20,284 research outputs found
Dual Computations of Non-abelian Yang-Mills on the Lattice
In the past several decades there have been a number of proposals for
computing with dual forms of non-abelian Yang-Mills theories on the lattice.
Motivated by the gauge-invariant, geometric picture offered by dual models and
successful applications of duality in the U(1) case, we revisit the question of
whether it is practical to perform numerical computation using non-abelian dual
models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an
accessible yet non-trivial case in which the gauge group is non-abelian. Using
methods developed recently in the context of spin foam quantum gravity, we
derive an algorithm for efficiently computing the dual amplitude and describe
Metropolis moves for sampling the dual ensemble. We relate our algorithms to
prior work in non-abelian dual computations of Hari Dass and his collaborators,
addressing several problems that have been left open. We report results of spin
expectation value computations over a range of lattice sizes and couplings that
are in agreement with our conventional lattice computations. We conclude with
an outlook on further development of dual methods and their application to
problems of current interest.Comment: v1: 18 pages, 7 figures, v2: Many changes to appendix, minor changes
throughout, references and figures added, v3: minor corrections, 22 page
Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: incandecence and luminescence in arbitrary geometries
We describe a fluctuating volume--current formulation of electromagnetic
fluctuations that extends our recent work on heat exchange and Casimir
interactions between arbitrarily shaped homogeneous bodies [Phys. Rev. B. 88,
054305] to situations involving incandescence and luminescence problems,
including thermal radiation, heat transfer, Casimir forces, spontaneous
emission, fluorescence, and Raman scattering, in inhomogeneous media. Unlike
previous scattering formulations based on field and/or surface unknowns, our
work exploits powerful techniques from the volume--integral equation (VIE)
method, in which electromagnetic scattering is described in terms of
volumetric, current unknowns throughout the bodies. The resulting trace
formulas (boxed equations) involve products of well-studied VIE matrices and
describe power and momentum transfer between objects with spatially varying
material properties and fluctuation characteristics. We demonstrate that thanks
to the low-rank properties of the associatedmatrices, these formulas are
susceptible to fast-trace computations based on iterative methods, making
practical calculations tractable. We apply our techniques to study thermal
radiation, heat transfer, and fluorescence in complicated geometries, checking
our method against established techniques best suited for homogeneous bodies as
well as applying it to obtain predictions of radiation from complex bodies with
spatially varying permittivities and/or temperature profiles
Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction
A method for concatenating quantum error-correcting codes is presented. The
method is applicable to a wide class of quantum error-correcting codes known as
Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate
in the Shannon theoretic sense and that are decodable in polynomial time are
presented. The rate is the highest among those known to be achievable by CSS
codes. Moreover, the best known lower bound on the greatest minimum distance of
codes constructible in polynomial time is improved for a wide range.Comment: 16 pages, 3 figures. Ver.4: Title changed. Ver.3: Due to a request of
the AE of the journal, the present version has become a combination of
(thoroughly revised) quant-ph/0610194 and the former quant-ph/0610195.
Problem formulations of polynomial complexity are strictly followed. An
erroneous instance of a lower bound on minimum distance was remove
Thermodynamic Analysis of Interacting Nucleic Acid Strands
Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality
Tailoring Three-Point Functions and Integrability
We use Integrability techniques to compute structure constants in N=4 SYM to
leading order. Three closed spin chains, which represent the single trace
gauge-invariant operators in N=4 SYM, are cut into six open chains which are
then sewed back together into some nice pants, the three-point function. The
algebraic and coordinate Bethe ansatz tools necessary for this task are
reviewed. Finally, we discuss the classical limit of our results, anticipating
some predictions for quasi-classical string correlators in terms of algebraic
curves.Comment: 52 pages, 6 figures. v2: Typos corrected, references added and
update
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