The relationship between partition function, particle density, refractive index, and temperature for atmospheric plasma is calculated based on thermodynamics and chemical equilibrium. Taking into account the contribut...
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The relationship between partition function, particle density, refractive index, and temperature for atmospheric plasma is calculated based on thermodynamics and chemical equilibrium. Taking into account the contribution of hydrogen-like levels to the atomic partition function, a compact method to calculate the atomic partition function is first used with the Eindhoven model to deduce the plasma's refractive index. Results calculated by the new approach and two other traditional simplified methods are compared and analyzed. For a better understanding on the temperature measurement accuracy deduced by different partition function disposal approaches, moire deflectometry is employed as the experimental scheme to acquire the refractive index position curve. Finally, applicability of different partition function disposal approaches are discussed, and results indicate that the optical properties deduced in this paper are well suited for the refractive index based plasma diagnosis.
Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+1 and 3+1 dimensions are explored. Many of our TQFTs are highly-interacting without fr...
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Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+1 and 3+1 dimensions are explored. Many of our TQFTs are highly-interacting without free quadratic analogs. Some of our bosonic TQFTs can be regarded as the continuum field theory formulation of Dijkgraaf-Witten twisted discrete gauge theories. Other bosonic TQFTs beyond the Dijkgraaf-Witten description and all fermionic TQFTs (namely the spin TQFTs) are either higher-form gauge theories where particles must have strings attached, or fermionic discrete gauge theories obtained by gauging the fermionic Symmetry-Protected Topological states (SPTs). We analytically calculate both the Abelian and non-Abelian braiding statistics data of anyonic particle and string excitations in these theories, where the statistics data can one-to-one characterize the underlying topological orders of TQFTs. Namely, we derive path integral expectation values of links formed by line and surface operators in these TQFTs. The acquired link invariants include not only the familiar Aharonov-Bohm linking number, but also Milnor triple linking number in 3 dimensions, triple and quadruple linking numbers of surfaces, and intersection number of surfaces in 4 dimensions. We also construct new spin TQFTs with the corresponding knot/link invariants of Arf(-Brown-Kervaire), Sato-Levine and others. We propose a new relation between the fermionic SPT partition function and the Rokhlin invariant. As an example, we can use these invariants and other physical observables, including ground state degeneracy, reduced modular S-xY and T-xY matrices, and the partition function on RP3 manifold, to identify all v is an element of Z(8) classes of 2+1 dimensional gauged Z(2)-Ising-symmetric Z(2)(f)-fermionic Topological Superconductors (realized by stacking v layers of a pair of chiral and anti-chiral p-wave superconductors [p+ip and p-ip], where boundary supports non-chiral Majorana-Wey
We study complex Chern-Simons theory on a Seifert manifold M (3) by embedding it into string theory. We show that complex Chern-Simons theory on M (3) is equivalent to a topologically twisted supersymmetric theory and...
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We study complex Chern-Simons theory on a Seifert manifold M (3) by embedding it into string theory. We show that complex Chern-Simons theory on M (3) is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in four-dimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between (1) the Verlinde algebra, (2) quantum cohomology of the Grassmannian, (3) Chern-Simons theory on and (4) index of a spin (c) Dirac operator on the moduli space of flat connections to a new set of relations between (1) the "equivariant Verlinde algebra" for a complex group, (2) the equivariant quantum K-theory of the vortex moduli space, (3) complex Chern-Simons theory on and (4) the equivariant index of a spin (c) Dirac operator on the moduli space of Higgs bundles.
In this paper, we analyze the steady state of the asymmetric simple exclusion process with open boundaries and second class particles by deforming it through the introduction of spectral parameters. The (unnormalized)...
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In this paper, we analyze the steady state of the asymmetric simple exclusion process with open boundaries and second class particles by deforming it through the introduction of spectral parameters. The (unnormalized) probabilities of the particle configurations get promoted to Laurent polynomials in the spectral parameters and are constructed in terms of non-symmetric Koornwinder polynomials. In particular, we show that the partition function coincides with a symmetric Macdonald-Koornwinder polynomial. As an outcome, we compute the steady current and the average density of first class particles.
