514 research outputs found
Quantum dots with two electrons: Singlet-triplet transitions
The magnetic character of the ground-state of two electrons on a double
quantum dot, connected in series to left and right single-channel leads, is
considered. By solving exactly for the spectrum of the two interacting
electrons, it is found that the coupling to the continuum of propagating states
on the leads, in conjunction with the electron-electron interactions, may
result in a delocalization of the bound state of the two electrons. This, in
turn, reduces significantly the range of the Coulomb interaction parameters
over which singlet-triplet transitions can be realized. It is also found that
the coupling to the leads favors the singlet ground-state.Comment: 8 pages, submitted to Phys. Rev.
Ground-state energy and spin in disordered quantum dots
We investigate the ground-state energy and spin of disordered quantum dots
using spin-density-functional theory. Fluctuations of addition energies
(Coulomb-blockade peak spacings) do not scale with average addition energy but
remain proportional to level spacing. With increasing interaction strength, the
even-odd alternation of addition energies disappears, and the probability of
non-minimal spin increases, but never exceeds 50%. Within a two-orbital model,
we show that the off-diagonal Coulomb matrix elements help stabilize a ground
state of minimal spin.Comment: 10 pages, 2 figure
Interactions and Disorder in Quantum Dots: Instabilities and Phase Transitions
Using a fermionic renormalization group approach we analyse a model where the
electrons diffusing on a quantum dot interact via Fermi-liquid interactions.
Describing the single-particle states by Random Matrix Theory, we find that
interactions can induce phase transitions (or crossovers for finite systems) to
regimes where fluctuations and collective effects dominate at low energies.
Implications for experiments and numerical work on quantum dots are discussed.Comment: 4 pages, 1 figure; version to appear in Phys Rev Letter
Spin and e-e interactions in quantum dots: Leading order corrections to universality and temperature effects
We study the statistics of the spacing between Coulomb blockade conductance
peaks in quantum dots with large dimensionless conductance g. Our starting
point is the ``universal Hamiltonian''--valid in the g->oo limit--which
includes the charging energy, the single-electron energies (described by random
matrix theory), and the average exchange interaction. We then calculate the
magnitude of the most relevant finite g corrections, namely, the effect of
surface charge, the ``gate'' effect, and the fluctuation of the residual e-e
interaction. The resulting zero-temperature peak spacing distribution has
corrections of order Delta/sqrt(g). For typical values of the e-e interaction
(r_s ~ 1) and simple geometries, theory does indeed predict an asymmetric
distribution with a significant even/odd effect. The width of the distribution
is of order 0.3 Delta, and its dominant feature is a large peak for the odd
case, reminiscent of the delta-function in the g->oo limit. We consider finite
temperature effects next. Only after their inclusion is good agreement with the
experimental results obtained. Even relatively low temperature causes large
modifications in the peak spacing distribution: (a) its peak is dominated by
the even distribution at kT ~ 0.3 Delta (at lower T a double peak appears); (b)
it becomes more symmetric; (c) the even/odd effect is considerably weaker; (d)
the delta-function is completely washed-out; and (e) fluctuation of the
coupling to the leads becomes relevant. Experiments aimed at observing the T=0
peak spacing distribution should therefore be done at kT<0.1 Delta for typical
values of the e-e interaction.Comment: 15 pages, 4 figure
Orthogonality Catastrophe in Parametric Random Matrices
We study the orthogonality catastrophe due to a parametric change of the
single-particle (mean field) Hamiltonian of an ergodic system. The Hamiltonian
is modeled by a suitable random matrix ensemble. We show that the overlap
between the original and the parametrically modified many-body ground states,
, taken as Slater determinants, decreases like , where is
the number of electrons in the systems, is a numerical constant of the
order of one, and is the deformation measured in units of the typical
distance between anticrossings. We show that the statistical fluctuations of
are largely due to properties of the levels near the Fermi energy.Comment: 12 pages, 8 figure
Distinct or shared actions of peptide family isoforms: II. Multiple pyrokinins exert similar effects in the lobster stomatogastric nervous system
