42 research outputs found
On the Stability and Single-Particle Properties of Bosonized Fermi Liquids
We study the stability and single-particle properties of Fermi liquids in
spatial dimensions greater than one via bosonization. For smooth non-singular
Fermi liquid interactions we obtain Shankar's renormalization- group flows and
reproduce well known results for quasi-particle lifetimes. We demonstrate by
explicit calculation that spin-charge separation does not occur when the Fermi
liquid interactions are regular. We also explore the relationship between
quantized bosonic excitations and zero sound modes and present a concise
derivation of both the spin and the charge collective mode equations. Finally
we discuss some aspects of singular Fermi liquid interactions.Comment: 13 pages plus three postscript figures appended; RevTex 3.0;
BUP-JBM-
Inelastic lifetimes of confined two-component electron systems in semiconductor quantum wire and quantum well structures
We calculate Coulomb scattering lifetimes of electrons in two-subband quantum
wires and in double-layer quantum wells by obtaining the quasiparticle
self-energy within the framework of the random-phase approximation for the
dynamical dielectric function. We show that, in contrast to a single-subband
quantum wire, the scattering rate in a two-subband quantum wire contains
contributions from both particle-hole excitations and plasmon excitations. For
double-layer quantum well structures, we examine individual contributions to
the scattering rate from quasiparticle as well as acoustic and optical plasmon
excitations at different electron densities and layer separations. We find that
the acoustic plasmon contribution in the two-component electron system does not
introduce any qualitatively new correction to the low energy inelastic
lifetime, and, in particular, does not produce the linear energy dependence of
carrier scattering rate as observed in the normal state of high-
superconductors.Comment: 16 pages, RevTeX, 7 figures. Also available at
http://www-cmg.physics.umd.edu/~lzheng
Mathematics and biology: a Kantian view on the history of pattern formation theory
Driesch’s statement, made around 1900, that the physics and chemistry of his day were unable to explain self-regulation during embryogenesis was correct and could be extended until the year 1972. The emergence of theories of self-organisation required progress in several areas including chemistry, physics, computing and cybernetics. Two parallel lines of development can be distinguished which both culminated in the early 1970s. Firstly, physicochemical theories of self-organisation arose from theoretical (Lotka 1910–1920) and experimental work (Bray 1920; Belousov 1951) on chemical oscillations. However, this research area gained broader acceptance only after thermodynamics was extended to systems far from equilibrium (1922–1967) and the mechanism of the prime example for a chemical oscillator, the Belousov–Zhabotinski reaction, was deciphered in the early 1970s. Secondly, biological theories of self-organisation were rooted in the intellectual environment of artificial intelligence and cybernetics. Turing wrote his The chemical basis of morphogenesis (1952) after working on the construction of one of the first electronic computers. Likewise, Gierer and Meinhardt’s theory of local activation and lateral inhibition (1972) was influenced by ideas from cybernetics. The Gierer–Meinhardt theory provided an explanation for the first time of both spontaneous formation of spatial order and of self-regulation that proved to be extremely successful in elucidating a wide range of patterning processes. With the advent of developmental genetics in the 1980s, detailed molecular and functional data became available for complex developmental processes, allowing a new generation of data-driven theoretical approaches. Three examples of such approaches will be discussed. The successes and limitations of mathematical pattern formation theory throughout its history suggest a picture of the organism, which has structural similarity to views of the organic world held by the philosopher Immanuel Kant at the end of the eighteenth century