58,183 research outputs found
On entropy of P-twists
We compute the categorical entropy of autoequivalences given by P-twists, and
show that these autoequivalences satisfy a Gromov-Yomdin type conjecture.Comment: 6 pages. Comments are welcome
Entropy of an autoequivalence on Calabi-Yau manifolds
We prove that the categorical entropy of the autoequivalence
on a Calabi-Yau manifold is the
unique positive real number satisfying We then use this
result to construct the first counterexamples of a conjecture on categorical
entropy by Kikuta and Takahashi.Comment: 10 pages. Comments are welcome
Theoretical Perspective of Convergence Complexity of Evolutionary Algorithms Adopting Optimal Mixing
The optimal mixing evolutionary algorithms (OMEAs) have recently drawn much
attention for their robustness, small size of required population, and
efficiency in terms of number of function evaluations (NFE). In this paper, the
performances and behaviors of OMEAs are studied by investigating the mechanism
of optimal mixing (OM), the variation operator in OMEAs, under two scenarios --
one-layer and two-layer masks. For the case of one-layer masks, the required
population size is derived from the viewpoint of initial supply, while the
convergence time is derived by analyzing the progress of sub-solution growth.
NFE is then asymptotically bounded with rational probability by estimating the
probability of performing evaluations. For the case of two-layer masks,
empirical results indicate that the required population size is proportional to
both the degree of cross competition and the results from the one-layer-mask
case. The derived models also indicate that population sizing is decided by
initial supply when disjoint masks are adopted, that the high selection
pressure imposed by OM makes the composition of sub-problems impact little on
NFE, and that the population size requirement for two-layer masks increases
with the reverse-growth probability.Comment: 8 pages, 2015 GECCO oral pape
Constructing positive maps from block matrices
Positive maps are useful for detecting entanglement in quantum information
theory. Any entangled state can be detected by some positive map. In this
paper, the relation between positive block matrices and completely positive
trace-preserving maps is characterized. Consequently, a new method for
constructing decomposable maps from positive block matrices is derived. In
addition, a method for constructing positive but not completely positive maps
from Hermitian block matrices is also obtained.Comment: 13 page
Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy
This paper is dedicated to provide theta function representations of
algebro-geometric solutions and related crucial quantities for the
two-component Hunter-Saxton (HS2) hierarchy through studying an
algebro-geometric initial value problem. Our main tools include the polynomial
recursive formalism, the hyperelliptic curve with finite number of genus, the
Baker-Akhiezer functions, the meromorphic function, the Dubrovin-type equations
for auxiliary divisors, and the associated trace formulas. With the help of
these tools, the explicit representations of the algebro-geometric solutions
are obtained for the entire HS2 hierarchy.Comment: 46 pages. accepted for publication J Nonl Math Phys, 2014. arXiv
admin note: substantial text overlap with arXiv:1406.6153, arXiv:1207.0574,
arXiv:1205.6062; and with arXiv:nlin/0105021 by other author
A Riemann-Hilbert approach to the Harry-Dym equation on the line
In this paper, we consider the Harry-Dym equation on the line with decaying
initial value. The Fokas unified method is used to construct the solution of
the Harry-Dym equation via a matrix Riemann Hilbert problem in the
complex plane. Further, one-cups soltion solution is expressed in terms of
solutions of the Riemann Hilbert problem.Comment: 17 page
Algebro-geometric solutions for the two-component Camassa-Holm Dym hierarchy
This paper is dedicated to provide theta function representations of
algebro-geometric solutions and related crucial quantities for the
two-component Camassa-Holm Dym (CHD2) hierarchy. Our main tools include the
polynomial recursive formalism, the hyperelliptic curve with finite number of
genus, the Baker-Akhiezer functions, the meromorphic function, the
Dubrovin-type equations for auxiliary divisors, and the associated trace
formulas. With the help of these tools, the explicit representations of the
algebro-geometric solutions are obtained for the entire CHD2 hierarchy.Comment: 39 pages. arXiv admin note: substantial text overlap with
arXiv:1207.0574, arXiv:1205.6062, arXiv:1305.0122; and with
arXiv:nlin/0105021 by other author
Gauged Supergroup Valued WZNW Field Theory
The gauged supergroup valued WZNW theory is considered. It is shown
that for G=\OSP, the theory tensoring a (, , , )
system is equivalent to the non-critical fermionic theory. The relation between
integral or half integral moded affine superalgebra and its reduced theory, the
NS or R superconformal algebra, is discussed in detail. The physical state
space, i.e. the BRST semi-infinite cohomology, is calculated, for the
\OSP/\OSP theory.Comment: AS-ITP-93-2
Zeno dynamics in quantum open systems
Quantum Zeno effect shows that frequent observations can slow down or even
stop the unitary time evolution of an unstable quantum system. This effect can
also be regarded as a physical consequence of the the statistical
indistinguishability of neighboring quantum states. The accessibility of
quantum Zeno dynamics under unitary time evolution can be quantitatively
estimated by quantum Zeno time in terms of Fisher information. In this work, we
investigate the accessibility of quantum Zeno dynamics in quantum open systems
by calculating noisy Fisher information, in which a trace preserving and
completely positive map is assumed. We firstly study the consequences of
non-Markovian noise on quantum Zeno effect and give the exact forms of the
dissipative Fisher information and the quantum Zeno time. Then, for the
operator-sum representation, an achievable upper bound of the quantum Zeno time
is given with the help of the results in noisy quantum metrology. It is of
significance that the noise affecting the accuracy in the entanglement-enhanced
parameter estimation can conversely be favorable for the accessibility of
quantum Zeno dynamics of entangled states.Comment: 6 pages, 2 figure
Quantum Metrological Bounds for Vector Parameter
Precise measurement is crucial to science and technology. However, the rule
of nature imposes various restrictions on the precision that can be achieved
depending on specific methods of measurement. In particular, quantum mechanics
poses the ultimate limit on precision which can only be approached but never be
violated. Depending on analytic techniques, these bounds may not be unique.
Here, in view of prior information, we investigate systematically the precision
bounds of the total mean-square error of vector parameter estimation which
contains independent parameters. From quantum Ziv-Zakai error bounds, we
derive two kinds of quantum metrological bounds for vector parameter
estimation, both of which should be satisfied. By these bounds, we show that a
constant advantage can be expected via simultaneous estimation strategy over
the optimal individual estimation strategy, which solves a long-standing
problem. A general framework for obtaining the lower bounds in a noisy system
is also proposed.Comment: 8 pages, 4 figure
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