Transition Metal (TM) silicides are potential materials for different high temperature applications due to their high melting points and chemical stability at elevated temperatures. In the present work, the possible use of Gr (VIB) disilicides: MoSi2 and CrSi2 for high temperature structural application and thermopower generation respectively are investigated. Literature reports on MoSi2 indicate this material to have excellent mechanical and thermal behaviors at temperatures greater than 1273 K. The major problems limiting its use are the low temperature brittleness and oxidation at intermediate temperatures and form the scope of this work. Also, CrSi2 is reported to be a narrow band gap semiconductor. Its feasibility as a thermoelectric material for power generation is investigated. The first chapter briefly summarizes the literature on MoSi2 and CrSi2 relevant to structural and thermoelectric applications respectively. Based on the available literature, the scope of further work is discussed. The second chapter describes the methods of synthesis employed for these materials and the characterization techniques adopted. Some experimental setups like thermal conductivity and hot pressing unit that were fabricated as part of the work are described in detail. The thermal conductivity apparatus is based on the principle of parallel heat flow technique. It allows accurate measurement of K and S in the temperature range 300-700 K. The induction based hot-pressing unit allows compaction of polycrystalline powders to near theoretical densities thereby allowing quantitative evaluation of the physical properties. In the third chapter, an understanding of ductility/brittleness based of electron charge density distribution is attempted. The electron charge density in Tin and simple metals (BCC and FCC) is analyzed using Bader’s Atoms in Molecule (AIM) theory. Also the relevant surface and dislocation energies in these materials are calculated according to the Rice Model. It is found that the electron densities at the critical points correlate in a simple way with the relevant stacking fault and surface energetics. Based on these results, a ductility parameter (DM odel) based on electron charge distribution, to predict the effects of chemical substitutions on ductility/brittleness in materials is proposed. In the fourth chapter, possible elements to impart ductility in MoSi2 are identified based on the DM odel values. Calculations indicate, Nb, Ta, Al, Mg and Ga to be suitable candidates for improving ductility in MoSi2. Also oxidation studies based on present experiments and reported literature data reveal, Al to improve the intermediate temperature (773-873 K) oxidation behavior. Thus to simultaneously improve the low temperature ductility and oxidation resistance, Nb and Al were identified as suitable candidates. In the fifth chapter, the experimental data of Nb and Al co-substituted MoSi2 samples are reported. Oxidation studies carried out by thermogravimetry show improved oxidation resistance in Nb and Al co-substituted samples compared to pure MoSi2 in the temperature range of 773-873 K. Mechanical characterization was carried out for (Mo0.99Nb0.01)(Si0.96Al0.04)2 co-substituted composition. Compression testing at room temperature show plastic deformation at low strain rates (10−3 /sec). Indentation experiments show a reduction in the hardness and stiffness compared to pure MoSi2. There is also an increase in the fracture toughness (K1C ) value with the fracture modes being predominantly transgranular. The sixth chapter describes the structural, thermal and transport properties of CrSi2. Structural refinement was carried out by Rietveld method and the positional, thermal parameters and occupancy were fixed. Thermo-gravimetric analysis shows oxidation resistance in powdered samples upto 1000 K. Thermal expansion (α) studies reveal anisotropy in the α values with an unusual decrease in the average αV values between 500 and 600 K. Measurements of electrical resistivity and seebeck coefficient indicate a degenerate semiconducting behavior. Electronic band structure calculations indicate a narrow indirect band gap (EG) material with EG~0.35 eV. Thermal conductivity (K) measurements show a decrease in K value with increasing temperature. Calculation of the thermoelectric figure of merit (ZT) show a maximum value of 0.18 at 800 K for the temperature range studied. Based on an analysis of the experimental and theoretical results, it is identified that further improvements in ZT of CrSi2 may be possible by reducing the lattice thermal conductivity and optimization of the carrier concentration. In chapter seven, the effect of particle size on ZT of CrSi2 is studied. Nano powders of CrSi2 were prepared by mechanical milling. Contamination is found to be a major problem during milling and the different milling parameters (milling speed, atmosphere, dispersant etc) were optimized to minimize contamination. The milled powders were further hot pressed to achieve high densities in a short duration thereby minimizing the grain growth. It is observed that the lattice thermal conductivity is reduced significantly with decreasing grain size. Measurements of ZT show a maximum value of 0.20 in the milled sample compared to 0.14 in arc melted CrSi2 at 600 K. In chapter eight the effect of chemical substitutions on ZT of CrSi2 is studied. Mn substitutions in Cr site were carried out to study the effect of atomic mass on lattice thermal conductivity (KP ). Al substitutions in Si site were carried out to tune the Fermi level. Results of Mn substitution show a large decrease in KP but also a reduction in the thermoelectric power factor (S2σ). The maximum ZT observed in the Mn substituted samples was 0.12 at 600 K. Al substitution results in an increase in the thermoelectric power factor and a subsequent increase in ZT. The maximum ZT observed was 0.27 at 700 K for 10% substitution of Al in Si site. The work reported in the thesis has been carried out by the candidate as a part of the Ph.D. training programme at Materials Research Centre, Indian Institute of Science, Bangalore, India. He hopes that this work would constitute a worthwhile contribution towards (a) basic understanding of ductility/brittleness in materials and understanding the effects of chemical substitutions, (b) Suitability of chemically substituted MoSi2 to overcome the problems of low temperature brittleness and oxidation. (c) Development of CrSi2 as a high temperature thermoelectric material.

