164 research outputs found
Even-odd correlations in capacitance fluctuations of quantum dots
We investigate effects of short range interactions on the addition spectra of
quantum dots using a disordered Hubbard model. A correlation function \cS(q) is
defined on the inverse compressibility versus filling data, and computed
numerically for small lattices. Two regimes of interaction strength are
identified: the even/odd fluctuations regime typical of Fermi liquid ground
states, and a regime of structureless \cS(q) at strong interactions. We
propose to understand the latter regime in terms of magnetically correlated
localized spins.Comment: 3 pages, Revtex, Without figure
Early-life environment and differences in costs of reproduction in a preindustrial human population
Reproduction is predicted to trade-off with long-term maternal survival, but the survival costs often vary between individuals, cohorts and populations, limiting our understanding of this trade-off, which is central to life-history theory. One potential factor generating variation in reproductive costs is variation in developmental conditions, but the role of early-life environment in modifying the reproduction-survival trade-off has rarely been investigated. We quantified the effect of early-life environment on the trade-off between female reproduction and survival in pre-industrial humans by analysing individual-based life-history data for >80 birth cohorts collected from Finnish church records, and between-year variation in local crop yields, annual spring temperature, and infant mortality as proxies of early-life environment. We predicted that women born during poor environmental conditions would show higher costs of reproduction in terms of survival compared to women born in better conditions. We found profound variation between the studied cohorts in the correlation between reproduction and longevity and in the early-life environment these cohorts were exposed to, but no evidence that differences in early-life environment or access to wealth affected the trade-off between reproduction and survival. Our results therefore do not support the hypothesis that differences in developmental conditions underlie the observed heterogeneity in reproduction-survival trade-off between individuals
Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots
We show that the parametric correlations of the conductance peak amplitudes
of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime
become universal upon an appropriate scaling of the parameter. We compute the
universal forms of this correlator for both cases of conserved and broken time
reversal symmetry. For a symmetric dot the correlator is independent of the
details in each lead such as the number of channels and their correlation. We
derive a new scaling, which we call the rotation scaling, that can be computed
directly from the dot's eigenfunction rotation rate or alternatively from the
conductance peak heights, and therefore does not require knowledge of the
spectrum of the dot. The relation of the rotation scaling to the level velocity
scaling is discussed. The exact analytic form of the conductance peak
correlator is derived at short distances. We also calculate the universal
distributions of the average level width velocity for various values of the
scaled parameter. The universality is illustrated in an Anderson model of a
disordered dot.Comment: 35 pages, RevTex, 6 Postscript figure
Magnetotunneling spectroscopy of mesoscopic correlations in two-dimensional electron systems
An approach to experimentally exploring electronic correlation functions in
mesoscopic regimes is proposed. The idea is to monitor the mesoscopic
fluctuations of a tunneling current flowing between the two layers of a
semiconductor double-quantum-well structure. From the dependence of these
fluctuations on external parameters, such as in-plane or perpendicular magnetic
fields, external bias voltages, etc., the temporal and spatial dependence of
various prominent correlation functions of mesoscopic physics can be
determined. Due to the absence of spatially localized external probes, the
method provides a way to explore the interplay of interaction and localization
effects in two-dimensional systems within a relatively unperturbed environment.
We describe the theoretical background of the approach and quantitatively
discuss the behavior of the current fluctuations in diffusive and ergodic
regimes. The influence of both various interaction mechanisms and localization
effects on the current is discussed. Finally a proposal is made on how, at
least in principle, the method may be used to experimentally determine the
relevant critical exponents of localization-delocalization transitions.Comment: 15 pages, 3 figures include
"Level Curvature" Distribution for Diffusive Aharonov-Bohm Systems: analytical results
We calculate analytically the distributions of "level curvatures" (LC) (the
second derivatives of eigenvalues with respect to a magnetic flux) for a
particle moving in a white-noise random potential.
We find that the Zakrzewski-Delande conjecture is still valid even if the
lowest weak localization corrections are taken into account. The ratio of mean
level curvature modulus to mean dissipative conductance is proved to be
universal and equal to in agreement with available numerical data.Comment: 12 pages. Submitted to Phys.Rev.
