Applications and identification of surface correlations

We compare theoretical, experimental, and computational approaches to random rough surfaces. The aim is to produce rough surfaces with desirable correlations and to analyze the correlation functions extracted from the surface profiles. Physical applications include ultracold neutrons in a rough waveguide, lateral electronic transport, and scattering of longwave particles and waves. Results provide guidance on how to deal with experimental and computational data on rough surfaces. A supplemental goal is to optimize the neutron waveguide for GRANIT experiments. The measured correlators are identified by fitting functions or by direct spectral analysis. The results are used to compare the calculated observables with theoretical values. Because of fluctuations, the fitting procedures lead to inaccurate physical results even if the quality of the fit is very good unless one guesses the right shape of the fitting function. Reliable extraction of the correlation function from the measured surface profile seems virtually impossible without independent information on the structure of the correlation function. Direct spectral analysis of raw data rarely works better than the use of a "wrong" fitting function. Analysis of surfaces with a large correlation radius is hindered by the presence of domains and interdomain correlations

Quantum Size Effect in Conductivity of Multilayer Metal Films

Conductivity of quantized multilayer metal films is analyzed with an emphasis on scattering by rough interlayer interfaces. Three different types of quantum size effect (QSE) in conductivity are predicted. Two of these QSE are similar to those in films with scattering by rough walls. The third type of QSE is unique and is observed only for certain positions of the interface. The corresponding peaks in conductivity are very narrow and high with a finite cutoff which is due only to some other scattering mechanism or the smearing of the interface. There are two classes of these geometric resonances. Some of the resonance positions of the interface are universal and do not depend on the strength of the interface potential while the others are sensitive to this potential. This geometric QSE gradually disappears with an increase in the width of the interlayer potential barrier.Comment: 12 pages, 10 figures, RevTeX4, to be published in Phys. Rev B (April 2003

Mode Coupling in Quantized High Quality Films

The effect of coupling of quantized modes on transport and localization in ultrathin films with quantum size effect (QSE) is discussed. The emphasis is on comparison of films with Gaussian, exponential, and power-law long-range behavior of the correlation function of surface, thickness, or bulk fluctuations. For small-size inhomogeneities, the mode coupling is the same for inhomogeneities of all types and the transport coefficients behave in the same way. The mode coupling becomes extremely sensitive to the correlators for large-size inhomogeneities leading to the drastically distinct behavior of the transport coefficients. In high-quality films there is a noticeable difference between the QSE patterns for films with bulk and surface inhomogeneities which explains why the recently predicted new type of QSE with large oscillations of the transport coefficients can be observed mostly in films with surface-driven relaxation. In such films with surface-dominated scattering the higher modes contribute to the transport only as a result of opening of the corresponding mode coupling channels and appear one by one. Mode coupling also explains a much higher transport contribution from the higher modes than it is commonly believed. Possible correlations between the inhomogeneities from the opposite walls provide, because of their oscillating response to the mode quantum numbers, a unique insight into the mode coupling. The presence of inhomogeneities of several sizes leads not to a mechanical mixture of QSE patterns, but to the overall shifting and smoothing of the oscillations. The results can lead to new, non-destructive ways of analysis of the buried interfaces and to study of inhomogeneities on the scales which are inaccessible for scanning techniques

Low-Temperature Spin Diffusion in a Spin-Polarized Fermi Gas

We present a finite temperature calculation of the transverse spin-diffusion coefficient, $D_\bot$, in a dilute degenerate Fermi gas in the presence of a small external magnetic field, $H$. While the longitudinal diffusion coefficient displays the conventional low-temperature Fermi-liquid behavior, $D_\parallel \propto T^{-2}$, the corresponding results for $D_\bot$ show three separate regimes: (a) $D_\bot \sim H^{-2}$ for $T \ll H$; (b) $D_\bot \sim T^{-2}$, $D_\bot /D_\parallel \neq 1$ for $T \gg H$ and large spin-rotation parameter $\xi \gg 1$, and (c) $D_\bot = D_\parallel \propto T^{-2}$ for $T \gg H$ and $\xi \ll 1$. Our results are qualitatively consistent with the available experimental data in weakly spin-polarized $^3{\rm He}$ and $^3{\rm He} - ^4{\rm He}$ mixtures.Comment: 13 pages, REVTEX, 3 figures available upon request, RU-94-4

