Temperature dependent magnetization measurements were conducted on Fe-based heterostructures. A linear increase of the magnetic critical temperature with increasing Fe thickness was found for Fe/V superlattices with strong interlayer exchange coupling. For weakly coupled Fe/V superlattices anomalous values of the critical exponent β were attributed to differences in the effective interlayer exchange coupling in the surface region and in the interior of the superlattice stack. Hydrogen loading of a sample containing a thin Fe film, up to a maximum pressure of 4 mbar gave an increase of the magnetic critical temperature of ≈21 K. A sample with a double layer of Fe, exchange coupled over V, showed oscillations in the critical temperature when loaded to increasing pressure of hydrogen. The oscillations in the critical temperature indicate the presence of quasi-2D phases. Superlattices of Fe and V were investigated by x-ray magnetic circular dichroism. It was found that the orbital magnetic moment shows the same trend as the magnetic anisotropy energy with thickness of the Fe layers. A model which takes into account a varying strain and interface density successfully described the changes in the orbital magnetic moment. The magnetization was measured as a function of temperature for a series of magnetically δ-doped Pd samples. A thin film of Fe induced a magnetic moment in surrounding Pd layers, leading to a magnetic thickness one order of magnitude larger than the thickness of the Fe film. A crossover in the magnetic spatial dimensionality was found as the thickness of the Fe film increased from ≈0.4 monolayers to ≈1 monolayer. First principle calculations of the magnetization profile together with a spin wave quantum well model were used to explain the dimensionality crossover by an increase in the available thermal energy for population of perpendicular spin wave modes.

<p>Boundary quantum phases ---a special type of quantum phenomena--- occur in the boundary part of the system. The boundary part can be a surface of a bulk material, an interface between two distinct system, and even it can be a single impurity or a impurity cluster embedded into a bulk system. The properties of the boundary degree of freedom can be affected by many strong electron correlation effects, mesoscopic effects, and topological effects, which, therefore, induce a vast variety of exotic boundary quantum phases. Many techniques for precise fabrication and measurement in nanostructures had been developed,</p><p>which can provide ways to prob, understand, and control those boundary quantum phases.</p><p>In this thesis, we focus on three types of the boundary quantum phases : Kondo effects, boundary quantum phase transitions, and Majorana fermions. Our motivation is to design and prob those effects by using a important type of nanostructures, i.e. quantum dots. A vast variety of models related to quantum dots (QDs) are studied theoretically, which includes a QD coupled to a mesoscopic bath, a quadruple QD system with metallic leads, a QD with dissipative environments, and a QD coupled to a Majorana fermion zero mode.</p><p>Quantum dots provide a way to study the interplay of Kondo effects and mesoscopic fuctuations. In chapter 5, we consider a model including an Anderson impurity (small QD) coupled to a mesoscopic bath (large QD). Both the weak and strong coupling Anderson impurity problems are characterized by Fermi-liquid theories with weakly interacting quasiparticles. We find that the fluctuations of single particle properties in the two limits are highly correlated and universal : The distributions of the spectrum within the Kondo temperature collapse to universal forms; and the strong coupling impurity changes the wave functions corresponding to the spectrum within the Kondo temperature. </p><p>Quantum dots also bring the possibility to study more complex quantum impurities (multi-QDs) and the competition among dierent interactions, which may induce exotic effects: boundary quantum phase transitions and novel Kondo effects. In chapter 7, we design a quadruple quantum dot system to study the competition among three types of interactions: Kondo, Heisenberg, and Ising. We find a rich phase diagram containing two sharp features : a Berezinsky-Kosterlitz-Thouless type quantum phase transition between a charge-ordered phase and a charge liquid phase and a U(1)XU(1) Kondo state with emergent symmetry from Z2 to U(1). In chapter 8, we study a dissipative resonant level model in which the coupling of a fermionc bath competes with a dissipation-induced bosonic bath. we establish an exact mapping from this dissipative resonant level model to a model of a quantum dot embedded into a Luttinger liquid wire, and we also find two kinds of boundary quantum phase transitions (a Berezinsky-Kosterlitz-Thouless type and a second order type).</p><p>Finally, in chapter 9, we propose an experimental system to detect Majorana fermion zero modes. This system consists of a spinless quantum do coupled to a Majorana fermion which exists in the end of a p-wave superconductor wire. The Majorana Fermion strongly infuence the transport properties of the quantum dot. The zero temperature conductance peak value (when the dot is on resonance and symmetrically coupled to the leads) is e^2/2h. In contrast, if the wire is in its topological trivial phase, the result is e^2/h; if the side-coupled mode is a regular fermionic zero mode, the result is zero. Driving the wire through the topological phase transition causes a sharp jump in the conductance by a factor of 1/2. This result can be used to detect the existence of Majorana fermions.</p> / Dissertation

