61 research outputs found
Appearance and Stability of Anomalously Fluctuating States in Shor's Factoring Algorithm
We analyze quantum computers which perform Shor's factoring algorithm, paying
attention to asymptotic properties as the number L of qubits is increased.
Using numerical simulations and a general theory of the stabilities of
many-body quantum states, we show the following: Anomalously fluctuating states
(AFSs), which have anomalously large fluctuations of additive operators, appear
in various stages of the computation. For large L, they decohere at anomalously
great rates by weak noises that simulate noises in real systems. Decoherence of
some of the AFSs is fatal to the results of the computation, whereas
decoherence of some of the other AFSs does not have strong influence on the
results of the computation. When such a crucial AFS decoheres, the probability
of getting the correct computational result is reduced approximately
proportional to L^2. The reduction thus becomes anomalously large with
increasing L, even when the coupling constant to the noise is rather small.
Therefore, quantum computations should be improved in such a way that all AFSs
appearing in the algorithms do not decohere at such great rates in the existing
noises.Comment: 11 figures. A few discussions were added in verion 2. Version 3 is
the SAME as version 2; only errors during the Web-upload were fixed. Version
4 is the publised version, in which several typos are fixed and the reference
list is update
A closer look at the uncertainty relation of position and momentum
We consider particles prepared by the von Neumann-L\"uders projection. For
those particles the standard deviation of the momentum is discussed. We show
that infinite standard deviations are not exceptions but rather typical. A
necessary and sufficient condition for finite standard deviations is given.
Finally, a new uncertainty relation is derived and it is shown that the latter
cannot be improved.Comment: 3 pages, introduction shortened, content unchange
G\"odel Incompleteness and the Black Hole Information Paradox
Semiclassical reasoning suggests that the process by which an object
collapses into a black hole and then evaporates by emitting Hawking radiation
may destroy information, a problem often referred to as the black hole
information paradox. Further, there seems to be no unique prediction of where
the information about the collapsing body is localized. We propose that the
latter aspect of the paradox may be a manifestation of an inconsistent
self-reference in the semiclassical theory of black hole evolution. This
suggests the inadequacy of the semiclassical approach or, at worst, that
standard quantum mechanics and general relavity are fundamentally incompatible.
One option for the resolution for the paradox in the localization is to
identify the G\"odel-like incompleteness that corresponds to an imposition of
consistency, and introduce possibly new physics that supplies this
incompleteness. Another option is to modify the theory in such a way as to
prohibit self-reference. We discuss various possible scenarios to implement
these options, including eternally collapsing objects, black hole remnants,
black hole final states, and simple variants of semiclassical quantum gravity.Comment: 14 pages, 2 figures; revised according to journal requirement
The future of sovereignty in multilevel governance Europe: a constructivist reading
Multilevel governance presents a depiction of contemporary structures in EU Europe as consisting of overlapping authorities and competing competencies. By focusing on emerging non-anarchical structures in the international system, hence moving beyond the conventional hierarchy/anarchy dichotomy to distinguish domestic and international arenas, this seems a radical transformation of the familiar Westphalian system and to undermine state sovereignty. Paradoxically, however, the principle of sovereignty proves to be resilient despite its alleged empirical decline. This article argues that social constructivism can explain the paradox, by considering sovereign statehood as a process-dependent institutional fact, and by showing that multilevel governance can feed into this process
Casimir Effect, Achucarro-Ortiz Black Hole and the Cosmological Constant
We treat the two-dimensional Achucarro-Ortiz black hole (also known as (1+1)
dilatonic black hole) as a Casimir-type system. The stress tensor of a massless
scalar field satisfying Dirichlet boundary conditions on two one-dimensional
"walls" ("Dirichlet walls") is explicitly calculated in three different vacua.
Without employing known regularization techniques, the expression in each
vacuum for the stress tensor is reached by using the Wald's axioms. Finally,
within this asymptotically non-flat gravitational background, it is shown that
the equilibrium of the configurations, obtained by setting Casimir force to
zero, is controlled by the cosmological constant.Comment: 20 pages, LaTeX, minor corrections, comments and clarifications
added, version to appear in Phys. Rev.
Olfactory Jump Reflex Habituation in Drosophila and Effects of Classical Conditioning Mutations
Habituation is a nonassociative learning mechanism, in which an initial response toward repeated stimuli gradually wanes. This is amongst the simplest and most widespread forms of behavioral plasticity. So far, neither the underlying molecular mechanisms nor the precise neural networks of habituation are well understood. We have developed a novel paradigm to quantify habituation of the olfactory jump reflex in Drosophila. We present data demonstrating several behavioral properties of this phenomenon, generally observed in other species. We also show that the dunce and rutabaga memory mutants behave abnormally in this assay, suggesting that this assay might be used in behavioral screens for new mutants with defects in this simpler form of behavioral plasticity
Casimir Effect in 2D Stringy Black Hole Backgrounds
We consider the two-dimensional "Schwarzschild" and "Reissner-Nordstrom"
stringy black holes as systems of Casimir type. We explicitly calculate the
energy-momentum tensor of a massless scalar field satisfying Dirichlet boundary
conditions on two one-dimensional "walls". These results are obtained using the
Wald's axioms. Thermodynamical quantities such as pressure, specific heat,
isothermal compressibility and entropy of the two-dimensional stringy black
holes are calculated. A comparison is made between the obtained results and the
laws of thermodynamics. The results obtained for the extremal (Q=M) stringy
two-dimensional charged black hole are identical in all three different vacua
used; a fact that indicates its quantum stability.Comment: RevTeX, 27 pages, no figures, to appear in Phys.Rev. D, Vol 64 (Dec.
2001
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