369 research outputs found
Thermodynamics as an alternative foundation for zero-temperature density functional theory and spin density functional theory
Thermodynamics provides a transparent definition of the free energy of
density functional theory (DFT), and of its derivatives - the potentials, at
finite temperatures T. By taking the T to 0 limit, it is shown here that both
DFT and spin-dependent DFT (for ground states) suffer from precisely the same
benign ambiguities: (a) charge and spin quantization lead to "up to a constant"
indeterminacies in the potential and the magnetic field respectively, and (b)
the potential in empty subspaces is undetermined but irrelevant. Surprisingly,
these simple facts were inaccessible within the standard formulation, leading
to recent discussions of apparent difficulties within spin-DFT.Comment: RevTeX, to appear in Phys. Rev.
The spectral form factor is not self-averaging
The spectral form factor, k(t), is the Fourier transform of the two level
correlation function C(x), which is the averaged probability for finding two
energy levels spaced x mean level spacings apart. The average is over a piece
of the spectrum of width W in the neighborhood of energy E0. An additional
ensemble average is traditionally carried out, as in random matrix theory.
Recently a theoretical calculation of k(t) for a single system, with an energy
average only, found interesting nonuniversal semiclassical effects at times t
approximately unity in units of {Planck's constant) /(mean level spacing). This
is of great interest if k(t) is self-averaging, i.e, if the properties of a
typical member of the ensemble are the same as the ensemble average properties.
We here argue that this is not always the case, and that for many important
systems an ensemble average is essential to see detailed properties of k(t). In
other systems, notably the Riemann zeta function, it is likely possible to see
the properties by an analysis of the spectrum.Comment: 4 pages, RevTex, no figures, submitted to Phys. Rev. Lett., permanent
e-mail address, [email protected]
Can the trace formula describe weak localisation?
We attempt to systematically derive perturbative quantum corrections to the
Berry diagonal approximation of the two-level correlation function (TLCF) for
chaotic systems. To this end, we develop a ``weak diagonal approximation''
based on a recent description of the first weak localisation correction to
conductance in terms of the Gutzwiller trace formula. This semiclassical method
is tested by using it to derive the weak localisation corrections to the TLCF
for a semiclassically disordered system. Unfortunately the method is unable to
correctly reproduce the ``Hikami boxes'' (the relatively small regions where
classical paths are glued together by quantum processes). This results in the
method failing to reproduce the well known weak localisation expansion. It so
happens that for the first order correction it merely produces the wrong
prefactor. However for the second order correction, it is unable to reproduce
certain contributions, and leads to a result which is of a different form to
the standard one.Comment: 23 pages in Latex (with IOP style files), 3 eps figures included, to
be a symposium paper in a Topical Issue of Waves in Random Media, 199
Characteristic Potentials for Mesoscopic Rings Threaded by an Aharonov-Bohm Flux
Electro-static potentials for samples with the topology of a ring and
penetrated by an Aharonov-Bohm flux are discussed. The sensitivity of the
electron-density distribution to small variations in the flux generates an
effective electro-static potential which is itself a periodic function of flux.
We investigate a simple model in which the flux sensitive potential leads to a
persistent current which is enhanced compared to that of a loop of
non-interacting electrons. For sample geometries with contacts the sensitivity
of the electro-static potential to flux leads to a flux-induced capacitance.
This capacitance gives the variation in charge due to an increment in flux. The
flux-induced capacitance is contrasted with the electro-chemical capacitance
which gives the variation in charge due to an increment in an electro-chemical
potential. The discussion is formulated in terms of characteristic functions
which give the variation of the electro-static potential in the interior of the
conductor due to an increment in the external control parameters (flux,
electro-chemical potentials). Paper submitted to the 16th Nordic Semiconductor
Meeting, Laugarvatan, Iceland, June 12-15, 1994. The proceedings will be
published in Physica Scripta.Comment: 23 pages + 4 figures, revtex, IBM-RC1955
Periodic-Orbit Theory of Anderson Localization on Graphs
We present the first quantum system where Anderson localization is completely
described within periodic-orbit theory. The model is a quantum graph analogous
to an a-periodic Kronig-Penney model in one dimension. The exact expression for
the probability to return of an initially localized state is computed in terms
of classical trajectories. It saturates to a finite value due to localization,
while the diagonal approximation decays diffusively. Our theory is based on the
identification of families of isometric orbits. The coherent periodic-orbit
sums within these families, and the summation over all families are performed
analytically using advanced combinatorial methods.Comment: 4 pages, 3 figures, RevTe
Semiclassical analysis of the quantum interference corrections to the conductance of mesoscopic systems
The Kubo formula for the conductance of a mesoscopic system is analyzed
semiclassically, yielding simple expressions for both weak localization and
universal conductance fluctuations. In contrast to earlier work which dealt
with times shorter than , here longer times are taken to
give the dominant contributions. For such long times, many distinct classical
orbits may obey essentially the same initial and final conditions on positions
and momenta, and the interference between pairs of such orbits is analyzed.
