712 research outputs found
Transport in Luttinger Liquids
We give a brief introduction to Luttinger liquids and to the phenomena of
electronic transport or conductance in quantum wires. We explain why the
subject of transport in Luttinger liquids is relevant and fascinating and
review some important results on tunneling through barriers in a
one-dimensional quantum wire and the phenomena of persistent currents in
mesoscopic rings. We give a brief description of our own work on transport
through doubly-crossed Luttinger liquids and transport in the Schulz-Shastry
exactly solvable Luttinger-like model.Comment: Latex file, 15 pages, four eps figure
Density of states near the Mott-Hubbard transition in the limit of large dimensions
The zero temperature Mott-Hubbard transition as a function of the Coulomb
repulsion U is investigated in the limit of large dimensions. The behavior of
the density of states near the transition at U=U_c is analyzed in all orders of
the skeleton expansion. It is shown that only two transition scenarios are
consistent with the skeleton expansion for U<U_c: (i) The Mott-Hubbard
transition is "discontinuous" in the sense that in the density of states finite
spectral weight is redistributed at U_c. (ii) The transition occurs via a point
at U=U_c where the system is neither a Fermi liquid nor an insulator.Comment: 4 pages, 1 figure; revised version accepted for publication in Phys.
Rev. Let
Bosonization of Fermi liquids
We bosonize a Fermi liquid in any number of dimensions in the limit of long
wavelengths. From the bosons we construct a set of coherent states which are
related with the displacement of the Fermi surface due to particle-hole
excitations. We show that an interacting hamiltonian in terms of the original
fermions is quadratic in the bosons. We obtain a path integral representation
for the generating functional which in real time, in the semiclassical limit,
gives the Landau equation for sound waves and in the imaginary time gives us
the correct form of the specific heat for a Fermi liquid even with the
corrections due to the interactions between the fermions. We also discuss the
similarities between our results and the physics of quantum crystals.Comment: 42 pages, RevteX, preprint UIUC (1993
Transport theory
The usual theories of electrical conductivity suffer from a number of weaknesses. A more general theory will be described which gives the entire density matrix of a system of charge carriers in the steady state. It will be shown that the usual theory is valid under certain limiting conditions, but that in general there are rather complicated corrections to it.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32468/1/0000553.pd
Generalization of the Luttinger Theorem for Fermionic Ladder Systems
We apply a generalized version of the Lieb-Schultz-Mattis Theorem to
fermionic ladder systems to show the existence of a low-lying excited state
(except for some special fillings). This can be regarded as a non-perturbative
proof for the conservation under interaction of the sum of the Fermi wave
vectors of the individual channels, corresponding to a generalized version of
the Luttinger Theorem to fermionic ladder systems. We conclude by noticing that
the Lieb-Schultz-Mattis Theorem is not applicable in this form to show the
existence of low-lying excitations in the limit that the number of legs goes to
infinity, e.g. in the limit of a 2D plane.Comment: RevTex, 4 pages with 4 eps figure
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