We describe a multi-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions and the corresponding photon statistics are discussed. Some applications to quantum optics, cavity quantum electrodynamics, and superfocusing in channeling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.

Abstract. We consider the radiation field operators in a cavity with varying dielectric medium in terms of solutions of Heisenberg's equations of motion for the most general one-dimensional quadratic Hamiltonian. Explicit solutions of these equations are obtained and applications to the radiation field quantization, including randomly varying media, are briefly discussed. [48] and the references therein). For a classical Hamiltonian system one replaces canonically conjugate coordinates and momenta by time-dependent operators q λ (t) and p λ (t) that satisfy the commutation rules Canonical QuantizationThe time-evolution is determined by the Heisenberg equations of motion [38]: In the present letter, we study the radiation field operators in a varying dispersive medium, which is mathematically described by the most general phenomenological quadratic Hamiltonian H in an abstract Hilbert space. (We concentrate on a single photon cavity mode, say υ, with frequency ω υ = 1 and use the units c = = 1. From now on, we shall usually omit the indices when dealing with the single mode under consideration.) In particular, our approach gives a natural Date: April 9, 2013. 2010 Mathematics Subject Classification. Primary 81Q05, 35C05. Secondary 42A38.

Solvent-based processes are often used as potential recovery agents in bitumen systems, with and without the addition of heat to the solvent. Solvents can sometimes be applied as a liquid phase, during SAGD start-up operations or processes aimed at developing injectivity into the oil. Light hydrocarbon liquids are traditionally tested for this application. Solvent injection may also occur in a vapour state and its objective is to reduce oil viscosity and improve mobility of bitumen under low temperatures Ͻ100°C. In general, hydrocarbon solvents such as propane are often used for this application. The objective of this study is to conduct CT-based measurement of static mixing of bitumen and both liquid and vapour phase solvents, and to quantify some of the time-dependent changes that occur during solvent mixing with bitumen.Diffusion experiments have been conducted with propane and DME (vapour phase) and with propane, DME, pentane and toluene (liquid phase) solvent systems. Solvents are mixed with medium viscosity Peace River bitumen and high viscosity Grosmont bitumen. The Tests are run under constant pressure and temperature, and Computer-Assisted Tomography (CT) is used to monitor mass transfer of solvent into oil as a function of time. The outcome of this study is measurements of mass transfer rates of solvent into oil, and the degree of oil phase swelling during the tests.During solvent injection processes in the field, the rate of mixing is a key parameter that will help in deciding which solvent is optimal for different processes. This study focuses on the rate of solvent mixing with oil. In vapour phase solvent systems, the analysis of the CT images allows for an understanding of the impact of oil phase swelling on the effective rate of penetration of solvent into oil. Overall, the test data provided in this work demonstrates that DME mixes into oil faster than other solvents, and leads to more swelling in a vapour solvent-bitumen system. The analysis of CT data provides an understanding of concentration-dependent diffusion coefficients and limitations from predicting mass transfer using constant coefficients in liquid and vapour solvent systems.

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Solvent-based processes have shown technical advantages over thermal techniques for recovery of heavy oil and bitumen. The success of these processes relies on accurate computation of molecular diffusion coefficient which determines how fast a solvent penetrates into oil. Concentration profile measurements of solvent in oil are used for the determination of the molecular diffusion coefficient. Although numerous experimental techniques have been proposed, the accurate estimation of this parameter is still a topic of debate in the literature. In this work, 1-D nuclear magnetic resonance imaging (MRI) is employed to obtain diffusivity data for a toluene–heavy oil system. Diffusion of toluene in heavy oil was monitored for 20 days at a controlled temperature of 35 °C and ambient pressure. Over time, toluene diffusion into oil leads to changes in spatial distribution of T 1 and T 2 that affect the received signal. This serves as the basis of the solvent and heavy oil concentration estimation. Consequently, concentration profiles were established by converting the MRI signals to concentration values. This conversion was achieved by creating samples with known concentrations of heavy oil–toluene and measuring their response in the same environment and parameter settings. A concentration-dependent diffusion coefficient was obtained from concentration profiles. The results show that relaxation based 1D MRI is an accurate and robust tool to obtain diffusivity data in complex fluids such as heavy oil.