2,274 research outputs found
Weak Chaos from Tsallis Entropy
We present a geometric, model-independent, argument that aims to explain why
the Tsallis entropy describes systems exhibiting "weak chaos", namely systems
whose underlying dynamics has vanishing largest Lyapunov exponent. Our argument
relies on properties of a deformation map of the reals induced by the Tsallis
entropy, and its conclusion agrees with all currently known results.Comment: 19 pages, Standard LaTeX2e, v2: addition of the last paragraph in
Section 4. Three additional refs. To be published in QScience Connec
Cayley--Klein Contractions of Quantum Orthogonal Groups in Cartesian Basis
Spaces of constant curvature and their motion groups are described most
naturally in Cartesian basis. All these motion groups also known as CK groups
are obtained from orthogonal group by contractions and analytical
continuations. On the other hand quantum deformation of orthogonal group is most easily performed in so-called symplectic basis. We reformulate its
standard quantum deformation to Cartesian basis and obtain all possible
contractions of quantum orthogonal group both for untouched and
transformed deformation parameter. It turned out, that similar to undeformed
case all CK contractions of are realized. An algorithm for obtaining
nonequivalent (as Hopf algebra) contracted quantum groups is suggested.
Contractions of are regarded as an examples.Comment: The statement of the basic theorem have correct. 30 pages, Latex.
Report given at X International Conference on Symmetry Methods in Physics,
August 13-19, 2003, Yerevan, Armenia. Submitted in Journal Physics of Atomic
Nucle
Virtually Abelian Quantum Walks
We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus
on the easiest case of virtually Abelian groups, and introduce a technique to
reduce the quantum walk to an equivalent one on an Abelian group with coin
system having larger dimension. We apply the technique in the case of two
quantum walks on virtually Abelian groups with planar Cayley graphs, finding
the exact solution.Comment: 10 pages, 3 figure
Quark--anti-quark potential in N=4 SYM
We construct a closed system of equations describing the quark--anti-quark
potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is
based on the Quantum Spectral Curve method supplemented with a novel type of
asymptotics. We present a high precision numerical solution reproducing the
classical and one-loop string predictions very accurately. We also analytically
compute the first 7 nontrivial orders of the weak coupling expansion.
Moreover, we study analytically the generalized quark--anti-quark potential
in the limit of large imaginary twist to all orders in perturbation theory. We
demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger
equation. In the process we establish a link between the Q-functions and the
solution of the Bethe-Salpeter equation.Comment: 31 pages, 1 figure; v2: minor correcton
On contractions of classical basic superalgebras
We define a class of orthosymplectic and unitary
superalgebras which may be obtained from and
by contractions and analytic continuations in a similar way as the
special linear, orthogonal and the symplectic Cayley-Klein algebras are
obtained from the corresponding classical ones. Casimir operators of
Cayley-Klein superalgebras are obtained from the corresponding operators of the
basic superalgebras. Contractions of and are regarded as
an examples.Comment: 15 pages, Late
On the Fermionic Frequencies of Circular Strings
We revisit the semiclassical computation of the fluctuation spectrum around
different circular string solutions in AdS_5xS^5 and AdS_4xCP^3, starting from
the Green-Schwarz action. It has been known that the results for these
frequencies obtained from the algebraic curve and from the worldsheet
computations sometimes do not agree. In particular, different methods give
different results for the half-integer shifts in the mode numbers of the
frequencies. We find that these discrepancies can be removed if one carefully
takes into account the transition matrices in the spin bundle over the target
space.Comment: 13 pages, 1 figur
Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
We consider N=4 SYM and a class of spin N, length-3, twist operators beyond
the well studied sl(2) subsector. They can be identified at one-loop with three
gluon operators. At strong coupling, they are associated with spinning strings
with two spins in AdS5. We exploit the Y-system to compute the leading
weak-coupling four loop wrapping correction to their anomalous dimension. The
result is written in closed form as a function of the spin N. We combine the
wrapping correction with the known four-loop asymptotic Bethe Ansatz
contribution and analyze special limits in the spin N. In particular, at large
N, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative
unphysical spin, we present a simple BFKL-like equation predicting the
rightmost leading poles.Comment: 18 page
Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM
We apply the recently proposed quantum spectral curve technique to the study
of twist operators in planar N=4 SYM theory. We focus on the small spin
expansion of anomalous dimensions in the sl(2) sector and compute its first two
orders exactly for any value of the 't Hooft coupling. At leading order in the
spin S we reproduced Basso's slope function. The next term of order S^2
structurally resembles the Beisert-Eden-Staudacher dressing phase and takes
into account wrapping contributions. This expansion contains rich information
about the spectrum of local operators at strong coupling. In particular, we
found a new coefficient in the strong coupling expansion of the Konishi
operator dimension and confirmed several previously known terms. We also
obtained several new orders of the strong coupling expansion of the BFKL
pomeron intercept. As a by-product we formulated a prescription for the correct
analytical continuation in S which opens a way for deriving the BFKL regime of
twist two anomalous dimensions from AdS/CFT integrability.Comment: 53 pages, references added; v3: due to a typo in the coefficients C_2
and D_2 on page 29 we corrected the rational part of the strong coupling
predictions in equations (1.5-6), (6.22-24), (6.27-30) and in Table
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