In this dissertation, I have studied theoretical problems in statistical physics and electrodynamics of Bose particles, namely, mesoscopic effects in statistics of Bose- Einstein condensate (BEC) of atoms and electromagnetic waveguide effects of planar Bragg structures in Free Electron Lasers. A mesoscopic system of a trapped gas of Bose atoms is the most difficult for the theoretical analysis in quantum statistical physics since it cannot be studied by neither a quantum mechanics of the simple microscopic systems of one or very few atoms nor a standard statistical physics of the macroscopic systems that implies a thermodynamic limit. I present analytical formulas and numerical calculations for the moments and cumulants of BEC fluctuations in both ideal and weakly interacting gas. I analyze the universal scaling and structure of the BEC statistics in a mesoscopic ideal gas in the critical region. I present an exactly solvable Gaussian model of BEC in a degenerate interacting gas and its solution that confirms the universality and constraint-cut-off origin of the strongly non-Gaussian BEC statistics. I consider a two-energy-level trap with arbitrary degeneracy of an upper level and find an analytical solution for the condensate statistics in a mesoscopic ideal gas. I show how to model BEC in real traps by BEC in the two-level or three-level traps. I study wave propagation in the open oversized planar Bragg waveguides, in particular, in a planar metal waveguide with corrugation. I show that a step perturbation in a corrugation phase provides a high selectivity over transverse modes. I present a new Free Electron Laser (FEL) amplifier scheme, in which the radiation is guided by the planar Bragg structure with slightly corrugated walls and a sheet electron beam is traveling at a significant angle to the waveguide axis. By means of nonlinear analysis, I demonstrate that the proposed scheme provides an effective mode filtration and control over the structure of the output radiation and allows one to achieve amplification up to 30 dB in the existing FEL machines.

The specific heat Cp has been showed at various temperatures in the literature, which shows a sharp increase labeled as the lambda-transition at the critical temperature. This transition has been observed previously among the phases of solid-nematic-isotropic liquid in p-azoxyanisole (PAA) and anisaldazine (AAD), and among the phases of solid-smectic-cholesteric-isotropic liquid in cholesteryl myristate (CM). In this thesis work, we analyze the experimental data for the temperature dependence of Cp and the thermal expansion alpha_p and also pressure dependence of alpha_p by a power-law formula. From the analysis of pressure dependence of alpha_p, we calculate the temperature dependencies of specific heat Cp and of the isothermal compressibility kappa_T for the phase transitions considered in PAA, AAD and CM. Our calculations for the temperature dependence of the p and kappa_T can be compared with the experimental data when available in the literature. Polarization, tilt angle and the dielectric constant have been reported in the literature at various temperatures close to the solid-smectic C*-smectic A-isotropic liquid transition in the ferroelectric liquid crystals of A7 and C7. The mean field model with the free energy expanded in terms of the order parameters (polarization and tilt angle) has been reported in the literature previously. In this thesis work, we apply the mean field model first time by fitting the expressions derived for the temperature dependence of the polarization, tilt angle and the dielectric constant to the experimental data for A7 and C7 from the literature. Since the mean field model studied here describes adequately the observed behaviour of A7 and C7, the expressions for the temperature dependence of the polarization, tilt angle and the dielectric constant which we derive, can also be applied to some other ferroelectric liquid crystals to explain their observed behaviour.

We study in this thesis work the spectroscopic and thermodynamic quantities of some substances such as ammonium halides (NH4Cl, NH4I), ferroelectric crystals of tris-sarcosine calcium chloride (TSCC), tris-sarcosine calcium bromide (TSCB), organic compounds of carbon tetrachloride (CCl4) and s-triazine (C3N3H3) close to the phase transitions. Various physical and chemical properties of those materials have been measured near the critical points and have been reported in the literature. In this study, the spectroscopic parameters of the frequency shifts, intensity and bandwidths are calculated as functions of temperature or pressure near the phase transitions in ammonium halides using the experimental data from the literature. The spectroscopic parameters are related to the crystal volume and the specific heat in these compounds. The thermodynamic quantities of the specific heat, thermal expansion and the isothermal compressibility are also calculated in the solid and liquid phases of carbon tetrachloride using the experimental data. In another part of this thesis work, we analyze the temperature dependence of the spontaneous polarization and the dielectric susceptibility at fixed pressures for TSCC and TSCB by using the experimental data from the literature. The temperature dependence of the damping constant for the s-triazine is also calculated here close to the I-II transition. We use the theoretical models on the basis of the observations in the literature to calculate the critical behaviour of these physical quantities and we compare the results with the observed data. Various experimental studies in the literature give us the opportunity to find the proper way of fitting the calculated and observed results. This study gives us the chance of a better understanding of the critical behavior of the studied materials by verifying the values of some critical exponents and the types of transitions as expected by different theoretical models.

