope, is implemented to mitigate atmospheric noise during observations. This study demonstrates that this approach effectively filters out atmospheric noise over integration times of up to 3000 seconds, achieving a standard deviation of the noise level on the order of 10−4 K in the 250 to 300 GHz range. These findings confirm that the instrument maintains photon-noise-limited perfor- mance under varying atmospheric conditions.

Finally, the observed spectrum of Mars is compared to its known spectral characteristics to validate the sensitivity and calibration of DESHIMA 2.0 for bright astronomical sources. Although the observed spectrum closely resembles the known spectrum of Mars, the remaining channel-to-channel deviations exceed what the photon-noise model predicts. This highlights the presence of systematic calibration er- rors and deviations in noise behaviour. These results underscore the need for further refinement of the calibration process and the ABBA chopping analysis to enhance performance for fainter astronomical sources.

Overall, this study establishes that DESHIMA 2.0 achieves photon-noise-limited performance under specific observational setups, marking an important milestone for high-sensitivity submillimetre astron- omy. However, further work is needed to optimize the system for detecting weaker signals from distant sources, such as dusty star-forming galaxies, where signal strengths are much weaker.

Each violin generates a unique sound with a distinct set of acoustic properties. In particular, the Stradivarius violins are said to have a very unique sound. The ultimate goal of this thesis is to aid in recreating the unique sound of the Stradivarius. Though, the field of research surrounding the violin and its acoustic properties is very broad and many aspects of this research, such as subtle structural differences between violins, fall beyond the scope of this thesis. Rather, the goal of this thesis is to provide the tools to find the differences between different violins. This thesis is split into two parts. In the first part, a literature review, describing the different parts of the violin, is presented along with an overview of different experiments and finite element models, describing the plate dynamics of the violin. In the second part, a model of the violin is devised, with modelling cycles based on consecutive simplification, and implemented in Python using finite difference equations and the method of lines. This model is made with the goal to provide a framework for creating a realistic model of the violin where differences in timbre between violins can shown. In the literature review, four subjects are addressed. First, an explanation on timbre is given with an illustration of its perception. Additionally the timbre of historical and contemporary violins is compared. Second, the radiated sound of the violin is discussed. In specific, the problem with directivity of radiation is brought to attention. Third, an overview of the bridge is given with a strong emphasis on the influence of the bridge admittance on the radiated sound. Last, the corpus is dissected into different parts which are investigated with optical sensors and modelled with the software packages Comsol and Abaqus. The model in the second part of the thesis is based on principle of consecutive simplification. To set the groundwork for further iterations of the model, the most important assumptions are kept track off. The method of lines is then used to simulate the vibrations of a wooden square plate using the flexural wave equation as the governing equation of motion. In this simulation, the forward Euler method is used for the numerical time integration. The steady state solutions of the numerical model are coherent with the analytical solutions to the flexural wave equation. However, the time dependent results diverge from the results shown in the literature study. This is either due numerical time integration method being unstable or due to the physical properties of the wood not being translated by the stiffness matrix in the model.

To better understand the formation of stars in dusty star-forming galaxies (DSFGs), and the evolution of this type of submillimeter galaxies (SMGs), it is of high significance to perform submillimeter/far-infrared surveys. The Deep Spectroscopic High-redshift Mapper 2.0 (DESHIMA2.0) on the ASTE telescope in Chile has been designed to observe the redshifted emission lines of these DSFGs to measure both their (spectroscopic) redshifts and molecular compositions. DESHIMA2.0 is designed to observe across the 220-440 GHz frequency band using its 347 channel integrated superconducting spectrometer (ISS) chip.

The current DESHIMA2.0 instrument has been tested in the lab. Its 332 filter channels with center frequencies in the range of 204-391 GHz have a spectral resolution of f/δf ≈ 340. Their coupling efficiencies can be approximated by Lorentzian functions.

The gravitationally lensed ultraluminous high-redshift DSFG J1329+2243 with redshift z = 2.04 shows emission lines of molecular gases like CO and H2O in the frequency band of DESHIMA2.0. Using the Time-dependent End-to-end Model for Post-process Optimization (TiEMPO), an 8-hour observation of the J1329+2243 galaxy has been simulated for both the lab-measured chip and the designed chip. Two measures of sensitivity, the noise equivalent flux density (NEFD) and the minimum detectable line flux (MDLF), are theoretically derived and subsequently used to be compared with the results of the simulations. The results yielded from these simulations are ultimately used to report on the overall performance of the lab-measured chip.