Crystalline order in superfluid 3He films

We predict an inhomogeneous phase of superfluid 3He films in which translational symmetry is spontaneously broken in the plane of the film. This phase is energetically favored over a range of film thicknesses, $D_{c_2}(T)<D<D_{c_1}(T)$, separating distinct homogeneous superfluid phases. The instability at the critical film thickness, $D_{c_2}\approx 9 \xi(T)$, is a single-mode instability generating striped phase order in the film. Numerical calculations of the order parameter and free energy indicate a second-order instability to a periodic lattice of degenerate B-like phases separated by domain walls at $D_{c_1}\approx 12 \xi(T)$. The striped phase should be identifiable in transport and nuclear magnetic resonance experiments.Comment: 4 pages, 4 figure

Transport in \u3csup\u3e3\u3c/sup\u3eHe-\u3csup\u3e4\u3c/sup\u3eHe Mixtures in Restricted Geometry

The effect of wall scattering on transport in dilute degenerate 3He–4He mixtures in quasi-2D flow channels or films is discussed. The calculation of the quasiparticle mean free path combines particle–wall and particle–particle collisions including the interference between them. The spin polarization affects the wall-driven contribution by changing bulk mean free path and particle wavelength. The expressions for the wall contribution to transport coefficients are especially transparent in the limiting cases of large and small bulk mean free paths. The calculated temperature, concentration, and polarization dependences of the transport coefficients allow one to extract parameters of surface roughness from experimental data on transport

Alkali-Metal Gases in Optical Lattices: Possible New Type of Quantum Crystals

Similarities between alkali-metal gases in optical lattices with noninteger occupation of the lattice sites and quantum crystals are explored. The analogy with the vacancy liquid (VL) provides an alternative explanation to the Mott transition for the recent experiment on the phase transition in the lattice. The VL can undergo Bose-Einstein condensation (BEC) with Tc within experimental reach. Direct and vacancy-assisted mechanisms of the band motion for hyperfine impurities are discussed. A large concentration of vacancies can result in the spatial decomposition of the system into pure hyperfine components. Below the vacancy condensation the impurity component resembles 3He in 3He–He II mixtures

Transport Equation and Diffusion in Ultrathin Channels and Films

A rigorous perturbative transport equation for ballistic particles in thin films with random rough walls is derived by the diagrammatic Keldysh technique for both quasiclassical and quantized motion across the film. The derivation is based on canonical Migdal transformation that replaces a transport problem with random rough walls by an equivalent problem with flat boundaries and randomly distorted bulk. The rigorous derivation requires a modification of our previously used transformation to avoid non-Hermitian perturbations. The unusual nondiagonal structure of the effective scattering operator makes the transport equation different from the standard Waldmann-Snider equation when the distance between quantized levels for the motion across the film is comparable to the wall-induced perturbation. Outside of this anomalous quantum resonance region, the transport equation is similar to that for scattering by bulk impurities. The magnitude of the anomaly is calculated for degenerate particles and Gaussian correlations of surface inhomogeneities. The transport problem is solved analytically for the single-band occupancy and in the limiting cases of very large and very small correlation radii of inhomogeneities for an arbitrary correlation function of surface roughness. Elsewhere, the transport equation is analyzed numerically for the Gaussian correlation function. Transport coefficients are expressed explicitly via the angular harmonics of the surface correlation function; in the anomalous region, the results contain certain supplemental correlators. The results reveal various effects of interwall correlations on transport including an oscillatory dependence on the number of occupied minibands. The transition from quantum to quasiclassical description of ballistic motion across the (thick) film can be hindered by residual interwall interference effects similar to those in classical optic problems for thick films without bulk attenuation. Erroneous matrix elements in our previous calculations have been corrected

Interference of Bulk and Boundary Scattering in Films with Quantum Size Effect

The interference between boundary and bulk scattering processes is analyzed for ultrathin films with random rough walls. The effective collision and transport relaxation times for scattering by random bulk and surface inhomogeneities are calculated, when possible analytically, in quantum size effect conditions. The transport and localization results are expressed via the bulk transport parameters and statistical characteristics of the surface corrugation. The diagrammatic calculation includes second-order effects for boundary scattering and full summation for bulk processes. The interference contribution is large in systems with robust bulk scattering and can be comparable to, or even exceed, the pure wall contribution to the transport coefficients