7,104 research outputs found
Comment on Frauchiger and Renner paper (Nat. Commun. 9, 3711 (2018)): the problem of stopping times
The Gedankenexperiment advanced by Frauchiger and Renner in their Nature
paper is based on an implicit assumption that one can synchronize stochastic
measurement intervals between two non-interacting systems. This hypothesis, the
author demonstrates, is equivalent to the complete entanglement of these
systems. Consequently, Frauchiger and Renner's postulate Q is too broad and, in
general, meaningless. Accurate reformulation of the postulate, Q1 does not seem
to entail any paradoxes with measurement. This paper is agnostic with respect
to particular interpretations of quantum mechanics. Nor does it refer to the
collapse of the wavefunction.Comment: The figure was added to the manuscript's Appendi
Ejection Energy of Photoelectrons in Strong Field Ionization
We show that zero ejection energy of the photoelectrons is classically
impossible for hydrogen-like ions, even when field ionization occurs
adiabatically. To prove this we transform the basic equations to those
describing two 2D anharmonic oscillators. The same method yields an alternative
way to derive the anomalous critical field of hydrogen-like ions. The
analytical results are confirmed and illustrated by numerical simulations. PACS
Number: 32.80.RmComment: 7 pages, REVTeX, postscript file including the figures is available
at http://www.physik.th-darmstadt.de/tqe/dieter/publist.html or via anonymous
ftp from ftp://tqe.iap.physik.th-darmstadt.de/pub/dieter/publ_I_pra_pre.ps,
accepted for publication in Phys. Rev.
Fictitious Level Dynamics: A Novel Approach to Spectral Statistics in Disordered Conductors
We establish a new approach to calculating spectral statistics in disordered
conductors, by considering how energy levels move in response to changes in the
impurity potential. We use this fictitious dynamics to calculate the spectral
form factor in two ways. First, describing the dynamics using a Fokker-Planck
equation, we make a physically motivated decoupling, obtaining the spectral
correlations in terms of the quantum return probability. Second, from an
identity which we derive between two- and three-particle correlation functions,
we make a mathematically controlled decoupling to obtain the same result. We
also calculate weak localization corrections to this result, and show for two
dimensional systems (which are of most interest) that corrections vanish to
three-loop order.Comment: 35 pages in REVTeX format including 10 postscript figures; to be
published in a special issue (on Topics in Mesoscopic Physics) of the Journal
of Mathematical Physics, October 199
The Zipf law for random texts with unequal probabilities of occurrence of letters and the Pascal pyramid
We model the generation of words with independent unequal probabilities of
occurrence of letters. We prove that the probability of occurrence of
words of rank has a power asymptotics. As distinct from the paper published
earlier by B. Conrad and M. Mitzenmacher, we give a brief proof by elementary
methods and obtain an explicit formula for the exponent of the power law.Comment: 4 page
Crossover from diffusive to strongly localized regime in two-dimensional systems
We have studied the conductance distribution function of two-dimensional
disordered noninteracting systems in the crossover regime between the diffusive
and the localized phases. The distribution is entirely determined by the mean
conductance, g, in agreement with the strong version of the single-parameter
scaling hypothesis. The distribution seems to change drastically at a critical
value very close to one. For conductances larger than this critical value, the
distribution is roughly Gaussian while for smaller values it resembles a
log-normal distribution. The two distributions match at the critical point with
an often appreciable change in behavior. This matching implies a jump in the
first derivative of the distribution which does not seem to disappear as system
size increases. We have also studied 1/g corrections to the skewness to
quantify the deviation of the distribution from a Gaussian function in the
diffusive regime.Comment: 4 pages, 4 figure
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