No description available.

This thesis presents the investigations of Rubidium atoms in magneto-optical traps and triply charged Thorium ions in electrodynamic traps for future advances in long-distance quantum telecommunication, next generation clocks, and fundamental tests of current physical theories. Experimental realizations of two core building blocks of a quantum repeater are described: a multiplexed quantum memory and a telecom interface for long-lived quantum memories. A color change of single-photon level light fields by several hundred nanometers in an optically thick cold gas is demonstrated, while preserving quantum entanglement with a remotely stored matter excitation. These are essential elements for long-distance quantum telecommunication, fundamental tests of quantum mechanics, and applications in secure communication and computation. The first trapping and laser cooling of Thorium-229 ions are described. Thorium-229 nuclear electric quadrupole moment is revealed by hyperfine spectroscopy of triply charged Thorium-229 ions. A system to search for the isomer nuclear transition in Thorium-229 is developed and tested with the excitation of a forbidden electronic transition at 717 nm. Direct excitation of the nuclear transition with laser light would allow for an extremely accurate clock and a sensitive test bed for variations of fundamental physical constants, including the fine structure constant.

This thesis describes the measurement of rate constants for gas phase reactions as a function of temperature (285 ≤ T/K ≤ 850) and pressure (48 ≤ P/Torr ≤ 700). One or both reactants was monitored directly in real time, using time–resolved resonance fluorescence (for atoms) and u.v. absorption (for radicals). Reactants were produced by exciplex laser flash photolysis. The technique was used to measure rate constants to high precision for the following reactions under the stated conditions: • H+O2+He->HO2+He and H+O2−→OH+O, for 800 ≤ T/K ≤ 850 and 100 ≤ P/Torr ≤ 259. A time–resolved study was performed at conditions close to criticality in the H2–O2 system. The competition between the two reactions affected the behaviour of the system after photolysis, and the rate constants were inferred from this behaviour. • H+C2H4+He<-->C2H5+He (T = 800 K, 97 ≤ P/Torr ≤ 600). The reactions were well into the fall–off region at all conditions studied. At 800 K, the system was studied under equilibrating conditions. The study provided values of the forward and reverse rate constants at high temperatures and enabled a test of a new theory of reversible unimolecular reactions. The controversial standard enthalpy of formation of ethyl, DH0f,298 (C2H5), was determined to be 120.2±0.8 kJ mol−1. Master Equation calculations showed that reversible and irreversible treatments of an equilibrating system should yield the same value for both thermal rate constants. • H+C3H5+He->C3H6+He (T = 291 K, 98 ≤ P/Torr ≤ 600) and O+C3H5 −→ products (286 ≤ T/K ≤ 500, 48 ≤ P/Torr ≤ 348). Both reactions were pressure–independent, and the latter was also independent of temperature with a value of (2.0±0.2) ×10−10 cm3 molecule−1 s−1. • H+C2H2+He<-->C2H3+He (298 ≤ T/K ≤ 845, 50 ≤ P/Torr ≤ 600). At 845 K, both reactions were in the fall–off region; rate constants were used to determine the standard enthalpy of formation of vinyl, ¢H0f,298 (C2H3), as 293±7 kJ mol−1. The value of this quantity has until recently been very controversial. • H+CH4 <--> CH3+H2. The standard enthalpy of formation of methyl, DH0 f,298 (CH3), was determined by re–analysing existing kinetic data at T = 825 K and 875 K. A value of 144.7±1.1 kJ mol−1 was determined. Preliminary models were examined to describe the loss of reactants from the observation region by diffusion and pump–out. Such models, including diffusion and drift, should prove useful in describing the loss of reactive species in many slow–flow systems, enabling more accurate rate constants to be determined.

