2,432 research outputs found
The Auslander-Gorenstein property for Z-algebras
We provide a framework for part of the homological theory of Z-algebras and
their generalizations, directed towards analogues of the Auslander-Gorenstein
condition and the associated double Ext spectral sequence that are useful for
enveloping algebras of Lie algebras and related rings. As an application, we
prove the equidimensionality of the characteristic variety of an irreducible
representation of the Z-algebra, and for related representations over quantum
symplectic resolutions. In the special case of Cherednik algebras of type A,
this answers a question raised by the authors.Comment: 31 page
Stability and Symmetry Breaking in Metal Nanowires
A general linear stability analysis of simple metal nanowires is presented
using a continuum approach which correctly accounts for material-specific
surface properties and electronic quantum-size effects. The competition between
surface tension and electron-shell effects leads to a complex landscape of
stable structures as a function of diameter, cross section, and temperature. By
considering arbitrary symmetry-breaking deformations, it is shown that the
cylinder is the only generically stable structure. Nevertheless, a plethora of
structures with broken axial symmetry is found at low conductance values,
including wires with quadrupolar, hexapolar and octupolar cross sections. These
non-integrable shapes are compared to previous results on elliptical cross
sections, and their material-dependent relative stability is discussed.Comment: 12 pages, 4 figure
Relation between Barrier Conductance and Coulomb Blockade Peak Splitting for Tunnel-Coupled Quantum Dots
We study the relation between the barrier conductance and the Coulomb
blockade peak splitting for two electrostatically equivalent dots connected by
tunneling channels with bandwidths much larger than the dot charging energies.
We note that this problem is equivalent to a well-known single-dot problem and
present solutions for the relation between peak splitting and barrier
conductance in both the weak and strong coupling limits. Results are in good
qualitative agreement with the experimental findings of F. R. Waugh et al.Comment: 19 pages (REVTeX 3.0), 3 Postscript figure
Universality in metallic nanocohesion: a quantum chaos approach
Convergent semiclassical trace formulae for the density of states and
cohesive force of a narrow constriction in an electron gas, whose classical
motion is either chaotic or integrable, are derived. It is shown that mode
quantization in a metallic point contact or nanowire leads to universal
oscillations in its cohesive force: the amplitude of the oscillations depends
only on a dimensionless quantum parameter describing the crossover from chaotic
to integrable motion, and is of order 1 nano-Newton, in agreement with recent
experiments. Interestingly, quantum tunneling is shown to be described
quantitatively in terms of the instability of the classical periodic orbits.Comment: corrects spelling of one author name on abstract page (paper is
unchanged
A non-Hermitian critical point and the correlation length of strongly correlated quantum systems
We study a non-Hermitian generalization of quantum systems in which an
imaginary vector potential is added to the momentum operator. In the
tight-binding approximation, we make the hopping energy asymmetric in the
Hermitian Hamiltonian. In a previous article, we conjectured that the
non-Hermitian critical point where the energy gap vanishes is equal to the
inverse correlation length of the Hermitian system and we confirmed the
conjecture for two exactly solvable systems. In this article, we present more
evidence for the conjecture. We also argue the basis of our conjecture by
noting the dispersion relation of the elementary excitation.Comment: 25 pages, 18 figure
Influence of Long-Range Coulomb Interactions on the Metal-Insulator Transition in One-Dimensional Strongly Correlated Electron Systems
The influence of long-range Coulomb interactions on the properties of
one-dimensional (1D) strongly correlated electron systems in vicinity of the
metal-insulator phase transition is considered. It is shown that unscreened
repulsive Coulomb forces lead to the formation of a 1D Wigner crystal in the
metallic phase and to the transformation of the square-root singularity of the
compressibility (characterizing the commensurate-incommensurate transition) to
a logarithmic singularity. The properties of the insulating (Mott) phase depend
on the character of the short-wavelength screening of the Coulomb forces. For a
sufficiently short screening length the characteristics of the charge
excitations in the insulating phase are totally determined by the Coulomb
interaction and these quasipartic les can be described as quasiclassical
Coulomb solitons.Comment: 14 pages, LaTeX, G{\"o}teborg preprint APR 94-3
Coherent Resonant Tunneling Through an Artificial Molecule
Coherent resonant tunneling through an artificial molecule of quantum dots in
an inhomogeneous magnetic field is investigated using an extended Hubbard
model. Both the multiterminal conductance of an array of quantum dots and the
persistent current of a quantum dot molecule embedded in an Aharanov-Bohm ring
are calculated. The conductance and persistent current are calculated
analytically for the case of a double quantum dot and numerically for larger
arrays using a multi-terminal Breit-Wigner type formula, which allows for the
explicit inclusion of inelastic processes. Cotunneling corrections to the
persistent current are also investigated, and it is shown that the sign of the
persistent current on resonance may be used to determine the spin quantum
numbers of the ground state and low-lying excited states of an artificial
molecule. An inhomogeneous magnetic field is found to strongly suppress
transport due to pinning of the spin-density-wave ground state of the system,
and giant magnetoresistance is predicted to result from the ferromagnetic
transition induced by a uniform external magnetic field.Comment: 23 pages, 12 figure
Giant Thermoelectric Effect from Transmission Supernodes
We predict an enormous order-dependent quantum enhancement of thermoelectric
effects in the vicinity of a higher-order `supernode' in the transmission
spectrum of a nanoscale junction. Single-molecule junctions based on
3,3'-biphenyl and polyphenyl ether (PPE) are investigated in detail. The
nonequilibrium thermodynamic efficiency and power output of a thermoelectric
heat engine based on a 1,3-benzene junction are calculated using many-body
theory, and compared to the predictions of the figure-of-merit ZT.Comment: 5 pages, 6 figure
TUNNELING SPECTROSCOPY OF QUANTUM CHARGE FLUCTUATIONS IN THE COULOMB BLOCKADE
We present a theory of Coulomb blockade oscillations in tunneling through a
pair of quantum dots connected by a tunable tunneling junction. The positions
and amplitudes of peaks in the linear conductance are directly related,
respectively, to the ground state energy and to the dynamics of charge
fluctuations. We study analytically both strong and weak interdot tunneling. As
the tunneling decreases, the period of the peaks doubles, as observed
experimentally. In the strong tunneling limit, we predict a striking power law
temperature dependence of the peak amplitudes.Comment: 4 pages, revtex3.0, 1 figure uuencode
Kondo Resonance in a Mesoscopic Ring Coupled to a Quantum Dot: Exact Results for the Aharonov-Bohm/Casher Effects
We study the persistent currents induced by both the Aharonov-Bohm and
Aharonov-Casher effects in a one-dimensional mesoscopic ring coupled to a
side-branch quantum dot at Kondo resonance. For privileged values of the
Aharonov-Bohm-Casher fluxes, the problem can be mapped onto an integrable
model, exactly solvable by a Bethe ansatz. In the case of a pure magnetic
Aharonov-Bohm flux, we find that the presence of the quantum dot has no effect
on the persistent current. In contrast, the Kondo resonance interferes with the
spin-dependent Aharonov-Casher effect to induce a current which, in the
strong-coupling limit, is independent of the number of electrons in the ring.Comment: Replaced with published version; 5 page
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