To run a TiEMPO simulation using the lab-measured chip, adaptations had to be made to the model for it to accept customizable chip data. Within TiEMPO, variable spectral resolutions and coupling efficiencies had to be introduced as well as a crucial addition to enable the creation of a new filterbank. Given the results of the simulations, it can be stated that this implementation of the lab-measured chip has been successful.

After applying an ON-OFF (dual) sky chopping technique to the simulated observation to cancel fluctuations of the atmospheric transmission, the atmosphere-corrected antenna temperature of the J1329+ 2243 galaxy could be found. The standard deviation of the noise showed to be scaling inversely proportional to the square root of the integration time. For five separate emission lines of the galaxy within the range of 200-310 GHz, a signal-to-noise ratio (SNR) analysis was performed and compared to the estimated theoretical proportionality to the square root of the integration time. For lines that show overlap in the spectrum, the detection was proven to be more difficult. Optimizations in the strategy used to define these signal-to-noise ratios would improve this finding.

The performance of the current DESHIMA2.0 instrument is sufficient to detect (SNR≥5) the bright CO(7-6) line of an ultraluminous high-redshift galaxy like J1329+2243 after 5.5 minutes of observation time. After 50 minutes of observation time, it is also capable of identifying the CO(6-5), the H2O(211-202), the [CI](2-1), and the CO(8-7) emission line.

This research investigates the impact of gravitational scatterings caused by close encounters between particles in an N-body Kepler system, addressing three main questions: (1) the influence of scatterings on system evolution, (2) the correspondence between simulated and expected average times between scatterings, and (3) the effect of increasing different parameters individually on the average scattering time. Simulations demonstrate an average scattering angle of 15.2 degrees for particles involved in the top 10 percent of scatterings. This would indicate a non-negligible impact of gravitational scatterings, especially for systems with heavier bodies. The results indicate that the simulated average time between scatterings is higher than the expected average, necessitating further research for accurate estimation. Moreover, the time between scatterings decreases over time, before reaching a stationary state after roughly 300 scatterings. On this domain, the correlation coefficient between the scattering time and the scattering counter was found to be  -0.08. By varying the test domains for different parameters, a new expression for the expected time between two scatterings is proposed based on simulation data. A clear connection was found between the scattering time and the number of particles, the maximum orbital radius and the maximum inclination angle. The study acknowledges limitations, including the non-stationary initialization state and linear approximations to most computations, suggesting avenues for future improvement. Overall, this research aims to find the role of gravitational scatterings in Kepler systems and underscores the need to consider these interactions, which are now often considered to be negligible.

For scaling up the qubits in silicon quantum computers, it is vital to determine crosstalk effects that can lower the fidelity of the computer.
In this computational project, we examine single-qubit gate-fidelities in the presence of crosstalk for uncoupled spin qubits that are driven with X-gates via electron dipole spin resonance (EDSR). We introduce two models: the first model introduces the AC Stark shift and the novel second model expands on this by adding a resonance frequency shift on top. We assume the latter resonance frequency shift to be due to heating effects. We optimize the gate-fidelity for a qubit coupled to up to six drives as a function of the overall driving time and -frequency of a single drive for both models using the Nelder-Mead algorithm.

Using the AC Stark shift model, we still obtain 0.99999 fidelity if we do not account for the crosstalk. However, when using the second model, the fidelity drops to 0.69 in the presence of two drives when we do not correct for the heating-induced resonance frequency shift and the AC Stark shift. Furthermore, the fidelity decreases linearly with the number of drives coupled to the qubit, implicating that the resonance frequency shift will become a significant problem for the scalability of silicon quantum computers. We find that we can correct for the resonance frequency shift entirely by using optimized driving time and -frequency, where most gain comes from optimizing the driving frequency. Moreover, we discover that there is a linearly increasing dependence of the resonance frequency shift at the theoretical driving time as a function of the total drives. Up to a translation factor of 0.5 MHz, we discover the same linear relationship for the correction needed on the theoretical driving frequency to hit maximum fidelity as a function of the total drives.

