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The density of states in delta profiled 2D and 1D quantum systems is calculated. It is shown that there are smooth crossovers in the density of states from a 3D square-root behavior to a 2D steplike behavior, and from a 2D to a 1D sawtooth-like behavior, as the confinements increase. Quantum well structures are being extensively studied for applications in ultra large scale integrated circuits and high-speed optoelectronics. As for these systems, the lateral confinement of originally quasi two dimensional (Q2D) electron layers to submicron dimensions has made possible the realization of quasi-one-dimensional (Q1D) electron systems. Among them, resonant tunneling structures are of great interest not only because of their potential applications, but also for the underlying basic physics., Prepared for publication in Physical Review B

The problem of quantization of the electromagnetic field inside a resonator filled with a dielectric medium with time-dependent characteristics in the presence of the external alternating current is studied. The exact propagator, coherent and Fock's states are obtained for a separate quantized mode of the field represented by a quantum oscillator with time-dependent frequency linearly coupled via momentum with the external current. Delta-pulse excitation of the medium is considered as an example.

We present the results of ground-state energies, radial distribution functions, liquid structure functions and effective interactions for a He impurity in a He background in two dimensions. The hypernetted-chain scheme for the system described by a Jastrow-type wavefunction is used, taking into account the triplet correlations and elementary diagrams up to fifth order. Solving the Euler Lagrange equations for the two-body distribution functions, which contain triplet correlation and elementary diagrams, improves the results considerably. Furthermore, as a He impurity is inserted into the He background the ground- state energy increases, but the equilibrium density decreases from 0.0350 A to the -2nd power to 0.0336 A to the -2nd power. The radial distribution function is broadened, while its maximum is lowered and shifted to the right (the direction of increasing radial distance) due to its larger zero-point energy, with therefore less localization of the He particle. The results are compared with Monte Carlo results and other studies., To be published in the Journal of Low Temperature Physics.

The contribution of three-phonon processes to the coefficient of first viscosity in bulk liquid helium is evaluated explicitly as a function of temperature, which is shown to have a 1/T dependence., Prepared in cooperation with Korea Univ., Seoul, Dept. of Physics.

For a damped oscillator forced by a time-dependent field, the exact wave function is obtained by three different methods: (i) Path-integral, (ii) Second quantization and (iii) Dynamical invariant. The explicit form of the dynamical invariant involves a solution to a corresponding auxiliary equation. The coherent states, defined as eigenstates of a new destruction operator, form a nonorthogonal, over complete set and correspond to the minimum uncertainty states. These coherent states give the exact classical motion of the damped driven harmonic oscillator.

The temperature variations of first-, second- and third-sound velocity and attenuation coefficients in one-dimensional superfluid helium are evaluated explicitly for very low temperatures and frequencies (omega s tau << 1, where omega s is the sound frequency and tau the characteristic time), by using the collisionless kinetic equation and superfluid hydrodynamic equations with the energy dissipation effect. The leading terms for these sounds vary as T2, and the ratio of second-sound to first-sound becomes unity as the temperature decreases to absolute zero. Superfluid helium, One dimensional, Sounds, Temperature variations, Hydrodynamics, Theory.

A molecular system adsorbed on a dielectric surface is modeled as a damped harmonic oscillator driven by a sinusoidal external force. The exact propagator and wavefunction through the Feynman path integral method are obtained. The second quantities are evaluated. The amplitude for transitions between harmonic oscillator states and damped driven oscillator states are obtained explicitly, and the result is applied to a two-level system. Keywords: Dielectric surface; Adsorbed molecular system; Quantum mechanics; Damped harmonic oscillator; Sinusoidal external force; Feynman path integral.

Temperature variations of the quasi-diffusion constant and thermal diffusion ratio between phonon and roton gases in two and three-dimensional liquid helium are evaluated explicitly through the scattering of phonons by rotons. The diffusion constants in both dimensions decrease exponentially over the whole temperature range, while the thermal diffusion ratios increase and then decrease as temperature increases in the range from about 0.6 to about 1.1 K.

The exact eigenenergy spectrum of an electron is calculated in a quantum well within an in-plane magnetic field. The numerical solutions for the excited energy states as well as the ground state energy are found for various quantum-well widths and barrier heights. The cyclotron orbits are considerably affected by the quantum well. The energy levels higher than the potential height of the quantum well and the energy levels lower than the potential height of the quantum well show quite different behaviors. These are explained with the properties of the combined potential and the wave function inherent to the system. Keywords: Quantum calculation, Bulk landau levels.

The ground state of a two-dimensional charged-boson system is investigated over the range of densities 1 somewhat < Rs somewhat < 10 in the self-consistent field approximation: Rsub s = Sqrt(1/((a sub o) sq rho pi)), where a is the Bohr radius and rho is the number density. Starting with numerical self-consistent calculations of the static structure factor, the elementary excitation, pair-correlation functions, pressure and ground-state energy are evaluated. These results are compared with those of the two- dimensional and three-dimensional systems obtained from other methods. The ground-state energy is given sub as E0 = -1.2918 Rs-2/3 + 0.03, which improves the result from the ring-diagram approximation.

The elementary excitations of one-dimensional Bose liquids interacting via a soft potential with a Lennard-Jones-type attractive tail are evaluated in the ring-diagram approximation. Starting with this potential, we have evaluated the structure factor, thermodynamic functions, pair-distribution function, ground-state energy, and sound velocity explicitly. The energy spectrum and structure factor ensemble the bulk cases, but the minimum energy is much lower and the first peak of the structure factor is higher. The pair-distribution function decreases as r to the minus 2nd power at large distances, which is characeristics of phonons in one dimension. The ground-state energy is expressed analytically in powers of a dimensionless parameter. The expression agrees with the one obtained from a Beta function-type potential.

The energy dispersion of liquid 4He in the phonon domain is shown to be anomalous. The theoretical cutoff momentum and energy and the group velocity are in good agreement with experiment.

Adopting a soft potential, we have made a microscopic approach to the velocity of third sound in liquid He films and derived an explicit formula for its temperature variation. This formula explains the temperature dependence of third sound without ad hoc assumptions such as those used by Rutledge, McMillan, Mochel, and Washburn. In particular, the source of the temperature dependence of the coefficient to the T term which resulted from their approach is naturally explained.

The decay threshold, phonon width and spreading angle evaluated from the anomalous energy dispersion, obtained from a microscopic theory, are found to be in good agreement with experiment. Relations with some other theories are also discussed. In the past ten years, there have been many discussions regarding the shape of the energy excitation spectrum of liquid He II at low momenta and temperatures. In this section, we shall discuss the decay threshold, the decay angle and the lifetime of the phonon Gamma based on our elementary excitation spectrum. We shall give numerical results in comparison with some other results.

Using the Caldirola-Kanai Hamiltonian for the damped harmonic oscillator, exact coherent states are constructed. These new coherent states satisfy the properties which coherent states should generally have. Keywords include: Damped harmonic oscillator, Coherent states, Caldirola-Kanai Hamiltonian, Quantum dissipative system.