Understanding the complexities of the interior of planets and stars requires the help of analyzing the effects of high pressures on certain elements believed to be found within. The Hartree-Fock method uses the Schr¨odinger equation, Kummer’s differential equations and a confinement potential to simulate an atom being squeezed to high pressures. The Hartree-Fock method was used to calculate the total energies of atoms. After being compared to Gaussian03 and VASP, the results were deemed accurate. It was also observed that the pressure versus density data closely approximated those pairs found in outer space in the interiors of, for example, Jupiter.

Thesis (Ph.D.); Submitted to Univ. of California, Berkeley, CA (US); 1 Jun 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--54350" Scielzo, Nicholas David. USDOE Director. Office of Science. Nuclear Physics (US) 06/01/2003. Report is also available in paper and microfiche from NTIS.

The thesis entitled “Addressing subtle physicochemical features exhibited by molecular crystals via Experimental and Theoretical Charge Density Analysis” consists of five chapters. An introductory note provides a brief description of experimental and theoretical charge density methodology, followed by its utilization in obtaining certain physical and chemical properties in molecular crystals. Chapter 1 addresses not so easily accessed molecular property arising due to electron conjugation, highlighting antiaromaticity in tetracyclones. A systematic study of six tetracyclone derivatives with electron withdrawing and electron donating substituents has been carried out using experimental and theoretical charge density analysis. A three pronged approach based on quantum theory of atoms in molecules (QTAIM), nucleus independent chemical shifts (NICS), and source function (SF) has been employed to establish the degree of antiaromaticity of the central five-membered ring in all the derivatives. Electrostatic potentials mapped on the is density surface reveal the finer effects of different electron withdrawing and electron donating substituents on the carbonyl group. Chapter 2 presents a temperature induced reversible first order single crystal to single crystal phase transition (Room temperature Orthorhombic, P22121 to low temperature Monoclinic, P21) in a  hybrid peptide, Boc-γ4(R)Val-Val-OH. The thermal behavior accompanying the phase transition of the dipeptide crystal was characterized by differential scanning calorimetry, visual changes in birefringence of the sample during heating and cooling cycles on a hot-stage microscope with polarized light. Variable-temperature unit cell check measurements from 300 to 100 K showed discontinuity in the volume and cell parameters near the transition temperature, supporting the first-order behavior. The reversible nature of the phase transition is traced to be due to an interplay between enthalpy and entropy. Chapter 3 brings out an unusual stabilizing interaction involving a cooperative -hole and ¬hole character in a short NCS···NCS bond. This chapter describes structural features of four isothiocyanate derivatives, FmocXCH2NCS; X=Leu, Ile, Val and Ala. Among these it is observed that only FmocLeuCH2NCS which crystallizes in a tetragonal space group, P41, (a=b=12.4405(5) Å; c= 13.4141(8) Å) transforms isomorphously to a low temperature form, P41, (a=b=17.4665(1) Å; c= 13.1291(1) Å). The characteristics of the phase transition have been monitored by Differential Scanning Calorimetry, variable temperature IR and temperature dependent unit cell measurements. The short NCS···NCS intermolecular interaction (3.296(1) Å) is analyzed based on detailed experimental charge density analysis which reveals the nature of this stabilizing interaction. Chapter 4 explains a comparative study of syn and anti conformations of carboxylic acids in peptides from both structural aspect and charge density features. Single crystal structures of four peptides having syn conformations [BocLeuγ4(R)Valγ4(R)ValOH, BocLeuγ4(R)ValLeuγ4(R)ValOH, Boc3(S)Leu3(S)LeuOH] and one with anti conformation, BocLeuγ4(R)ValValOH have been analyzed. Experimental charge density analysis has been carried out exclusively on BocLeuγ4(R)ValValOH having anti form, because of its rare occurrence in literature. However, low temperature datasets on the four peptides with syn conformations were collected and theoretical charge density analysis has been carried out on two of these compounds. Electrostatic potentials mapped on is density surface bring out a significant difference at the oxygen atoms of the carboxyl group in the two conformations. However, lone pair orientation of different types of Oxygen atoms in the two forms (urethane, amide, acid) doesn’t exclusively indicate the differences in the corresponding charge density features. Chapter 5 addresses the issue of how sensitive are the charge density features associated with amino acid residues when the backbone conformational angles are varied. Three model systems, 1, L-alanyl–L-alanyl–L-alanine dehydrate; 2, anhydrous L-alanyl–L-alanyl–L¬alanine and 3, cyclo-(D,L-Pro)2(L-Ala)4 monohydrate have been chosen for this evaluation. Compound 1 has ant parallel alignment of tripe tide strands, and compound 2 has parallel alignment. All the alanine residues in compound 1 and 2 are in the -sheet region of the Ramachandran plot, whereas, the four Alanine residues in the cyclic hex peptide 3 span different regions of the Ramachandran plot. Theoretical multipole modelling has been carried out in order to explore the plausibility of transferring multipole parameters across different regions of Ramachandran Plot. Appendix I contains a brief description of charge shift bonding in Ph-CH2-Se-Se-CH2-Ph, as determined based on both experimental and theoretical charge density analysis. Appendix II contains a reprint of a published article on “Conformation-Changing Aggregation in Hydroxyacetone: A Combined Low-Temperature FTIR, Jet, and Crystallographic Study”.