A class of balanced games, called exact partition games, is introduced. Within this class, it is shown that the egalitarian solution of Dutta and Ray (1989) behaves as in the class of convex games. Moreover, we provid...
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A class of balanced games, called exact partition games, is introduced. Within this class, it is shown that the egalitarian solution of Dutta and Ray (1989) behaves as in the class of convex games. Moreover, we provide two axiomatic characterizations by means of suitable properties such as consistency, rationality and Lorenz-fairness. As a by-product, alternative characterizations of the egalitarian solution over the class of convex games are obtained. (C) 2017 Elsevier B.V. All rights reserved.
The N = 2* supersymmetric gauge theory is a massive deformation of N = 4, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-) Abelian N = 2* theory, and compute suitable top...
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The N = 2* supersymmetric gauge theory is a massive deformation of N = 4, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-) Abelian N = 2* theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual N = 2chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter Omega-background, in agreement with a recent proposal. (C) 2017 The Author(s). Published by Elsevier B.V.
Motivation: DNA data is transcribed into single-stranded RNA, which folds into specific molecular structures. In this paper we pose the question to what extent sequence-and structure-information correlate. We view thi...
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Motivation: DNA data is transcribed into single-stranded RNA, which folds into specific molecular structures. In this paper we pose the question to what extent sequence-and structure-information correlate. We view this correlation as structural semantics of sequence data that allows for a different interpretation than conventional sequence alignment. Structural semantics could enable us to identify more general embedded 'patterns' in DNA and RNA sequences. Results: We compute the partition function of sequences with respect to a fixed structure and connect this computation to the mutual information of a sequence-structure pair for RNA secondary structures. We present a Boltzmann sampler and obtain the a priori probability of specific sequence patterns. We present a detailed analysis for the three PDB-structures, 2JXV (hairpin), 2N3R (3-branch multi-loop) and 1EHZ (tRNA). We localize specific sequence patterns, contrast the energy spectrum of the Boltzmann sampled sequences versus those sequences that refold into the same structure and derive a criterion to identify native structures. We illustrate that there are multiple sequences in the partition function of a fixed structure, each having nearly the same mutual information, that are nevertheless poorly aligned. This indicates the possibility of the existence of relevant patterns embedded in the sequences that are not discoverable using alignments.
The results of extensive ab initio calculations of the vibrational-rotational energy spectrum in the ground electronic state of the BC2 molecule are presented. These data were employed to discuss the evaluation of the...
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The results of extensive ab initio calculations of the vibrational-rotational energy spectrum in the ground electronic state of the BC2 molecule are presented. These data were employed to discuss the evaluation of the corresponding partition functions. Special attention was paid to the problems connected with the calculation of the partition functions for the bending vibrations and rotations about the axis corresponding to the smallest moment of inertia.
The wavefunction of the free-fermion six-vertex model was found to give a natural realization of the Tokuyama combinatorial formula for the Schur polynomials by Bump, Brubaker and Friedberg. Recently, we studied the c...
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The wavefunction of the free-fermion six-vertex model was found to give a natural realization of the Tokuyama combinatorial formula for the Schur polynomials by Bump, Brubaker and Friedberg. Recently, we studied the correspondence between the dual version of the wavefunction and the Schur polynomials, which gave rise to another combinatorial formula. In this paper, we extend the analysis to the reflecting boundary condition and show the exact correspondence between the dual wavefunction and the symplectic Schur functions. This gives a dual version of the integrable model realization of the symplectic Schur functions by Ivanov. We also generalize to the correspondence between the wavefunction, the dual wavefunction of the six-vertex model and the factorial symplectic Schur functions by the inhomogeneous generalization of the model.
Here we prove that Benford's law holds for coefficients of an infinite class of modular forms. Expanding the work of Bringmann and Ono on exact formulas for harmonic Maass forms, we derive the necessary asymptotic...
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Here we prove that Benford's law holds for coefficients of an infinite class of modular forms. Expanding the work of Bringmann and Ono on exact formulas for harmonic Maass forms, we derive the necessary asymptotics. This implies that the unrestricted partition function p(n), as well as other natural partition functions, satisfies Benford's law.
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