This thesis deals with various functional materials from first-principles methods and is divided into two major parts according to the underlying atomic structure of the system under study. The first part of the thesis deals with the temperature-induced structural phase transitions in metallic  β'-AuZn and perovskite oxide LiOsO3. The former one, i.e. binary AuZn, belongs to a class of shape-memory alloys that regain their initial shape due to a reversible martensitic phase transformation. Here, by means of density functional and density functional perturbation theories, we show that the martensitic transition is due to coupling between the Fermi surface nesting and anomalies in the phonon dispersion relations. The other metallic system, perovskite LiOsO3, exhibits a ferroelectric-like transition and is currently the first and sole realization of the Anderson and Blount idea. By means of ab initio molecular dynamics simulations, we investigate the mechanism behind this structural phase transformation. Another part of the thesis is dedicated to modelling and characterization of topologically disordered materials on atomic level. The structural and electronic properties of amorphous W-S-N are addressed regarding its outstanding tribological properties, i.e. almost vanishing friction coefficient. Molecular dynamics “melt-and-quench” technique has been employed in order to construct a model structure of amorphous W-S-N. Further analysis of the atomic structure revealed a formation of quasi-free N2 molecules trapped in S cages, which, together with the complex atomic structure of W-S-N, is the key to ultra-low-friction in this functional material. In the last chapter of the thesis a magnetic class of amorphous materials is addressed. Magnetic order in amorphous Gd-Fe ferrimagnet has been shown to undergo magnezation switching driven by a femtosecond laser pulse. Here, we combine first-principles density functional theory and atomistic spin dynamics simulations to explore this phenomena. A possible mechanism behind magnetization reversal in Gd-Fe based on a combination of the Dzyaloshinskii-Moriya interaction and exchange frustration is proposed.

n this paper, two different applications of phase transitions to exploration seismology will be discussed. The first application concerns a phase diagram ruling the recovery conditions for seismic data volumes from incomplete and noisy data while the second phase transition describes the behavior of bi-compositional mixtures as a function of the volume fraction. In both cases, the phase transitions are the result of randomness in large system of equations in combination with nonlinearity. The seismic recovery problem from incomplete data involves the inversion of a rectangular matrix. Recent results from the field of "compressive sensing" provide the conditions for a successful recovery of functions that are sparse in some basis (wavelet) or frame (curvelet) representation, by means of a sparsity ($\ell_1$-norm) promoting nonlinear program. The conditions for a successful recovery depend on a certain randomness of the matrix and on two parameters that express the matrix' aspect ratio and the ratio of the number of nonzero entries in the coefficient vector for the sparse signal representation over the number of measurements. It appears that the ensemble average for the success rate for the recovery of the sparse transformed data vector by a nonlinear sparsity promoting program, can be described by a phase transition, demarcating the regions for the two ratios for which recovery of the sparse entries is likely to be successful or likely to fail. Consistent with other phase transition phenomena, the larger the system the sharper the transition. The randomness in this example is related to the construction of the matrix, which for the recovery of spike trains corresponds to the randomly restricted Fourier matrix. It is shown, that these ideas can be extended to the curvelet recovery by sparsity-promoting inversion (CRSI) . The second application of phase transitions in exploration seismology concerns the upscaling problem. To counter the intrinsic smoothing of singularities by conventional equivalent medium upscaling theory, a percolation-based nonlinear switch model is proposed. In this model, the transport properties of bi-compositional mixture models for rocks undergo a sudden change in the macroscopic transport properties as soon as the volume fraction of the stronger material reaches a critical point. At this critical point, the stronger material forms a connected cluster, which leads to the creation of a cusp-like singularity in the elastic moduli, which in turn give rise to specular reflections. In this model, the reflectivity is no longer explicitly due to singularities in the rocks composition. Instead, singularities are created whenever the volume fraction exceeds the critical point. We will show that this concept can be used for a singularity-preserved lithological upscaling.