Quantum memories are key components in photonics-based quantum information processing networks. Their ability to store and retrieve information on demand makes repeat-until-success strategies scalable. Warm alkali-metal vapours are interesting candidates for the implementation of such memories, thanks to their very long storage times as well as their experimental simplicity and versatility. Operation with the Raman memory protocol enables high time-bandwidth products, which denote the number of possible storage trials within the memory lifetime. Since large time-bandwidth products enable multiple synchronisation trials of probabilistically operating quantum gates via memory-based temporal multiplexing, the Raman memory is a promising tool for such tasks. Particularly, the broad spectral bandwidth allows for direct and technologically simple interfacing with other photonic primitives, such as heralded single photon sources. Here, this kind of light-matter interface is implemented using a warm caesium vapour Raman memory. Firstly, we study the storage of polarisation-encoded quantum information, a common standard in quantum information processing. High quality polarisation preservation for bright coherent state input signals can be achieved, when operating the Raman memory in a dual-rail configuration inside a polarisation interferometer. Secondly, heralded single photons are stored in the memory. To this end, the memory is operated on-demand by feed-forward of source heralding events, which constitutes a key technological capability for applications in temporal multiplexing. Prior to storage, single photons are produced in a waveguide-based spontaneous parametric down conversion source, whose bespoke design spectrally tailors the heralded photons to the memory acceptance bandwidth. The faithful retrieval of stored single photons is found to be currently limited by noise in the memory, with a signal-to-noise ratio of approximately 0.3 in the memory output. Nevertheless, a clear influence of the quantum nature of an input photon is observed in the retrieved light by measuring the read-out signal's photon statistics via the g⁽²⁾-autocorrelation function. Here, we find a drop in g⁽²⁾ by more than three standard deviations, from g⁽²⁾ ~ 1.69 to g⁽²⁾ ~ 1.59 upon changing the input signal from coherent states to heralded single photons. Finally, the memory noise processes and their scalings with the experimental parameters are examined in detail. Four-wave-mixing noise is determined as the sole important noise source for the Raman memory. These experimental results and their theoretical description point towards practical solutions for noise-free operation.