Application to a chain of classically ergodic scatterers connected in
series gives the following results: for the
weak localization correction to the zero--temperature dimensionless
conductance, and for the variance of its
fluctuations. These results interpolate between the well known ones of random
scattering matrices for , and those of the one--dimensional diffusive wire
for .Comment: 53 pages, using RevTeX, plus 3 postscript figures mailed separately.
A short version of this work is available as cond-mat/950207
Toward semiclassical theory of quantum level correlations of generic chaotic systems
In the present work we study the two-point correlation function
of the quantum mechanical spectrum of a classically chaotic system. Recently
this quantity has been computed for chaotic and for disordered systems using
periodic orbit theory and field theory. In this work we present an independent
derivation, which is based on periodic orbit theory. The main ingredient in our
approach is the use of the spectral zeta function and its autocorrelation
function . The relation between and is
constructed by making use of a probabilistic reasoning similar to that which
has been used for the derivation of Hardy -- Littlewood conjecture. We then
convert the symmetry properties of the function into relations
between the so-called diagonal and the off-diagonal parts of . Our
results are valid for generic systems with broken time reversal symmetry, and
with non-commensurable periods of the periodic orbits.Comment: 15 pages(twocolumn format), LaTeX, EPSF, (figures included
Spectral statistics of disordered metals in the presence of several Aharonov-Bohm fluxes
The form factor for spectral correlations in a diffusive metal is calculated
in the presence of several Aharonov-Bohm fluxes. When the fluxes are
equal, the correlations are universal functions of where is
the dimensionless conductance and is the number of applied fluxes. This
explains recent flux dependence of the correlations found numerically at the
metal-insulator transition.Comment: 3 pages, Latex, 1 figure, to appear in Phys. Rev. B Rapid Com
Observations Of Rotating Radio Transients With The First Station Of The Long Wavelength Array
Rotating Radio Transients (RRATs) are a subclass of pulsars first identified in 2006 that are detected only in searches for single pulses and not through their time averaged emission. Here, we present the results of observations of 19 RRATs using the first station of the Long Wavelength Array (LWA1) at frequencies between 30 MHz and 88 MHz. The RRATs observed here were first detected in higher frequency pulsar surveys. Of the 19 RRATs observed, 2 sources were detected and their dispersion measures, periods, pulse profiles, and flux densities are reported and compared to previous higher frequency measurements. We find a low detection rate (11%), which could be a combination of the lower sensitivity of LWA1 compared to the higher frequency telescopes, and the result of scattering by the interstellar medium or a spectral turnover. Taylor, G B; Stovall, K; McCrackan, M; McLaughlin, M A; Miller, R; Karako-Argaman, C; Dowell, J; Schinzel, F
Leading off-diagonal contribution to the spectral form factor of chaotic quantum systems
We semiclassically derive the leading off-diagonal correction to the spectral
form factor of quantum systems with a chaotic classical counterpart. To this
end we present a phase space generalization of a recent approach for uniformly
hyperbolic systems (M. Sieber and K. Richter, Phys. Scr. T90, 128 (2001); M.
Sieber, J. Phys. A: Math. Gen. 35, L613 (2002)). Our results coincide with
corresponding random matrix predictions. Furthermore, we study the transition
from the Gaussian orthogonal to the Gaussian unitary ensemble.Comment: 8 pages, 2 figures; J. Phys. A: Math. Gen. (accepted for publication
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