Approach to Equilibrium of a Nondegenerate Quantum System: Decay of Oscillations and Detailed Balance as Separate Effects of a Reservoir

The approach to equilibrium of a nondegenerate quantum system involves the damping of microscopic population oscillations, and, additionally, the bringing about of detailed balance, i.e. the achievement of the correct Boltzmann factors relating the populations. These two are separate effects of interaction with a reservoir. One stems from the randomization of phases and the other from phase space considerations. Even the meaning of the word `phase' differs drastically in the two instances in which it appears in the previous statement. In the first case it normally refers to quantum phases whereas in the second it describes the multiplicity of reservoir states that corresponds to each system state. The generalized master equation theory for the time evolution of such systems is here developed in a transparent manner and both effects of reservoir interactions are addressed in a unified fashion. The formalism is illustrated in simple cases including in the standard spin-boson situation wherein a quantum dimer is in interaction with a bath consisting of harmonic oscillators. The theory has been constructed for application in energy transfer in molecular aggregates and in photosynthetic reaction centers

Investigation of chemically reacting and radiating supersonic internal flows

The two-dimensional spatially elliptic Navier-Stokes equations are used to investigate the chemically reacting and radiating supersonic flow of the hydrogen-air system between two parallel plates and in a channel with a ten degree compression-expansion ramp at the lower boundary. The explicit unsplit finite-difference technique of MacCormack is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The tangent slab approximation is employed in the radiative flux formation. Both pseudo-gray and nongray models are used to represent the absorption characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the flow field

Investigation of radiative interactions in supersonic internal flows

Analyses and numerical procedures are presented to study the radiative interactions of absorbing emitting species in chemically reacting supersonic flow in various ducts. The 2-D time dependent Navier-Stokes equations in conjunction with radiative flux equation are used to study supersonic flows undergoing finite rate chemical reaction in a hydrogen air system. The specific problem considered is the flow of premixed radiating gas between parallel plates. Specific attention was directed toward studying the radiative contribution of H2O, OH, and NO under realistic physical and flow conditions. Results are presented for the radiative flux obtained for different gases and for various combination of these gases. The problem of chemically reacting and radiating flows was solved for the flow of premixed hydrogen-air through a 10 deg compression ramp. Results demonstrate that the radiative interaction increases with an increase in pressure, temperature, amount of participating species, plate spacing, and Mach number. Most of the energy, however, is transferred by convection in the flow direction. In general the results indicate that radiation can have a significant effect on the entire flow field

Temperature dependence of the spin relaxation in highly degenerate ZnO thin films

Zinc oxide is a wide-bandgap semiconductor which is considered a potential candidate for fabricating next-generation transparent spintronic devices. However, before this can be practically achieved, a thorough, scientific understanding of the various spin transport and relaxation processes undergone in this material is essential. In the present paper we report our investigations into these processes via temperature dependent, non-local Hanle experiments. Epitaxial ZnO thin films were deposited on c-axis sapphire substrates using a pulsed laser deposition technique. Careful structural, optical, and electrical characterizations of the films were performed. Temperature dependent Hanle measurements were carried out, using an all-electrical scheme for spin injection and detection, in a non-local geometry over the temperature range of 20 - 300 K. Carrier concentration in these films, as determined by Hall effect measurements, was found to be of the order of 10^19 cm^-3. It was determined that in such a degenerately doped system it is essential to use Fermi-Dirac statistics to explain the transport of carriers in the system. From the Hanle data, spin relaxation time in the ZnO films was determined at different temperatures. Our analysis of the temperature-dependent spin relaxation time data suggests that the dominant mechanism of spin relaxation in ZnO films is the Dyakonov-Perel (DP) mechanism modified for the wurtzite crystalline structure in which a hexagonal c-axis reflection asymmetry is present. As a result of this modification the spin-relaxation rate is linear-in-momentum.Comment: 19 pages, 5 figure

Classification of Lie point symmetries for quadratic Lieˊ\acute{\textbf{e}}nard type equation x¨+f(x)x˙2+g(x)=0\ddot{x}+f(x)\dot{x}^2+g(x)=0

In this paper we carry out a complete classification of the Lie point symmetry groups associated with the quadratic Li$\acute{e}$nard type equation, $\ddot {x} + f(x){\dot {x}}^{2} + g(x)= 0$, where $f(x)$ and $g(x)$ are arbitrary functions of $x$. The symmetry analysis gets divided into two cases, $(i)$ the maximal (eight parameter) symmetry group and $(ii)$ non-maximal (three, two and one parameter) symmetry groups. We identify the most general form of the quadratic Li$\acute{e}$nard equation in each of these cases. In the case of eight parameter symmetry group, the identified general equation becomes linearizable as well as isochronic. We present specific examples of physical interest. For the nonmaximal cases, the identified equations are all integrable and include several physically interesting examples such as the Mathews-Lakshmanan oscillator, particle on a rotating parabolic well, etc. We also analyse the underlying equivalence transformations

Classical Electron Model with Negative Energy Density in Einstein-Cartan Theory of Gravitation

Experimental result regarding the maximum limit of the radius of the electron \sim 10^{-16} cm and a few of the theoretical works suggest that the gravitational mass which is a priori a positive quantity in Newtonian mechanics may become negative in general theory of relativity. It is argued that such a negative gravitational mass and hence negative energy density also can be obtained with a better physical interpretation in the framework of Einstein-Cartan theory.Comment: 12 Latex pages, added refs and conclusion