2,375 research outputs found
Approximating the Permanent of a Random Matrix with Vanishing Mean
We show an algorithm for computing the permanent of a random matrix with
vanishing mean in quasi-polynomial time. Among special cases are the Gaussian,
and biased-Bernoulli random matrices with mean 1/lnln(n)^{1/8}. In addition, we
can compute the permanent of a random matrix with mean 1/poly(ln(n)) in time
2^{O(n^{\eps})} for any small constant \eps>0. Our algorithm counters the
intuition that the permanent is hard because of the "sign problem" - namely the
interference between entries of a matrix with different signs. A major open
question then remains whether one can provide an efficient algorithm for random
matrices of mean 1/poly(n), whose conjectured #P-hardness is one of the
baseline assumptions of the BosonSampling paradigm
Deterministic Annealing and Nonlinear Assignment
For combinatorial optimization problems that can be formulated as Ising or
Potts spin systems, the Mean Field (MF) approximation yields a versatile and
simple ANN heuristic, Deterministic Annealing. For assignment problems the
situation is more complex -- the natural analog of the MF approximation lacks
the simplicity present in the Potts and Ising cases. In this article the
difficulties associated with this issue are investigated, and the options for
solving them discussed. Improvements to existing Potts-based MF-inspired
heuristics are suggested, and the possibilities for defining a proper
variational approach are scrutinized.Comment: 15 pages, 3 figure
A Simple FPTAS for Counting Edge Covers
An edge cover of a graph is a set of edges such that every vertex has at
least an adjacent edge in it. Previously, approximation algorithm for counting
edge covers is only known for 3 regular graphs and it is randomized. We design
a very simple deterministic fully polynomial-time approximation scheme (FPTAS)
for counting the number of edge covers for any graph. Our main technique is
correlation decay, which is a powerful tool to design FPTAS for counting
problems. In order to get FPTAS for general graphs without degree bound, we
make use of a stronger notion called computationally efficient correlation
decay, which is introduced in [Li, Lu, Yin SODA 2012].Comment: To appear in SODA 201
Correlation Effects in Orbital Magnetism
Orbital magnetization is known empirically to play an important role in
several magnetic phenomena, such as permanent magnetism and ferromagnetic
superconductivity. Within the recently developed ''modern theory of orbital
magnetization'', theoretical insight has been gained into the nature of this
often neglected contribution to magnetism, but is based on an underlying
mean-field approximation. From this theory, a few treatments have emerged which
also take into account correlations beyond the mean-field approximation. Here,
we apply the scheme developed in a previous work [Phys. Rev. B , 161104(R) (2016)] to the Haldane-Hubbard model to investigate the
effect of charge fluctuations on the orbital magnetization within the
approximation. Qualitatively, we are led to distinguish between two quite
different situations: (i) When the lattice potential is larger than the nearest
neighbor hopping, the correlations are found to boost the orbital
magnetization. (ii) If the nearest neighbor hopping is instead larger than the
lattice potential, the correlations reduce the magnetization.Comment: 8 pages, 9 figure
Quantum scattering in the strip: from ballistic to localized regimes
Quantum scattering is studied in a system consisting of randomly distributed
point scatterers in the strip. The model is continuous yet exactly solvable.
Varying the number of scatterers (the sample length) we investigate a
transition between the ballistic and the localized regimes. By considering the
cylinder geometry and introducing the magnetic flux we are able to study time
reversal symmetry breaking in the system. Both macroscopic (conductance) and
microscopic (eigenphases distribution, statistics of S-matrix elements)
characteristics of the system are examined.Comment: 17 pages and 10 figures (15 eps files); accepted for publication in
EPJ
Statistical Theory of Parity Nonconservation in Compound Nuclei
We present the first application of statistical spectroscopy to study the
root-mean-square value of the parity nonconserving (PNC) interaction matrix
element M determined experimentally by scattering longitudinally polarized
neutrons from compound nuclei. Our effective PNC interaction consists of a
standard two-body meson-exchange piece and a doorway term to account for
spin-flip excitations. Strength functions are calculated using realistic
single-particle energies and a residual strong interaction adjusted to fit the
experimental density of states for the targets, ^{238} U for A\sim 230 and
^{104,105,106,108} Pd for A\sim 100. Using the standard Desplanques, Donoghue,
and Holstein estimates of the weak PNC meson-nucleon coupling constants, we
find that M is about a factor of 3 smaller than the experimental value for
^{238} U and about a factor of 1.7 smaller for Pd. The significance of this
result for refining the empirical determination of the weak coupling constants
is discussed.Comment: Latex file, no Fig
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