4,258 research outputs found
The diagonalization method in quantum recursion theory
As quantum parallelism allows the effective co-representation of classical
mutually exclusive states, the diagonalization method of classical recursion
theory has to be modified. Quantum diagonalization involves unitary operators
whose eigenvalues are different from one.Comment: 15 pages, completely rewritte
Undecidability of the Spectral Gap in One Dimension
The spectral gap problem - determining whether the energy spectrum of a
system has an energy gap above ground state, or if there is a continuous range
of low-energy excitations - pervades quantum many-body physics. Recently, this
important problem was shown to be undecidable for quantum spin systems in two
(or more) spatial dimensions: there exists no algorithm that determines in
general whether a system is gapped or gapless, a result which has many
unexpected consequences for the physics of such systems. However, there are
many indications that one dimensional spin systems are simpler than their
higher-dimensional counterparts: for example, they cannot have thermal phase
transitions or topological order, and there exist highly-effective numerical
algorithms such as DMRG - and even provably polynomial-time ones - for gapped
1D systems, exploiting the fact that such systems obey an entropy area-law.
Furthermore, the spectral gap undecidability construction crucially relied on
aperiodic tilings, which are not possible in 1D.
So does the spectral gap problem become decidable in 1D? In this paper we
prove this is not the case, by constructing a family of 1D spin chains with
translationally-invariant nearest neighbour interactions for which no algorithm
can determine the presence of a spectral gap. This not only proves that the
spectral gap of 1D systems is just as intractable as in higher dimensions, but
also predicts the existence of qualitatively new types of complex physics in 1D
spin chains. In particular, it implies there are 1D systems with constant
spectral gap and non-degenerate classical ground state for all systems sizes up
to an uncomputably large size, whereupon they switch to a gapless behaviour
with dense spectrum.Comment: 7 figure
Numerical Investigation of Graph Spectra and Information Interpretability of Eigenvalues
We undertake an extensive numerical investigation of the graph spectra of
thousands regular graphs, a set of random Erd\"os-R\'enyi graphs, the two most
popular types of complex networks and an evolving genetic network by using
novel conceptual and experimental tools. Our objective in so doing is to
contribute to an understanding of the meaning of the Eigenvalues of a graph
relative to its topological and information-theoretic properties. We introduce
a technique for identifying the most informative Eigenvalues of evolving
networks by comparing graph spectra behavior to their algorithmic complexity.
We suggest that extending techniques can be used to further investigate the
behavior of evolving biological networks. In the extended version of this paper
we apply these techniques to seven tissue specific regulatory networks as
static example and network of a na\"ive pluripotent immune cell in the process
of differentiating towards a Th17 cell as evolving example, finding the most
and least informative Eigenvalues at every stage.Comment: Forthcoming in 3rd International Work-Conference on Bioinformatics
and Biomedical Engineering (IWBBIO), Lecture Notes in Bioinformatics, 201
Late-time vacuum phase transitions: Connecting sub-eV scale physics with cosmological structure formation
We show that a particular class of postrecombination phase transitions in the
vacuum can lead to localized overdense regions on relatively small scales,
roughly 10^6 to 10^10 M_sun, potentially interesting for the origin of large
black hole seeds and for dwarf galaxy evolution. Our study suggests that this
mechanism could operate over a range of conditions which are consistent with
current cosmological and laboratory bounds. One byproduct of phase transition
bubble-wall decay may be extra radiation energy density. This could provide an
avenue for constraint, but it could also help reconcile the discordant values
of the present Hubble parameter (H_0) and sigma_8 obtained by cosmic microwave
background (CMB) fits and direct observational estimates. We also suggest ways
in which future probes, including CMB considerations (e.g., early dark energy
limits), 21-cm observations, and gravitational radiation limits, could provide
more stringent constraints on this mechanism and the sub-eV scale
beyond-standard-model physics, perhaps in the neutrino sector, on which it
could be based. Late phase transitions associated with sterile neutrino mass
and mixing may provide a way to reconcile cosmological limits and laboratory
data, should a future disagreement arise.Comment: 17 pages, 18 figures. v2: includes additional references and minor
corrections/clarifications. v3: includes additional text, figures, and
references (matches published version
Effective Physical Processes and Active Information in Quantum Computing
The recent debate on hypercomputation has arisen new questions both on the
computational abilities of quantum systems and the Church-Turing Thesis role in
Physics. We propose here the idea of "effective physical process" as the
essentially physical notion of computation. By using the Bohm and Hiley active
information concept we analyze the differences between the standard form
(quantum gates) and the non-standard one (adiabatic and morphogenetic) of
Quantum Computing, and we point out how its Super-Turing potentialities derive
from an incomputable information source in accordance with Bell's constraints.
On condition that we give up the formal concept of "universality", the
possibility to realize quantum oracles is reachable. In this way computation is
led back to the logic of physical world.Comment: 10 pages; Added references for sections 2 and
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