This thesis investigates the properties of an atomic system exhibiting a giant Kerr nonlinearity. The atomic energy level scheme involves four energy levels. A three level A subsystem in the atom exhibits the effect of electromagnetically induced transparency (EIT), reducing the spontaneous emission noise. The fourth level leads to an ac-Stark shift of the ground state, which in turn leads to a giant, noiseless Kerr nonlinearity. Two different environments are explored. First, a system comprising of large number of atoms in an optical cavity is analysed. Detailed aspects of noise reduction in this system are investigated. In particular, strong squeezing in the quadrature in phase with the field driving the cavity mode is found, if the effective coupling of light to the atoms is strong. However, the linewidth of the predicted squeezing is found to be very narrow. This is attributed to a very steep linear susceptibility of the atomic medium. Since the widening of the squeezing window is possible only for weaker effective coupling, in turn reducing the squeezing level, a different environment is proposed. This involves a single four level atom, strongly coupled to the cavity mode. In such a strongly coupled system, the most appropriate approach is found to be that formulated in terms of polaritons – composite excitations of the 'atom-cavity molecule'. Adopting the polariton approach, nonclassical correlations in the field leaving the cavity are investigated. Strong photon antibunching is found and the effect of photon blockade predicted and described. The photon blockade effect can also be found in a system comprised of a two level atom coupled to the cavity mode, if the external driving is tuned to one of the vacuum Rabi resonances. A comparison between the two schemes is performed, and it is found that the four level scheme exhibits much better photon blockade. The reason for this is quantum interference between secondary transitions in the dressed states picture. Destructive interference cancels the transitions that would otherwise introduce a second photon into the system, hence producing a more robust photon blockade. All of these results are valid in the regime where external driving is weak. If the external driving strength is increased, the photon statistics (as measured by the zero-delay second order correlation function) changes from strong antibunching to strong bunching, over a relatively narrow range of driving strengths. The occurrence of this change can again be attributed to quantum interference. It is shown that the interference effect prevents the excitation of the composite system by a second photon, but not excitation by a two-photon transition (following the first excitation). Therefore, the third excitation manifold is excited, which then decays back to the first manifold in a two photon cascade. This two photon cascade is the source of correlated photon pairs causing an increase in the second order correlation function. The dynamics of forward scattering of light is presented, and nonclassical behaviour of the delay dependence of correlation function ('overshoots' and 'undershoots') is discussed. For the analytical treatment of this system, a method based on the polariton approach is devised, which includes the treatment of driving and damping. It is shown that this method is ideally suited to the analysis of strongly coupled systems, where only a few photons contribute to the dynamics.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

The theory of radiative transfer is applied to the problem of multiple wave scattering in a one-dimensional multilayer. A new mathematical model of a multilayer is presented in which both the refractive index and width of each layer are randomized. The layer widths are generated by a new probability distribution which allows for strong layer width disorder. An expression for the transport mean free path of the multilayer is derived based on its single-scattering properties. It will be shown that interference between the field reflected from adjacent layer interfaces remains significant even in the presence of strong layer width disorder. It will be proven that even when the scattering is weak, the field in a random multilayer localizes at certain frequencies. The effect of increasing layer width randomization on this form of localization is quantified. The radiative transfer model of time-harmonic scattering in multilayers is extended to narrow-band pulse propagation in weakly scattering media. The tendency of pulses to broaden in this medium is discussed. A radiative transport model of the system is developed and compared to numerical solutions of the wave equation. It is observed that pulse broadening is not described by simple transfer theory. The radiative transfer model is extended by the addition of a Laplacian term in an attempt to model the effect of ensemble average pulse broadening. Numerical simulation results in support of this proposal are given, and applications for the theory suggested. Finally, the problem of acoustic wave scattering by planar screens is considered. The study was motivated by the idea that multiple scattering experiments may prove possible in a medium composed of such scatterers. Successful multiple scattering in a medium of planar scatterers will depend on the scattering cross-section at angles away from normal incidence. The scattering cross-section is calculated for a circular disc using a new technique for solving the acoustic wave equation on planar surfaces. The method is validated by comparison with available analytic solutions and the geometric theory of diffraction.

Zero-point energy is the energy of the vacuum. Disturbing the vacuum results in a change in the zero-point energy. In 1948, Casimir considered the change in the zeropoint energy when the vacuumis disturbed by two parallelmetal plates. The plates disturb the vacuum by restricting the quantum fluctuations of the electromagnetic field. Casimir found that the change in the zero-point energy implies that the plates are attracted to each other. With the recent advances made in the experimental verification of this remarkable result, theoretical interest has been rekindled. In addition to the original parallel plate configuration, several other boundaries have been studied. In this thesis, two novel boundaries are considered: elliptic-cylindrical and spheroidal. The results for these boundaries lead to the conjecture that zero-point energy does not change for small deformations of the boundary that preserve volume. Assuming the conjecture, it is shown that zero-point energy plays a stabilizing role in quantum chromodynamics, the leading theory of the strong interaction.