DESHIMA (the Deep Spectroscopic High-Redshift Mapper) is a 347 channel superconducting spectrometer with spectral resolution R =500 that operates in the range of 220GHz to 440GHz and can therefore accurately measure the frequency of spectral lines in order to calculate redshift z.
This report investigates the sensitivity of DESHIMA-like spectrometers by investigating photon noise due to Poisson and bunching effects. It gives a broad overview of photon statistics and explains, through an analogous model, that photon bunching occurs due to an underlying change in the probabilistics, rather than the act of detecting itself. After that I investigate photon and quasiparticle recombination noise for a DESHIMA-like spectrometer with Lorentzian filters and find a closed form equation for NEP per channel for a constant power spectral density arriving at the filters.
Previously the bandwidth of the filters was assumed to be negligible, resulting in an overestimation of the bunching. Because the photons that are impinging on the detector span a bigger bandwidth, the bunching is a factor of π/2 smaller than previously approximated.
This NEPτ is defined at an integration time of τ=0.5s. For other integration times this is scalable, however this will only hold while the integration time is much bigger than the coherence time τ≫tcoh. Because of the correlation between photons arriving shorter than a coherence time apart, the scaling of the NEPτ drops in cases when τ≫̸tcoh.

Finally I propose and describe modifications to the sensitivity model DESHIMA uses. The following features have been be improved and added:

- Integrate over the entire power spectrum when calculating photon noise
- Use arbritatry filter designs loaded from a file
- Improve estimations of the quantities that express sensitivity

I compare the proposed modifications to the old model, which has previously been compared with measurement results, and use it to validate the changes. Other than the previously mentioned factor of π/2 for the bunching term and the smoothing out in local extrema, the modified simulation results are similar to the old model. This is because the Lorentzian filters have a small bandwidth ν≫Δν, such that the previous narrowband approximation held for most non-extreme cases.

In this research, the implementations of quantum random walks in superconducting circuit-QED are studied. In particular, a walk that moves across the Fock states of a quantum harmonic oscillator by a Jaynes-Cummings model is investigated, which is difficult to implement because of different Rabi frequencies for different Fock states. Theoretically, the lower boundary vacuum state of the harmonic oscillator causes a reflection of the probability amplitudes in the distribution. A walk that moves across a grid of coherent states |nα+imα〉 in phase space is then investigated. A setup for a 1D and 2D quantum random walk is suggested, using controlled displacements of a resonator dispersively coupled to one or two superconducting transmon qubits in circuit-QED, followed by Hadamard gates. From numerical simulations it was observed that the 2D walk commutes for α·β = 0 mod π/2 for which the variance is proportional to the number of steps t squared. For other values of α·β the horizontal and vertical displacements do not commute, resulting in extra phase factors. The numerical simulations showed that for most values of α· β with a larger distance to 0 mod π/2 than 0.01, the probability distribution of the
walk collapses to a distribution centered around origin within t = 100 steps, similar to a classical random walk. Exceptions are the 2D walks for α·β = ±π/6 mod π/2 or ±
π/4 mod π/2, for which the variance is still proportional to the number of steps squared.

Magnons are quanta of spin waves, i.e. modes of collectively precessing spins. Thermally excited magnons in thin magnetic films generate stray fields at the film surface which can be detected using nitrogen-vacancy (NV) centers. NVs are lattice defects in diamond and are able to couple with magnon stray fields. Assuming a thermal occupancy of magnon modes, we study the magnetization dynamics of magnons propagating through thin magnetic insulators using the Landau-Lifshitz-Gilbert equation. We implement a numerical model to predict and understand the response of the NV center to proximal magnons in thin films. We investigate how the NV relaxation rate changes for different NV orientations by extending and generalizing the existing theory on chiral magnetic noise, and simulate an experimental setup for an NV placed just above the surface of a thin magnetic insulator. The simulation includes a static bias field in an arbitrary orientation with respect to the quantization axis of the NV center using the diamond's tetrahedral symmetry. This extended model is in demand due to limitations in present-day measurement techniques to align the bias field with an NV center. We use it to detect magnons that contribute to the relaxation rate of the NV, and determine an NV-to-film distance of 0.28(3) μm, from measured relaxation rates of an NV center placed above an yttrium-iron-garnet film with a thickness of 235(10) nm. Our model is available as an open-source Python module.