Dans cette thèse, après une introduction où nous présentons brièvement la physique des forces de Casimir, nous montrons nos résultats obtenus pendant le doctorat. D'abord, nous montrons notre travail sur les interactions de van der Waals / Casimir-Polder lorsque le système est dans une configuration hors équilibre à cause du mouvement uniformément accéléré des atomes. Nous étudions le système de deux atomes uniformément accélérés dans le vide quantique quand ils sont dans leur état fondamental ou dans un état corrélé (un atome excité et un atome dans son état fondamental). Nous analysons ce système avec un modèle heuristique semi-classique et une méthode plus rigoureuse qui nous avons étendu à partir d'une procédure générale développée dans la littérature. Nous trouvons un changement de la dépendance de l'interaction de la distance en raison de l'accélération. Nous montrons que les forces de Casimir-Polder entre deux atomes uniformément accélérés en mouvement relativiste, qui interagissent avec le champ scalaire, présentent une transition à partir d'un comportement thermique à courtes distances, comme prédit par l'effet Unruh, à un comportement non thermique à longues distances, associé à la rupture de la description inertielle et locale du système. En plus, lorsque le cas d'atomes qui interagissent avec le champ électromagnétique quantique est considéré, on constate que de nouvelles caractéristiques apparaissent dans l'interaction.Ensuite, nous présentons notre travail sur un nouveau couplage opto-mécanique d'un miroir oscillant de façon efficace avec un gaz d'atomes de Rydberg, médié par la force atome-miroir dynamique de Casimir-Polder. Nous constatons que ce couplage peut produire une excitation de résonance atomique de champ proche, qui n'est pas liée à l'excitation des atomes par les quelques photons réels attendus de l'effet Casimir dynamique. Dans des conditions expérimentales accessibles, cette probabilité d'excitation est importante (environ 20 %) et rend possible l'observation de ce nouvel effet Casimir-Polder dynamique. Donc nous proposons une configuration expérimentale réaliste pour réaliser ce système fait d'un gaz d'atomes froids piégés mis en face d'un substrat semi-conducteur, dont les propriétés diélectriques sont modulées dans le temps.Enfin, nous nous concentrons sur nos résultats obtenus pour le calcul de la pression Casimir-Lifshitz entre deux réseaux lamellaires diélectriques différents. Ce système est supposé dans une configuration hors équilibre thermique. En fait, les deux réseaux présentent deux températures différentes et ils sont immergés dans un bain thermique ayant une troisième température. Le calcul de la pression est basé sur une méthode qui exploite les opérateurs de diffusion des réseaux, déduits en utilisant la méthode modale de Fourier. Nous présentons nos résultats numériques caractérisant en détail le comportement de la pression, en faisant varier les trois températures et en modifiant les paramètres géométriques des réseaux. Cette variation des paramètres du système permet de régler la force de répulsive à attractive ou de réduire fortement la pression pour des intervalles de températures. En outre, on montre que la combinaison des effets de non-équilibre et géométriques rend ce système particulièrement intéressant pour l'observation de la force de Casimir répulsive. / In this thesis, after an introduction where we briefly present the general context of Casimir physics, we present the results obtained during the PhD. At first, we show our work about the van der Waals/Casimir-Polder interactions between two atoms in an out-of-equilibrium condition due to their uniformly accelerated motion. We study the system of two uniformly accelerated atoms in vacuum space, when they are in their ground-state and when they are in a correlated state (one excited and one ground-state atom). We analyze this system both with an heuristic semiclassical model and with a more rigorous method, based on a separation of radiation reaction and vacuum fluctuations contributions, that we extend starting from a general procedure known in literature. We find a change of the distance-dependence of the interaction due to the acceleration. We show that Casimir-Polder forces between two relativistic uniformly accelerated atoms, interacting with the scalar field, exhibit a transition from the short-distance thermal-like behavior predicted by the Unruh effect to a long-distance nonthermal behavior, associated with the breakdown of a local inertial description of the system. In addition, we obtain new features of the resonance interaction in the case of atoms interacting with the quantum electromagnetic field.Next, we present our work about a new optomechanical coupling of an effectively oscillating mirror with a Rydberg atoms gas, mediated by the dynamical atom-mirror Casimir-Polder force. We find that this coupling may produce a near-field resonant atomic excitation not related to the excitation of atoms by the few real photons expected by dynamical Casimir effect. In accessible experimental conditions, this excitation probability is significant (about 20%) making the observation of this new dynamical Casimir-Polder effect possible. For this reason, we propose a realistic experimental configuration to realize this system made of a cold atom gas trapped in front of a semiconductor substrate, whose dielectric properties are periodically modulated in time.Finally, we focus on our results obtained for the Casimir-Lifshitz pressure between two different dielectric lamellar gratings. This system is assumed to be in an out-of-thermal-equilibrium configuration, i.e. the two gratings have two different temperatures and they are immersed in a thermal bath having a third temperature. The computation of the pressure is based on a method exploiting the scattering operators of the bodies, deduced using the Fourier modal method. In our numerical results we characterize in detail the behavior of the pressure, both by varying the three temperatures and by changing the geometrical parameters of the gratings. In this way we show that it is possible to tune the force from attractive to repulsive or to strongly reduce the pressure for large ranges of temperatures. Moreover, we stress that the interplay between nonequilibrium effects and geometrical periodicity make this system particularly interesting for the observation of the repulsive Casimir force.