Firstly, the effect of pectin on acid milk gels in concentrated, quiescent systems was investigated by passive microrheology using two complementary techniques: diffusive wave spectroscopy (DWS) and multiple particle tracking (MPT). DWS, by allowing probing the mechanical properties of the network at high frequency, gave information on its microstructure. The addition of high methoxyl pectins was shown to change the network structure which has been explained by bridging of the casein micelles by the polymer as the system was undergoing acidification. On the other hand, the presence of low methoxyl pectin in the acid milk gel was shown to have no effect on the microstructure of the network at low concentration of polymer (0.1%w/w) which has been attributed to the sensitivity of this low DM pectin to calcium: LM pectin are trapped by calcium and not able to interact with casein micelles anymore. Multiple particle tracking was used to probe the effect of pectin on the heterogeneity of the system by following the distribution of the displacements of added micro beads at a given time lag during the gelation using the Van Hove distribution. Furthermore, the surface chemistry of the probes was modified in an attempt to control their location in the system. Finally, the mean square displacements of the casein micelles obtained by DWS and, of k-casein coated particles obtained by MPT were shown to give good agreement for the same acid milk system. Having established that the interaction between casein micelles and low methoxyl pectin is prevented by the pectin sensitivity to calcium, the effect of the pectin fine structure was investigated on the interaction between k-casein and pectin by surface plasmon resonance (SPR). The amount of pectin binding on a k-casein coated gold surface was shown to be strongly dependant on the pectin fine structure. It was concluded that small negative patches on the pectin backbone, likely to comprise of around two consecutive unmethylesterified galacturonic acid, are the most effective for pectin binding to k-casein. The effect of the direct interaction between pectin and k- casein on ‘calcium-free casein micelle mimics’ in pectin solution was then investigated using coated latex beads. A pectin structure with a limited number of negative patches on its backbone was also shown to limit the potential for destabilization via bridging.

The possibility and feasibility is investigated of including in the modelling of nuclear cluster reactions a unified treatment of the effects both of the non-orthogonalities between transfer channels, and of the antisymmetrisation required by the Pauli Principle. The deuteron - nucleus interaction, the simplest cluster reaction, is considered in detail within the Coupled Channels framework. The Coupled Channels formalism was chosen because it accurately handles inelastic and transfer couplings of arbitary strengths. The fact that transfer channels are orthogonal to each other only asymptotically is taken into account by reallocating the wave function in the internal region, from the deuteron channels to the transfer channels, taking components from the deuteron channels in ways exactly analogous to the way the antisymmetrisation requirements remove blocked deuteron-core components. Thus a unified treatment of the two effects is facilitated. It is found further that when all possible transfer channels are included, along with all Pauli blockings from the core nucleons, then under certain conditions at low energies, the wave function in the deuteron channel is small and oscillatory in the internal region, leaving the deuteron as a cluster to have largely asymptotic significance. In this limit, the exact non-local potential governing the deuteron channel simplifies considerably in one approximation to be replaceable by just several orthogonality conditions, and these are easily modelled in solving the coupled equations for the radial wave functions. This simplified and unified model has the advantage, since the deuteron's internal wave form is significant only asymptotically, of allowing automatically for arbitary deuteron polarisation by the core (though not vice-versa). Furthermore, the asymptotic matching is not at a fixed radius as in R-matrix theory, but is a continuous process that depends on the binding energies of the actual proton & neutron bound states in the residual nucleus.

The possibility and feasibility is investigated of including in the modelling of nuclear cluster reactions a unified treatment of the effects both of the non-orthogonalities between transfer channels, and of the antisymmetrisation required by the Pauli Principle. The deuteron - nucleus interaction, the simplest cluster reaction, is considered in detail within the Coupled Channels framework. The Coupled Channels formalism was chosen because it accurately handles inelastic and transfer couplings of arbitary strengths. The fact that transfer channels are orthogonal to each other only asymptotically is taken into account by reallocating the wave function in the internal region, from the deuteron channels to the transfer channels, taking components from the deuteron channels in ways exactly analogous to the way the antisymmetrisation requirements remove blocked deuteron-core components. Thus a unified treatment of the two effects is facilitated. It is found further that when all possible transfer channels are included, along with all Pauli blockings from the core nucleons, then under certain conditions at low energies, the wave function in the deuteron channel is small and oscillatory in the internal region, leaving the deuteron as a cluster to have largely asymptotic significance. In this limit, the exact non-local potential governing the deuteron channel simplifies considerably in one approximation to be replaceable by just several orthogonality conditions, and these are easily modelled in solving the coupled equations for the radial wave functions. This simplified and unified model has the advantage, since the deuteron's internal wave form is significant only asymptotically, of allowing automatically for arbitary deuteron polarisation by the core (though not vice-versa). Furthermore, the asymptotic matching is not at a fixed radius as in R-matrix theory, but is a continuous process that depends on the binding energies of the actual proton & neutron bound states in the residual nucleus.

The possibility and feasibility is investigated of including in the modelling of nuclear cluster reactions a unified treatment of the effects both of the non-orthogonalities between transfer channels, and of the antisymmetrisation required by the Pauli Principle. The deuteron - nucleus interaction, the simplest cluster reaction, is considered in detail within the Coupled Channels framework. The Coupled Channels formalism was chosen because it accurately handles inelastic and transfer couplings of arbitary strengths. The fact that transfer channels are orthogonal to each other only asymptotically is taken into account by reallocating the wave function in the internal region, from the deuteron channels to the transfer channels, taking components from the deuteron channels in ways exactly analogous to the way the antisymmetrisation requirements remove blocked deuteron-core components. Thus a unified treatment of the two effects is facilitated. It is found further that when all possible transfer channels are included, along with all Pauli blockings from the core nucleons, then under certain conditions at low energies, the wave function in the deuteron channel is small and oscillatory in the internal region, leaving the deuteron as a cluster to have largely asymptotic significance. In this limit, the exact non-local potential governing the deuteron channel simplifies considerably in one approximation to be replaceable by just several orthogonality conditions, and these are easily modelled in solving the coupled equations for the radial wave functions. This simplified and unified model has the advantage, since the deuteron's internal wave form is significant only asymptotically, of allowing automatically for arbitary deuteron polarisation by the core (though not vice-versa). Furthermore, the asymptotic matching is not at a fixed radius as in R-matrix theory, but is a continuous process that depends on the binding energies of the actual proton & neutron bound states in the residual nucleus.