15,615 research outputs found
Triple Products and Yang-Baxter Equation (II): Orthogonal and Symplectic Ternary Systems
We generalize the result of the preceeding paper and solve the Yang-Baxter
equation in terms of triple systems called orthogonal and symplectic ternary
systems. In this way, we found several other new solutions.Comment: 38 page
Superconformal defects in the tricritical Ising model
We study superconformal defect lines in the tricritical Ising model in 2
dimensions. By the folding trick, a superconformal defect is mapped to a
superconformal boundary of the N=1 superconformal unitary minimal model of
c=7/5 with D_6-E_6 modular invariant. It turns out that the complete set of the
boundary states of c=7/5 D_6-E_6 model cannot be interpreted as the consistent
set of superconformal defects in the tricritical Ising model since it does not
contain the "no defect" boundary state. Instead, we find a set of 18 consistent
superconformal defects including "no defect" and satisfying the Cardy
condition. This set also includes some defects which are not purely
transmissive or purely reflective.Comment: 25 pages, 3 figures. v2: typos corrected. v3: clarification about
spin structure aligned theory added, references adde
New Universality of Lyapunov Spectra in Hamiltonian Systems
A new universality of Lyapunov spectra {\lambda_i} is shown for Hamiltonian
systems. The universality appears in middle energy regime and is different from
another universality which can be reproduced by random matrices in the
following two points. One is that the new universality appears in a limited
range of large i/N rather than the whole range, where N is degrees of freedom.
The other is Lyapunov spectra do not behave linearly while random matrices give
linear behavior even on 3D lattice. Quadratic terms with smaller nonlinear
terms of potential functions play an intrinsic role in the new universality.Comment: 19 pages, 16 Encapsulated Postscript figures, LaTeX (100 kb
Electron spin manipulation and resonator readout in a double quantum dot nano-electromechanical system
Magnetically coupling a nano-mechanical resonator to a double quantum dot
confining two electrons can enable the manipulation of a single electron spin
and the readout of the resonator's natural frequency. When the Larmor frequency
matches the resonator frequency, the electron spin in one of the dots can be
selectively flipped by the magnetised resonator. By simultaneously measuring
the charge state of the two-electron double quantum dots, this transition can
be detected thus enabling the natural frequency of the mechanical resonator to
be determined.Comment: 7 pages, fixed typos, updated figures 4 and
How to realize Lie algebras by vector fields
An algorithm for embedding finite dimensional Lie algebras into Lie algebras
of vector fields (and Lie superalgebras into Lie superalgebras of vector
fields) is offered in a way applicable over ground fields of any
characteristic. The algorithm is illustrated by reproducing Cartan's
interpretations of the Lie algebra of G(2) as the Lie algebra that preserves
certain non-integrable distributions. Similar algorithm and interpretation are
applicable to other exceptional simple Lie algebras, as well as to all
non-exceptional simple ones and many non-simple ones, and to many Lie
superalgebras.Comment: 17 pages, LaTe
More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
Fixing a gauge in the non-perturbative domain of Yang-Mills theory is a
non-trivial problem due to the presence of Gribov copies. In particular, there
are different gauges in the non-perturbative regime which all correspond to the
same definition of a gauge in the perturbative domain. Gauge-dependent
correlation functions may differ in these gauges. Two such gauges are the
minimal and absolute Landau gauge, both corresponding to the perturbative
Landau gauge. These, and their numerical implementation, are described and
presented in detail. Other choices will also be discussed.
This investigation is performed, using numerical lattice gauge theory
calculations, by comparing the propagators of gluons and ghosts for the minimal
Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is
found that the propagators are different in the far infrared and even at energy
scales of the order of half a GeV. In particular, also the finite-volume
effects are modified. This is observed in two and three dimensions. Some
remarks on the four-dimensional case are provided as well.Comment: 23 pages, 16 figures, 6 tables; various changes throughout most of
the paper; extended discussion on different possibilities to define the
Landau gauge and connection to existing scenarios; in v3: Minor changes,
error in eq. (3) & (4) corrected, version to appear in PR
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