Conductance Fluctuations of Generic Billiards: Fractal or Isolated?

We study the signatures of a classical mixed phase space for open quantum systems. We find the scaling of the break time up to which quantum mechanics mimics the classical staying probability and derive the distribution of resonance widths. Based on these results we explain why for mixed systems two types of conductance fluctuat ions were found: quantum mechanics divides the hierarchically structured chaotic component of phase space into two parts - one yields fractal conductance fluctuations while the other causes isolated resonances. In general, both types appear together, but on different energy scales.Comment: restructured and new figure

MONTE CARLO SIMULATION OF ICE Ih : COMPARISON OF BULK MELTING AT CONSTANT PRESSURE AND STRUCTURE OF ICE LAYERS ON AN ICE NUCLEATING SUBSTRATE

Recently effective pair potentials (1) and Metropolis Monte Carlo methods have been used to study the melting of a periodic rigid molecule model ice system at constant volume (2, 3) near 290 K. We have extended these studies to examination of the system at constant pressure and present the results for approximately 1 atm pressure. In this approach the constant number, pressure and temperature (NPT) ensemble is approximated by treating the volume as an additional variable in the Metropolis Monte Carlo procedure (4-7). The unit cell for these calculations contains 192 rigid central force (1) water molecules and the initial configurations are taken from the constant number, volume and temperature (NVT) equilibrated system (3) at 260 K. This initial ice Ih unit cell has approximately zero dipole and quadrupole moments and was shown to remain in the ice Ih structure over a range of temperature from 20 K to about 290 K in constant NVT ensemble studies. The pressure is found to be extremely sensitive to the intermolecular interactions and to the instantaneous density of molecules in the unit cell. The unit cell properties (dipole moment, ice structure factors, specific heat, and pair correlation functions) will be presented. A comparison will be made with simulations of two water layers on a model ice nucleating substrate (8) at 200 K and 265 K near zero pressure. At 200 K the structure of the top layer of this system shows considerable disorder and liquid - like properties, while the water layer adjacent to the substrate has a solid ice - like hexagonal ring structure. There appears to be no preference for water dipole orientation in the exposed layer of water molecules. The liquid-like properties of the exposed layers in this system at 200 K and the melting of the bulk near 290 K are consistent with recent observations that surface layers have noticably reduced solid-liquid transition temperatures (9). When these absorbed water layers are subjected to a large external electric field or constant presure (~ 200 atm) there appears to no significant change in the exposed layer structure and liquid-like states. Unit cell properties for the layer systems will be discussed. The motivation for these studies has been to examine the effect of pressure, temperature and other external perturbations (such as substrate structure and substrate defects) on atmospheric ice nucleation

Scaling of Nucleation Rates

The homogeneous nucleation rate, J, for T ≪ Tc can be cast into a corresponding states form by exploiting scaled expressions for the vapor pressure and for the surface tension, σ. In the vapor-to-liquid case with σ = σ0[Tc-T], the classical cluster energy of formation /kT = [16π/3]·Ω3[Tc/T-1]3/(ln S)2 ≡ [x0/x]2, where Ω ≡ σ0[k ñ2/3] and ñ is liquid number density. The Ω ≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications of σ and Ω.) The above [x0/x]2 is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data. In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with ln J ≈ const. - [x0/x]2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (Γc), where Γc is the inverse thermal wavelength cubed per second at T = Tc. The ln (Γc) is ≈ 60 in cgs units (74 in SI units) for most materials. A physical basis for the latter form, which includes the behavior at small n, the discrete integer behavior of n, and a configurational entropy term, τ ln (n), is presented