Mathematical Physics

New submissions

[ total of 19 entries: 1-19 ]
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New submissions for Fri, 22 Jun 18

[1]
Title: Deformation of algebroid bracket of differential forms and Poisson manifold
Subjects: Mathematical Physics (math-ph); Differential Geometry (math.DG); Dynamical Systems (math.DS)

We construct the family of algebroid brackets $[\cdot,\cdot]_{c,v}$ on the tangent bundle $T^*M$ to a Poisson manifold $(M,\pi)$ starting from an algebroid bracket of differential forms. We use these brackets to generate Poisson structures on the tangent bundle $TM$. Next, in the case when $M$ is equipped with a bi-Hamiltonian structure $(M,\pi_1, \pi_2)$ we show how to construct another family of Poisson structures. Moreover we present how to find Casimir functions for those structures and we discuss some particular examples.

[2]
Title: Equilibrium States, Phase Transitions and Dynamics in Quantum Anharmonic Crystals
Authors: Yuri Kozitsky
Comments: to appear in Stochastic Partial Differential Equations and Related Fields In Honor of Michael Roeckner SPDERF, Bielefeld, Germany, October 10 -14, 2016
Subjects: Mathematical Physics (math-ph)

The basic elements of the mathematical theory of states of thermal equilibrium of infinite systems of quantum anharmonic oscillators (quantum crystals) are outlined. The main concept of this theory is to describe the states of finite portions of the whole system (local states) in terms of stochastically positive KMS systems and path measures. The global states are constructed as Gibbs path measures satisfying the corresponding DLR equation. The multiplicity of such measures is then treated as the existence of phase transitions. This effect can be established by analyzing the properties of the Matsubara functions corresponding to the global states. The equilibrium dynamics of finite subsystems can also be described by means of these functions. Then three basic results of this theory are presented and discussed: (a) a sufficient condition for a phase transition to occur at some temperature; (b) a sufficient condition for the suppression of phase transitions at all temperatures (quantum stabilization); (c) a statement showing how the phase transition can affect the local equilibrium dynamics.

[3]
Title: Irregular conformal blocks and connection formulae for Painlevé V functions
Subjects: Mathematical Physics (math-ph)

We prove a Fredholm determinant and short-distance series representation of the Painlev\'e V tau function $\tau(t)$ associated to generic monodromy data. Using a relation of $\tau(t)$ to two different types of irregular $c=1$ Virasoro conformal blocks and the confluence from Painlev\'e VI equation, connection formulas between the parameters of asymptotic expansions at $0$ and $i\infty$ are conjectured. Explicit evaluations of the connection constants relating the tau function asymptotics as $t\to 0,+\infty,i\infty$ are obtained. We also show that irregular conformal blocks of rank 1, for arbitrary central charge, are obtained as confluent limits of the regular conformal blocks.

Cross-lists for Fri, 22 Jun 18

[4]  arXiv:1806.05992 (cross-list from hep-th) [pdf, ps, other]
Title: A Unique Connection for Born Geometry
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph); Differential Geometry (math.DG)

It has been known for a while that the effective geometrical description of compactified strings on $d$-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an $O(d,d)$ pairing $\eta$ and an $O(2d)$ generalized metric $\mathcal{H}$. More recently it has been shown that in order to include T-duality as an effective symmetry, the generalized geometry also needs to carry a phase space structure or more generally a para-Hermitian structure encoded into a skew-symmetric pairing $\omega$. The consistency of string dynamics requires this geometry to satisfy a set of compatibility relations that form what we call a Born geometry. In this work we prove an analogue of the fundamental theorem of Riemannian geometry for Born geometry. We show that there exists a unique connection which preserves the Born structure $(\eta,\omega,\mathcal{H})$ and which is torsionless in a generalized sense. This resolves a fundamental ambiguity that is present in the double field theory formulation of effective string dynamics.

[5]  arXiv:1806.07880 (cross-list from math.CA) [pdf, other]
Title: On the uncertainty product of spherical functions
Subjects: Classical Analysis and ODEs (math.CA); Mathematical Physics (math-ph)

The uncertainty product of a function is a quantity that measures the trade-off between the space and the frequency localization of the function. Its boundedness from below is the content of various uncertainty principles. In the present paper, functions over the $n$-dimensional sphere are considered. A formula is derived that expresses the uncertainty product of a continuous function in terms of its Fourier coefficients. It is applied to a directional derivative of a zonal wavelet, and the behavior of the uncertainty product of this function is discussed.

