7,261 research outputs found
Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
We derive the finite temperature Keldysh response theory for interacting
fermions in the presence of quenched disorder, as applicable to any of the 10
Altland-Zirnbauer classes in an Anderson delocalized phase with at least a U(1)
continuous symmetry. In this formulation of the interacting Finkel'stein
nonlinear sigma model, the statistics of one-body wave functions are encoded by
the constrained matrix field, while physical correlations follow from the
hydrodynamic density or spin response field, which decouples the interactions.
Integrating out the matrix field first, we obtain weak (anti)localization and
Altshuler-Aronov quantum conductance corrections from the hydrodynamic response
function. This procedure automatically incorporates the correct infrared
physics, and in particular gives the Altshuler-Aronov-Khmelnitsky (AAK)
equations for dephasing of weak (anti)localization due to electron-electron
collisions. We explicate the method by deriving known quantum corrections in
two dimensions for the symplectic metal class AII, as well as the spin-SU(2)
invariant superconductor classes C and CI. We show that conductance corrections
due to the special modes at zero energy in nonstandard classes are
automatically cut off by temperature, as previously expected, while the
Wigner-Dyson class Cooperon modes that persist to all energies are cut by
dephasing. We also show that for short-ranged interactions, the standard
self-consistent solution for the dephasing rate is equivalent to a diagrammatic
summation via the self-consistent Born approximation. This should be compared
to the AAK solution for long-ranged Coulomb interactions, which exploits the
Markovian noise correlations induced by thermal fluctuations of the
electromagnetic field. We discuss prospects for exploring the many-body
localization transition from the ergodic side as a dephasing catastrophe in
short-range interacting models.Comment: 68 pages, 23 figure
Stability of an oscillating boundary layer
Levchenko and Solov'ev (1972, 1974) have developed a stability theory for space periodic flows, assuming that the Floquet theory is applicable to partial differential equations. In the present paper, this approach is extended to unsteady periodic flows. A complete unsteady formulation of the stability problem is obtained, and the stability characteristics over an oscillating period are determined from the solution of the problem. Calculations carried out for an oscillating incompressible boundary layer on a plate showed that the boundary layer flow may be regarded as a locally parallel flow
Generation and development of small-amplitude disturbances in a laminar boundary layer in the presence of an acoustic field
A low-turbulence subsonic wind tunnel was used to study the influence of acoustic disturbances on the development of small sinusoidal oscillations (Tollmien-Schlichting waves) which constitute the initial phase of turbulent transition. It is found that acoustic waves propagating opposite to the flow generate vibrations of the model (plate) in the flow. Neither the plate vibrations nor the acoustic field itself have any appreciable influence on the stability of the laminar boundary layer. The influence of an acoustic field on laminar boundary layer disturbances is limited to the generation of Tollmien-Schlichting waves at the leading-edge of the plate
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