Many neuropeptides are members of peptide families, with multiple structurally similar isoforms frequently found even within a single species. This raises the question of whether the individual peptides serve common or distinct functions. In the accompanying paper, we found high isoform specificity in the responses of the lobster (Homarus americanus) cardiac neuromuscular system to members of the pyrokinin peptide family: only one of five crustacean isoforms showed any bioactivity in the cardiac system. Because previous studies in other species had found little isoform specificity in pyrokinin actions, we examined the effects of the same five crustacean pyrokinins on the lobster stomatogastric nervous system (STNS). In contrast to our findings in the cardiac system, the effects of the five pyrokinin isoforms on the STNS were indistinguishable: they all activated or enhanced the gastric mill motor pattern, but did not alter the pyloric pattern. These results, in combination with those from the cardiac ganglion, suggest that members of a peptide family in the same species can be both isoform specific and highly promiscuous in their modulatory capacity. The mechanisms that underlie these differences in specificity have not yet been elucidated; one possible explanation, which has yet to be tested, is the presence and differential distribution of multiple receptors for members of this peptide family
Interactions in Chaotic Nanoparticles: Fluctuations in Coulomb Blockade Peak Spacings
We use random matrix models to investigate the ground state energy of
electrons confined to a nanoparticle. Our expression for the energy includes
the charging effect, the single-particle energies, and the residual screened
interactions treated in Hartree-Fock. This model is applicable to chaotic
quantum dots or nanoparticles--in these systems the single-particle statistics
follows random matrix theory at energy scales less than the Thouless energy. We
find the distribution of Coulomb blockade peak spacings first for a large dot
in which the residual interactions can be taken constant: the spacing
fluctuations are of order the mean level separation Delta. Corrections to this
limit are studied using the small parameter 1/(kf L): both the residual
interactions and the effect of the changing confinement on the single-particle
levels produce fluctuations of order Delta/sqrt(kf L). The distributions we
find are significantly more like the experimental results than the simple
constant interaction model.Comment: 17 pages, 4 figures, submitted to Phys. Rev.
Integrable model for interacting electrons in metallic grains
We find an integrable generalization of the BCS model with non-uniform
Coulomb and pairing interaction. The Hamiltonian is integrable by construction
since it is a functional of commuting operators; these operators, which
therefore are constants of motion of the model, contain the anisotropic Gaudin
Hamiltonians. The exact solution is obtained diagonalizing them by means of
Bethe Ansatz. Uniform pairing and Coulomb interaction are obtained as the
``isotropic limit'' of the Gaudin Hamiltonians. We discuss possible
applications of this model to a single grain and to a system of few interacting
grains.Comment: 4 pages, revtex. Revised version to be published in Phys. Rev. Let
Ground-State Magnetization for Interacting Fermions in a Disordered Potential : Kinetic Energy, Exchange Interaction and Off-Diagonal Fluctuations
We study a model of interacting fermions in a disordered potential, which is
assumed to generate uniformly fluctuating interaction matrix elements. We show
that the ground state magnetization is systematically decreased by off-diagonal
fluctuations of the interaction matrix elements. This effect is neglected in
the Stoner picture of itinerant ferromagnetism in which the ground-state
magnetization is simply determined by the balance between ferromagnetic
exchange and kinetic energy, and increasing the interaction strength always
favors ferromagnetism. The physical origin of the demagnetizing effect of
interaction fluctuations is the larger number of final states available for
interaction-induced scattering in the lower spin sectors of the Hilbert space.
We analyze the energetic role played by these fluctuations in the limits of
small and large interaction . In the small limit we do second-order
perturbation theory and identify explicitly transitions which are allowed for
minimal spin and forbidden for higher spin. These transitions then on average
lower the energy of the minimal spin ground state with respect to higher spin.
For large interactions we amplify on our earlier work [Ph. Jacquod and A.D.
Stone, Phys. Rev. Lett. 84, 3938 (2000)] which showed that minimal spin is
favored due to a larger broadening of the many-body density of states in the
low-spin sectors. Numerical results are presented in both limits.Comment: 35 pages, 24 figures - final, shortened version, to appear in
Physical Review
The Parallel Magnetoconductance of Interacting Electrons in a Two Dimensional Disordered System
The transport properties of interacting electrons for which the spin degree
of freedom is taken into account are numerically studied for small two
dimensional diffusive clusters. On-site electron-electron interactions tend to
delocalize the electrons, while long-range interactions enhance localization.
On careful examination of the transport properties, we reach the conclusion
that it does not show a two dimensional metal insulator transition driven by
interactions. A parallel magnetic field leads to enhanced resistivity, which
saturates once the electrons become fully spin polarized. The strength of the
magnetic field for which the resistivity saturates decreases as electron
density goes down. Thus, the numerical calculations capture some of the
features seen in recent experimental measurements of parallel
magnetoconductance.Comment: 10 pages, 6 figure
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