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Understanding the low-temperature properties of strongly correlated materials requires accurate measurement of the physical properties of these systems. Specific heat and nuclear spin-lattice relaxation are two such properties that allow the investigation of the electronic behavior of the system.  In this thesis, nanocalorimetry is used to measure specific heat, but also as basis for new experimental approach, developed to disentangle the different contributions to specific heat at low temperatures. The technique, that we call Thermal Impedance Spectroscopy (TISP) allows independent measurement of the electronic and nuclear specific heat at low temperatures based on the frequency response of the calorimeter-sample assembly. The method also enables simultaneous measurements of the nuclear spin-lattice relaxation time (T1). The nuclear spin lattice relaxation, as 1/T1T, and electronic specific heat, as C/T, provide information about the same quantity, electronic density of states, in the system. By comparing these properties in strongly correlated systems, we can obtain insights of electronic interactions.  Metallic indium is studied using thermal impedance spectroscopy from 0.3 K to 7 K at 35 T. The magnetic field dependence of nuclear spin-lattice relaxation rate is measured. Indium is a simple metallic system and the expected behavior of the nuclear spin-lattice relaxation is similar to that of the electronic specific heat. The results of the measurement are matched with the expectation from a simple metallic system and Nuclear Magnetic Resonance (NMR) measurements. This demonstrates the effectiveness of the new technique.  The heavy-fermion superconductor CeCoIn5 is studied using thermal impedance spectroscopy and ac-calorimetry. This material is located near a quantum critical point (QCP) bordering antiferromagnetism, as evidenced by doping studies. The nature of its quantum criticality and unconventional superconductivity is still elusive. Contrasting specific heat and nuclear spin-lattice relaxation in this correlated system helps to reveal the character of its quantum criticality.  The quantum criticality in CeCoIn5 is also studied using X-ray Absorption Spectroscopy (XAS) across the superconducting transition and X-ray Magnetic Circular Dichroism (XMCD) at 0.1 K and 6 T. The element-specific probe zooming in on cerium in this material indicates two things, a mixed valence of Ce in the superconducting state and a very small magnetic moment, that implies resonance-bond like antiferromagnetic local ordering in the system.

The work in this thesis is basically divided into two related but separate investigations. The first part treats simple chemical reactions of adsorbate molecules on metallic surfaces, induced by means of a scanning tunneling probe (STM). The investigation serves as a parameter free extension to existing theories. The theoretical framework is based on a combination of density functional theory (DFT) and non-equilibrium Green's functions (NEGF). Tunneling electrons that pass the adsorbate molecule are assumed to heat up the molecule, and excite vibrations that directly correspond to the reaction coordinate. The theory is demonstrated for an OD molecule adsorbed on a bridge site on a Cu(110) surface, and critically compared to the corresponding experimental results. Both reaction rates and pathways are deduced, opening up the understanding of energy transfer between different configurational geometries, and suggests a deeper insight, and ultimately a higher control of the behaviour of adsorbate molecules on surfaces. The second part describes a method to calculate STM images in the low bias regime in order to overcome the limitations of localized orbital DFT in the weak coupling limit, i.e., for large vacuum gaps between a tip and the adsorbate molecule. The theory is based on Bardeen's approach to tunneling, where the orbitals computed by DFT are used together with the single-particle Green's function formalism, to accurately describe the orbitals far away from the surface/tip. In particular, the theory successfully reproduces the experimentally well-observed characteristic dip in the tunneling current for a carbon monoxide (CO) molecule adsorbed on a Cu(111) surface. Constant height/current STM images provide direct comparisons to experiments, and from the developed method further insights into elastic tunneling are gained.

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In this master thesis, a 2D device simulator run on a hybrid classical-quantum computer was developed. The simulator was developed to treat statistical quantum effects such as quantum tunneling and quantum confinement in nanoscale transistors. The simulation scheme is based on a self-consistent solution of the coupled non-linear 2D SchrödingerPoisson equations. The Open Boundary Condition (OBC) of the Schrödinger equation, which allows for electrons to pass through the device between the leads (source and drain), are modeled with the QuantumTransmitting Boundary Method (QTBM). The differential equations are discretized with the finite-element method, using rectangular mesh elements. The self-consistent loop is a very time-consuming process, mainly due to the solution of the discretized OBC Schrödinger equation. To accelerate the solution time of the Schrödinger equation, a quantum assisted domain decomposition method is implemented. The domain decomposition method of choice is the Block Cyclic Reduction (BCR) method. The BCR method is at least 15 times faster (CPU time) than solving the whole linear system of equations with the Python solver numpy.linalg.solve, based on the LAPACK routine _gesv. In the project, we also propose an alternative approach of the BCR method called the "extra layer BCR" that shows an improved accuracy for certain types of solutions. In a quantum assisted version, the matrix inverse solver as a step in the BCR method was computed on the D-Wave quantum annealer chip ADVANTAGE_SYSTEM4.1 [4]. Two alternative methods to solve the matrix inverses on a quantum annealer were compared. One is called the "unit vector" approach, based on work by Rogers and Singleton [5], and the other is called the "whole matrix" approach which was developed in the thesis. Because of the limited amount of qubits available on the quantum annealer, the "unit vector" approach was more suitable for adaption in the BCR method. Comparing the quantum annealer to the Python inverse solver numpy.linalg.inv, also based on LAPACK, it was found that an accurate solution can be achieved, but the simulation time (CPU time) is at best 500 times slower than numpy.linalg.inv.

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