Energy level dynamics in systems with weakly multifractal eigenstates: equivalence to 1D correlated fermions
It is shown that the parametric spectral statistics in the critical random
matrix ensemble with multifractal eigenvector statistics are identical to the
statistics of correlated 1D fermions at finite temperatures. For weak
multifractality the effective temperature of fictitious 1D fermions is
proportional to (1-d_{n})/n, where d_{n} is the fractal dimension found from
the n-th moment of inverse participation ratio. For large energy and parameter
separations the fictitious fermions are described by the Luttinger liquid model
which follows from the Calogero-Sutherland model. The low-temperature
asymptotic form of the two-point equal-parameter spectral correlation function
is found for all energy separations and its relevance for the low temperature
equal-time density correlations in the Calogero-Sutherland model is
conjectured.Comment: 4 pages, Revtex, final journal versio
Statistics of pre-localized states in disordered conductors
The distribution function of local amplitudes of single-particle states in
disordered conductors is calculated on the basis of the supersymmetric
-model approach using a saddle-point solution of its reduced version.
Although the distribution of relatively small amplitudes can be approximated by
the universal Porter-Thomas formulae known from the random matrix theory, the
statistics of large amplitudes is strongly modified by localization effects. In
particular, we find a multifractal behavior of eigenstates in 2D conductors
which follows from the non-integer power-law scaling for the inverse
participation numbers (IPN) with the size of the system. This result is valid
for all fundamental symmetry classes (unitary, orthogonal and symplectic). The
multifractality is due to the existence of pre-localized states which are
characterized by power-law envelopes of wave functions, , . The pre-localized states in short quasi-1D wires have the
power-law tails , too, although their IPN's
indicate no fractal behavior. The distribution function of the
largest-amplitude fluctuations of wave functions in 2D and 3D conductors has
logarithmically-normal asymptotics.Comment: RevTex, 17 twocolumn pages; revised version (several misprint
corrected
Which Kubo formula gives the exact conductance of a mesoscopic disordered system?
In both research and textbook literature one often finds two ``different''
Kubo formulas for the zero-temperature conductance of a non-interacting Fermi
system. They contain a trace of the product of velocity operators and
single-particle (retarded and advanced) Green operators: or . The study investigates the relationship between
these expressions, as well as the requirements of current conservation, through
exact evaluation of such quantum-mechanical traces for a nanoscale (containing
1000 atoms) mesoscopic disordered conductor. The traces are computed in the
semiclassical regime (where disorder is weak) and, more importantly, in the
nonperturbative transport regime (including the region around
localization-delocalization transition) where concept of mean free path ceases
to exist. Since quantum interference effects for such strong disorder are not
amenable to diagrammatic or nonlinear -model techniques, the evolution
of different Green function terms with disorder strength provides novel insight
into the development of an Anderson localized phase.Comment: 7 pages, 5 embedded EPS figures, final published version (note: PRB
article has different title due to editorial censorship
Elastic deformation of a fluid membrane upon colloid binding
When a colloidal particle adheres to a fluid membrane, it induces elastic
deformations in the membrane which oppose its own binding. The structural and
energetic aspects of this balance are theoretically studied within the
framework of a Helfrich Hamiltonian. Based on the full nonlinear shape
equations for the membrane profile, a line of continuous binding transitions
and a second line of discontinuous envelopment transitions are found, which
meet at an unusual triple point. The regime of low tension is studied
analytically using a small gradient expansion, while in the limit of large
tension scaling arguments are derived which quantify the asymptotic behavior of
phase boundary, degree of wrapping, and energy barrier. The maturation of
animal viruses by budding is discussed as a biological example of such
colloid-membrane interaction events.Comment: 14 pages, 9 figures, REVTeX style, follow-up on cond-mat/021242
Alternative Technique for "Complex" Spectra Analysis
. The choice of a suitable random matrix model of a complex system is very
sensitive to the nature of its complexity. The statistical spectral analysis of
various complex systems requires, therefore, a thorough probing of a wide range
of random matrix ensembles which is not an easy task. It is highly desirable,
if possible, to identify a common mathematcal structure among all the ensembles
and analyze it to gain information about the ensemble- properties. Our
successful search in this direction leads to Calogero Hamiltonian, a
one-dimensional quantum hamiltonian with inverse-square interaction, as the
common base. This is because both, the eigenvalues of the ensembles, and, a
general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary
initial conditions. The varying nature of the complexity is reflected in the
different form of the evolution parameter in each case. A complete
investigation of Calogero Hamiltonian can then help us in the spectral analysis
of complex systems.Comment: 20 pages, No figures, Revised Version (Minor Changes
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