277 research outputs found
On weak rotors, Latin squares, linear algebraic representations, invariant differentials and cryptanalysis of Enigma
Since the 1920s until today it was assumed that rotors in Enigma cipher machines do not have a particular weakness or structure. A curious situation compared to hundreds of papers about S-boxes and weak setup in block ciphers. In this paper we reflect on what is normal and what is not normal for a cipher machine rotor, with a reference point being a truly random permutation. Our research shows that most original wartime Enigma rotors ever made are not at all random permutations and conceal strong differential properties invariant by rotor rotation. We also exhibit linear/algebraic properties pertaining to the ring of integers modulo 26. Some rotors are imitating a certain construction of a perfect quasigroup which however only works when N is odd. Most other rotors are simply trying to approximate the ideal situation. To the best of our knowledge these facts are new and were not studied before 2020
On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS
We consider measures which are invariant under a measurable iterated function
system with positive, place-dependent probabilities in a separable metric
space. We provide an upper bound of the Hausdorff dimension of such a measure
if it is ergodic. We also prove that it is ergodic iff the related skew product
is.Comment: 16 pages; to appear in Journal of Stat. Phy
Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet
In this note, we show that on certain Gatzouras-Lalley carpet, there exist
more than one ergodic measures with full Hausdorff dimension. This gives a
negative answer to a conjecture of Gatzouras and Peres
Excitations in Spin Chains and Specific-Heat Anomalies in Yb(4)As(3)
An explanation is given for the observed magnetic-field dependence of the
low-temperature specific heat coefficient of Yb(4)As(3). It is based on a
recently developed model for that material which can explain the observed
heavy-fermion behaviour. According to it the Yb(3+)-ions are positioned in a
net of parallel chains with an effective spin coupling of the order of J = 25
K. The magnetic-field dependence can be understood by including a weak magnetic
coupling J' between adjacent chains. The data require a ratio J'/J of about
10^{-4}. In that case the experimental results can be reproduced very well by
the theory.Comment: 5 pages, 5 PostScript-figures, needs LaTeX2e and the graphics-packag
Dynamics of an inhomogeneous quantum phase transition
We argue that in a second order quantum phase transition driven by an
inhomogeneous quench density of quasiparticle excitations is suppressed when
velocity at which a critical point propagates across a system falls below a
threshold velocity equal to the Kibble-Zurek correlation length times the
energy gap at freeze-out divided by . This general prediction is
supported by an analytic solution in the quantum Ising chain. Our results
suggest, in particular, that adiabatic quantum computers can be made more
adiabatic when operated in an "inhomogeneous" way.Comment: 7 pages; version to appear in a special issue of New J. Phy
Single Chain Magnet Based on Cobalt II Thiocyanate as XXZ Spin Chain
The cobalt(II) in [Co(NCS)(2)(4-methoxypyridine)(2)](n) are linked by pairs of thiocyanate anions into linear chains. In contrast to a previous structure determination, two crystallographically independent cobalt(II) centers have been found to be present. In the antiferromagnetic state, below the critical temperature (T-c=3.94 K) and critical field (H-c=290 Oe), slow relaxations of the ferromagnetic chains are observed. They originate mainly from defects in the magnetic structure, which has been elucidated by micromagnetic Monte Carlo simulations and ac measurements using pristine and defect samples. The energy barriers of the relaxations are Delta(tau 1)=44.9(5) K and Delta(tau 2)=26.0(7) K for long and short spin chains, respectively. The spin excitation energy, measured by using frequency-domain EPR spectroscopy, is 19.1 cm(-1) and shifts 0.1 cm(-1) due to the magnetic ordering. Ab initio calculations revealed easy-axis anisotropy for both Co-II centers, and also an exchange anisotropy J(xx)/J(zz) of 0.21. The XXZ anisotropic Heisenberg model (solved by using the density renormalization matrix group technique) was used to reconcile the specific heat, susceptibility, and EPR data
Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent
We consider an inhomogeneous quantum phase transition across a multicritical
point of the XY quantum spin chain. This is an example of a Lifshitz transition
with a dynamical exponent z = 2. Just like in the case z = 1 considered in New
J. Phys. 12, 055007 (2010) when a critical front propagates much faster than
the maximal group velocity of quasiparticles vq, then the transition is
effectively homogeneous: density of excitations obeys a generalized
Kibble-Zurek mechanism and scales with the sixth root of the transition rate.
However, unlike for z = 1, the inhomogeneous transition becomes adiabatic not
below vq but a lower threshold velocity v', proportional to inhomogeneity of
the transition, where the excitations are suppressed exponentially.
Interestingly, the adiabatic threshold v' is nonzero despite vanishing minimal
group velocity of low energy quasiparticles. In the adiabatic regime below v'
the inhomogeneous transition can be used for efficient adiabatic quantum state
preparation in a quantum simulator: the time required for the critical front to
sweep across a chain of N spins adiabatically is merely linear in N, while the
corresponding time for a homogeneous transition across the multicritical point
scales with the sixth power of N. What is more, excitations after the adiabatic
inhomogeneous transition, if any, are brushed away by the critical front to the
end of the spin chain.Comment: 10 pages, 6 figures, improved version accepted in NJ
A model of semimetallic behavior in strongly correlated electron systems
Metals with values of the resistivity and the Hall coefficient much larger
than typical ones, e.g., of sodium, are called semimetals. We suggest a model
for semimetals which takes into account the strong Coulomb repulsion of the
charge carriers, especially important in transition-metal and rare-earth
compounds. For that purpose we extend the Hubbard model by coupling one
additional orbital per site via hybridization to the Hubbard orbitals. We
calculate the spectral function, resistivity and Hall coefficient of the model
using dynamical mean-field theory. Starting from the Mott-insulating state, we
find a transition to a metal with increasing hybridization strength
(``self-doping''). In the metallic regime near the transition line to the
insulator the model shows semimetallic behavior. We compare the calculated
temperature dependence of the resistivity and the Hall coefficient with the one
found experimentally for . The comparison demonstrates that the
anomalies in the transport properties of possibly can be
assigned to Coulomb interaction effects of the charge carriers not captured by
standard band structure calculations.Comment: 9 pages RevTeX with 7 ps figures, accepted by PR
Characterization of defect structures in nanocrystalline materials by X-ray line profile analysis
X-ray line profile analysis is a powerful alternative tool for determining dislocation densities, dislocation type, crystallite and subgrain size and size-distributions, and planar defects, especially the frequency of twin boundaries and stacking faults. The method is especially useful in the case of submicron grain size or nanocrystalline materials, where X-ray line broadening is a well pronounced effect, and the observation of defects with very large density is often not easy by transmission electron microscopy. The fundamentals of X-ray line broadening are summarized in terms of the different qualitative breadth methods, and the more sophisticated and more quantitative whole pattern fitting procedures. The efficiency and practical use of X-ray line profile analysis is shown by discussing its applications to metallic, ceramic, diamond-like and polymer nanomaterials
Sixty Years of Fractal Projections
Sixty years ago, John Marstrand published a paper which, among other things,
relates the Hausdorff dimension of a plane set to the dimensions of its
orthogonal projections onto lines. For many years, the paper attracted very
little attention. However, over the past 30 years, Marstrand's projection
theorems have become the prototype for many results in fractal geometry with
numerous variants and applications and they continue to motivate leading
research.Comment: Submitted to proceedings of Fractals and Stochastics
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