280 research outputs found
Quantum particle statistics on the holographic screen leads to Modified Newtonian Dynamics (MOND)
Employing a thermodynamic interpretation of gravity based on the holographic
principle and assuming underlying particle statistics, fermionic or bosonic,
for the excitations of the holographic screen leads to Modified Newtonian
Dynamics (MOND). A connection between the acceleration scale appearing in
MOND and the Fermi energy of the holographic fermionic degrees of freedom is
obtained. In this formulation the physics of MOND results from the
quantum-classical crossover in the fermionic specific heat. However, due to the
dimensionality of the screen, the formalism is general and applies to two
dimensional bosonic excitations as well. It is shown that replacing the
assumption of the equipartition of energy on the holographic screen by a
standard quantum-statistical-mechanics description wherein some of the degrees
of freedom are frozen out at low temperatures is the physical basis for the
MOND interpolating function . The interpolating function is calculated within the statistical mechanical formalism and compared to
the leading phenomenological interpolating functions, most commonly used. Based
on the statistical mechanical view of MOND, its cosmological implications are
re-interpreted: the connection between and the Hubble constant is
described as a quantum uncertainty relation; and the relationship between
and the cosmological constant is better understood physically
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
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
Bell's Theorem and the Causal Arrow of Time
Einstein held that the formalism of Quantum Mechanics (QM) entails "spooky
actions at a distance". Indeed, in the 60's Bell showed that the predictions of
QM disagree with the results of any locally causal description. Accepting
non-local descriptions while retaining causality leads to a clash with the
theory of relativity. Furthermore, the causal arrow of time by definition
contradicts time-reversal symmetry. For these reasons, some authors (Feynman
and Wheeler, Costa de Beauregard, Cramer, Price) have advocated abandoning
microscopic causality. In the present article, a simplistic but concrete
example of following this line of thought is presented, in the form of a
retro-causal toy-model which is stochastic and which provides an appealing
description of the specific quantum correlations discussed by Bell. One
concludes that Einstein's "spooky actions" may occur "in the past" rather than
"at a distance", resolving the tension between QM and relativity, and opening
unexplored possibilities for future reformulations of QM.Comment: Extensive changes. Conditionally accepted by American Journal of
Physic
Electron-electron interactions in one- and three-dimensional mesoscopic disordered rings: a perturbative approach
We have computed persistent currents in a disordered mesoscopic ring in the
presence of small electron-electron interactions, treated in first order
perturbation theory. We have investigated both a contact (Hubbard) and a
nearest neighbour interaction in 1D and 3D. Our results show that a repulsive
Hubbard interaction produces a paramagnetic contribution to the average current
(whatever the dimension) and increases the value of the typical current. On the
other hand, a nearest neighbour repulsive interaction results in a diamagnetic
contribution in 1D and paramagnetic one in 3D, and tends to decrease the value
of the typical current in any dimension. Our study is based on numerical
simulations on the Anderson model and is justified analytically in the presence
of very weak disorder. We have also investigated the influence of the amount of
disorder and of the statistical (canonical or grand-canonical) ensemble.Comment: 7 pages in REVTEX, 4 figure
LEVEL CORRELATIONS DRIVEN BY WEAK LOCALIZATION IN 2-D SYSTEMS
We consider the two-level correlation function in two-dimensional disordered
systems. In the non-ergodic diffusive regime, at energy
( is the Thouless energy), it is shown to be completely determined by
the weak localization effects, thus being extremely sensitive to time-reversal
and spin symmetry breaking: it decreases drastically in the presence of
magnetic field or magnetic impurities and changes its sign in the presence of a
spin-orbit interaction. In contrast to this, the variance of the levels number
fluctuations is shown to be almost unaffected by the weak localization effects.Comment: 4 pages, 2 figures, in self-ectracting uuencoded file, submitted to
Phys. Rev. Letters
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
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
Correlations and fluctuations of a confined electron gas
The grand potential and the response of a phase-coherent confined noninteracting electron gas depend
sensitively on chemical potential or external parameter . We compute
their autocorrelation as a function of , and temperature. The result
is related to the short-time dynamics of the corresponding classical system,
implying in general the absence of a universal regime. Chaotic, diffusive and
integrable motions are investigated, and illustrated numerically. The
autocorrelation of the persistent current of a disordered mesoscopic ring is
also computed.Comment: 12 pages, 1 figure, to appear in Phys. Rev.
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