The advancement in the eld of cold-atoms has generated a lot of interest in the condensed matter community. Cold-atom experiments can simulate clean, disor-der/impurity free systems very easily. In these systems, we have a control over various parameters like tuning the interaction between particles by the Feshbach resonance, tuning the hopping between lattice sites by laser intensity and so on. As a result, these systems can be used to mimic various theoretical models, which was hindered because of various experimental limitations. Thus, we have an ex-perimental tool in which we can start with a simple theoretical model and later tune the model experimentally and theoretically to simulate the real materials. This will be helpful in studying the physics of the real materials as we can control interactions as well as the impurities can also be taken care of. But the advance-ment in the eld of cold atoms has seen a roadblock for the fermions in optical lattices. The super uid and anti-ferromagnetic phases has not been achieved for fermions in optical lattices due to the \cooling problem" (entropy issues). In this thesis, we have addressed the issue of the \cooling problem" for fermions in optical lattice systems and studied the system with determinant quantum Monte Carlo technique. We start by giving a general idea of cold-atoms and optical lat-tice potentials, and a brief review of the experimental work going on in the cold-atomic systems. Experimental limitations like \fermionic cooling problem" have been discussed in some detail. Then we proposed a bilayer band-insulator model to circumvent the \entropy problem" and simultaneously increasing the transi-tion temperature for fermions in optical lattices. We have studied the attractive Hubbard model, which is the minimal model for fermions in optical lattices. The techniques that we have used to study the model are mean- eld theory, Gaussian uctuation theory and determinant quantum Monte Carlo numerical technique. . Chapter-1 : provides a general introduction to the ultra-cold atoms, optical lattice and Feshbach resonance. In this chapter we have discussed about cold-atom experiments in optical lattice systems. Here, we have brie y discussed the control over various parameters in the experiments. The goal of these experiments is to realize or mimic many many-body Hamiltonians in experiments, which until now was just a theoretical tool to describe various many-body physics. In the end we give a brief idea for introducing disorder in the cold-atom experiments discuss the limitations of these experiments in realizing the \interesting" super uid and anti-ferromagnetic phases of fermionic Hubbard model in optical lattices. Chapter-2 : gives a brief idea of \Determinant Quantum Monte-Carlo" (DQM C) technique that has been used to study these systems. In this chapter we will discuss the DQM C algorithm and the observables that can be calculated. We will discuss certain limitation of the DQM C algorithm like numerical instability and sign problem. We will brie y discuss how sign problem doesn't occur in the model we studied. Chapter-3 : discusses the way by which we can bypass the \cooling problem" (high entropy state) to get a fermionic super uid state in the cold atom experi-ments. In this chapter we propose a model whose idea hinges on a low-entropy band-insulator state, which can be tuned to super uid state by tuning the on-site attractive interaction by Feshbach resonance. We show through Gaussian uctua-tion theory that the critical temperature achieved is much higher in our model as compared to the single-band Hubbard model. Through detailed variational Monte Carlo calculations, we have shown that the super uid state is indeed the most stable ground state and there is no other competing order. In the end we give a proposal for its realization in the ultra-cold atom optical lattice systems. Chapter-4 : discusses the DQM C study of the model proposed in chapter- 3. Here we have studied the various single-particle properties like momentum distribution, double occupancies which can be easily measured in cold-atom ex-periments. We also studied the pair-pair and the density-density correlations in detail through DQM C algorithm and mapped out the full T U phase diagram. We show that the proposed model doesn't favor the charge density wave for the interaction strengths we are interested in. Chapter-5 : gives a brief idea of the e ect of adding an on-site random disorder in our proposed bilayer-Hubbard model. We study the e ect of random disorder on various single-particle properties which can be easily veri ed in cold-atom ex-periments. We studied the suppression of the pair-pair correlations as we increase the disorder strength in our proposed model. We nd that the critical value of the interaction doesn't change in the weak-disorder limit. We estimated the critical disorder strength needed to destroy the super uid state and argued that the tran-sition from the super uid to Bose-glass phase in presence of disorder lies in the universality class of (d + 1) XY model. In the end, we give a schematic U V phase diagram for our system. Chapter-6 : We studied the bilayer attractive Hubbard model in different lattice geometry, the bilayer honeycomb lattice, both in presence and in absence of the on-site random disorder. We discussed how the pair-pair and density-density cor-relations behave in the presence and absence of disorder. Through the finite-size scaling analysis we see the co-existence of the super fluid and the charge density wave order at half- lling. An in nitesimal disorder destroys the CDW order com-pletely while the super uid phase found to be robust against weak-disorder. We estimated the critical interaction strength, the critical temperature and the critical disorder strength through nite-size scaling, and provide a putative phase diagram for the system considered.