The behavior of sp-valent solids and liquids under compression is a field of intense re- search. At high pressure, they often undergo phase transitions to new structures with novel properties such as superconductivity, high-energy density, and superhardness. Furthermore, knowledge of these materials is essential for understanding the structure and evolution of planets. Molecular systems such as nitrogen and carbon dioxide are particularly interesting as energetic materials: their strong molecular bonds break under compression spawning transformations to exotic polymeric phases. We have used first-principles theory and molecular dynamics to make predictions for the properties of dense nitrogen, carbon dioxide, magnesium silicate, and magnesium oxide. For nitrogen, we provide evidence for a rare first-order liquid-liquid phase transition; only the second such transition seen in an elemental fluid. New finite-temperature structure search techniques have been developed and applied to predict a thermodynamically stable polymeric metal phase of solid nitrogen. Regarding carbon dioxide, we have computed its high-pressure liquid phase diagram over a broad pressure-temperature range, revealing rich structural diversity. We have also designed new free energy methods to explore the stability of free CO2 under deep mantle conditions. Lastly, first-principles molecular dynamics and finite-temperature free energy methods were used to predict a high-pressure phase separation transition in liquid MgSiO3 and also characterize the high-pressure phase diagram of MgO, including its melting curve.

We correlate in the first part of this study the specific heat and thermal expansivity to the temperature-and pressure-dependent frequency shifts, respectively, in ammonia solid I, solid II, hexagonal ice and ice close to their melting points. This is carried out for some fixed pressures for the two translational and one librational modes in ammonia solid I. By obtaining linear plots of specific heat and thermal expansivity against temperature-and pressure-dependent frequency shifts, the values of slope were deduced and compared with experimental values. The correlation between the thermal expansivity and frequency shifts was constructed in the ammonia solid II by calculating the Raman frequencies of the translational and the librational modes for some fixed pressures. Calculated values of slope were compared with experimental values. Temperature and pressure dependent frequency shifts of the translational modes in hexagonal and ice are correlated to the specific heat and the thermal expansivity, respectively. When the mode Gr&uuml / neisen parameter depends on temperature and pressure, correlations among the specific heat, thermal expansivity and, temperature-and pressure-dependent frequency shifts, respectively, are reexamined in hexagonal ice. When the mode Gr&uuml / neisen parameter depends on temperature, correlation between the specific heat and the frequency shifts is reexamined using translational modes in NH4Cl. In the second part of this study, we predict the damping constant for ammonium halides (NH4Cl and NH4Br) for zero pressure, and for the tricritical and second order phase transitions for a lattice mode of NH4Cl. Also, the observed Raman intensities of this mode are analyzed at those two pressures.

Solid-state amorphization of a crystalline solid to an amorphous phase is extensively studied as a first order phase transition at low temperature for almost thirty years. In this dissertation, we report the recent progress on phenomenological models employed for thermodynamic description of macroscopic systems and fluctuations and nucleation of mesoscopic inhomogeneous systems in binary solid solutions under polymorphic constraints with no long-range diffusion involved. Based on our understanding on atomic picture of solid-state amorphization in binary solid solutions, we propose a Landau free energy to describe amorphization as the first order phase transition. The order parameter is defined which represents the loss of long-range translational order. The elastic strain field induced by composition disorder plays the important role through the bilinear coupling with the order parameter. Elastic softening and amorphization happen simultaneously. From the similarity between the melting and amorphization, we use the temperature and composition as two external variables and treat solid-state amorphization as low temperature melting under polymorphic constraints. For homogeneous system, the phase diagrams for endothermic melting and exothermic melting are built separately and the corresponding thermodynamic quantities are presented. A microscopic homogeneous nucleation mechanism is proposed conceptually in binary solid solutions under polymorphic constraints. The formation of an amorphous embryo is initiated from the composition modulation in the crystal state and a subsequent polymorphous nucleation within the as-formed heterophase fluctuation. This homogeneous nucleation path is thought to be associated with the nonlinear energy localization mechanism connected with the localized large-amplitude excitations of atoms, which are induced by nonlinear and disorder. A Landau-Ginzburg free energy is constructed to describe the critical nucleus and the growth of the new phase in one-dimensional systems. Analytical and numerical methods contribute to the understanding the fluctuations and nucleation processes. Size-dependent melting and amorphization in nanosolids are investigated. Two models are proposed for nanocrystalline solid solutions to glass transformations. Based on the thin film model with finite thickness, we build one-dimensional Landau-Ginzburg approach, which includes surface contribution and size dependence, and numerical results do show similarity with experimentsâ results qualitatively.