For NP-hard optimisation problems no polynomial-time algorithms exist for finding a solution. Therefore, heuristic methods are often used, especially when approximate solutions can be satisfactory. One such method is quantum annealing, a method where some initial Hamiltonian is slowly perturbed to anneal towards a problem Hamiltonian. The annealing schedule should follow the adiabatic theorem of quantum mechanics and should therefore be slow to yield the most accurate results. Finding a schedule that is both fast and still accurate has been referred to as a 'black art' and is usually just guessed. In this thesis reinforcement learning (RL) is explored to see if it can help with finding the optimal quantum annealing (QA) schedules. The Hamiltonians used are of
the form of a transverse field Ising model. These are well studied Hamiltonians that can map to many NP-complete problems [1]. Finding a good balance between going both fast and being precise proved to be difficult and needs further research. Therefore this thesis mainly dealt with training an RL agent to find the most accurate QA schedule. The results show that the agent learns to find the most accurate (slowest) annealing schedule after 300,000 learning steps for a problem Hamiltonian with a single coupling constant J and no reward shaping. Annealing in an environment with a spin glass problem Hamiltonian proved to be difficult and has not shown good results in this thesis This needs further investigation. Nonetheless, the result on the single coupling constant Hamiltonian shows the potential of an RL agent for learning in a quantum annealing environment with very sparse rewards. This paves the way for further research into an RL agent that can find a schedule that is both fast and accurate on a wide range of problem Hamiltonians.

In this thesis the matrix product state(MPS) formalism is applied to simulate a device created for remote detection in atomic spin chains. Although simulation of the full device quickly becomes infeasible for direct algorithms, MPS allowed for highly accurate simulations while requiring only modest computational resources. It has been verified that the simulation conserves energy and maintains normalization. Furthermore, the simulation is shown to successfully perform both a coherent real-time evolution and iteration towards the ground state. Thus MPS is a very promising tool that has potential to serve as a guide for further experiment as well as a tool to understand experimental results.

Plastic pollution is a big problem all over the world. Every year more plastic is produced, a lot of plastic litter is mismanaged and enters the ocean. It’s important to know where these plastics accumulate. With this information the problem can be quantified and the plastic litter can be cleaned up. In this project, the transport of micro plastics will be studied. These are plastic particles with a diameter smaller than 5 mm.

To model micro plastics in an accurate way, it is important to include the physical properties of plastics in a transport model. Plastic particles have an extra upwards buoyancy force in the vertical direction, this force has to be taken into account in the model. Therefore, the two-dimensional vertical behavior of plastic particles is studied in this project. Two common transport models are explored: the advection-diffusion equation and a stochastic random walk model. The properties of plastics are discussed and how the transport models can be adapted to be adequate to model micro plastics.

Micro plastics are assumed as spheres in fluid. With this assumption, the flow regime around a plastic particle is estimated with the Reynolds number. These assumptions make it possible to calculate a terminal buoyancy velocity, due to the floating character of plastic. This velocity is added in the vertical direction to
both transport models. To model the turbulence in the ocean, the eddy diffusivity coefficient is defined. This is a variable that states how turbulent the flow is, it can be described as an enhanced diffusion coefficient. The eddy diffusivity coefficient can be estimated with the model Prandlt defined. Here we used a simplified turbulence model for the tests described. In combination with Delft3D-FM the eddy diffusivity from the turbulence model in there can be used.

Both models are implemented in Matlab. The characteristics of the model match with the expected behavior of floating plastics. Plastic particles will perfectly follow the velocity field, except for the extra vertical velocity. When this term is non-zero, the particles will float. Both models have some limitations in efficiency
for modeling plastic particles. The advection-diffusion equation is not suitable for high concentration gradients. The random walk model is not suitable for big areas or long timescales. The choice between both models is depending on the sort of case that someone wants to model.

This project has been carried out at Deltares, an independent water research institute. At Deltares there is a two-dimensional horizontal model available to model particles in the ocean. In the future the existing model of Deltares and the model in this project could be combined. This combined model can be tested for
real-life situations in the ocean. With this combined model, the physical properties of plastics are included in a three-dimensional particle model.