[6]  arXiv:1806.07881 (cross-list from math.CA) [pdf, ps, other]
Title: A continuous spherical wavelet transform for~$\mathcal C(\mathcal S^n)$
Subjects: Classical Analysis and ODEs (math.CA); Mathematical Physics (math-ph); Functional Analysis (math.FA)

In the present paper, a wavelet family over the $n$-dimensional sphere is constructed such that for each scale the wavelet is a polynomial and the inverse wavelet transform of a continuous function converges in the supremum norm.

[7]  arXiv:1806.07960 (cross-list from math.CA) [pdf]
Title: Series solutions of Heun-type equation in terms of orthogonal polynomials
Authors: A. D. Alhaidari
Subjects: Classical Analysis and ODEs (math.CA); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

We introduce a nine-parameter Heun-type differential equation and obtain three classes of its solutions as series of square integrable functions written in terms of the Jacobi polynomial. The expansion coefficients of the series satisfy three-term recursion relations, which are solved in terms of orthogonal polynomials with continuous and/or discrete spectra. Some of these are well-known polynomials while others are either new or modified versions of known ones.

[8]  arXiv:1806.07962 (cross-list from math.CA) [pdf, ps, other]
Title: Generalizations of Russell-style integrals
Authors: Mark W. Coffey
Subjects: Classical Analysis and ODEs (math.CA); Mathematical Physics (math-ph)

First some definite integrals of W. H. L. Russell, almost all with trigonometric function integrands, are derived, and many generalized. Then a list is given in Russell-style of generalizations of integral identities of Amdeberhan and Moll. We conclude with a brief and noncomprehensive description of directions for further investigation, including the significant generalization to elliptic functions.

[9]  arXiv:1806.08003 (cross-list from math.QA) [pdf, other]
Title: Quantum moment maps and symmetric bounded domains quantizations
Subjects: Quantum Algebra (math.QA); Mathematical Physics (math-ph)

We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.

[10]  arXiv:1806.08254 (cross-list from hep-ph) [pdf, ps, other]
Title: Analyticity domain of a Quantum Field Theory and Accelero-summation
Subjects: High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

From 't Hooft's argument, one expects that the analyticity domain of an asymptotically free quantum field theory is horned shaped. In the usual Borel summation, the function is obtained through a Laplace transform and thus has a much larger analyticity domain. However, if the summation process goes through the process called acceleration by Ecalle, one obtains such a horn shaped analyticity domain. We therefore argue that acceleration, which allows to go beyond standard Borel summation, must be an integral part of the toolkit for the study of exactly renormalisable quantum field theories. We sketch how this procedure is working and what are its consequences.

[11]  arXiv:1806.08270 (cross-list from hep-th) [pdf, other]
Title: Opers, surface defects, and Yang-Yang functional
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

We explore the non-perturbative Dyson-Schwinger equations obeyed by the partition functions of the $\Omega$-deformed $\mathcal{N}=2, d=4$ supersymmetric linear quiver gauge theories in the presence of surface defects. We demonstrate that the partition functions of different types of defects (orbifold or vortex strings) are related by analytic continuation. We introduce Darboux coordinates on a patch of the moduli space of $SL(N)$-flat connections on a sphere with special punctures, which generalize the NRS coordinates defined in the $SL(2)$ case. Finally, we compare the generating function of the Lagrangian variety of opers in these Darboux coordinates with the effective twisted superpotential of the linear quiver theory in the two-dimensional $\Omega$-background, thereby proving the NRS conjecture and its generalization to the $SL(3)$ case.

Replacements for Fri, 22 Jun 18

[12]  arXiv:1607.02242 (replaced) [pdf, other]
Title: Global topology of Weyl semimetals and Fermi arcs
Comments: 9 pages, 4 figures, JPhysA Highlight in 2017, Free access in 2018
Journal-ref: J.Phys.A: Math.Theor.(Letter) vol.50 (2017) 11LT01 (11pp)
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[13]  arXiv:1609.05410 (replaced) [pdf, other]
Title: A new integrable equation valued on a Cayley-Dickson algebra
Comments: 21 pages. In this version we generalize the previous system using effectively the structure of the Cayley-Dickson algebra, adding an additional term to the previous one system. We also obtain one and two soliton solutions, in the octonionic case, from the B\"acklund transformation and give the associated Lax pair for the new general resulting system. We add some references
Subjects: Mathematical Physics (math-ph)
[14]  arXiv:1710.09927 (replaced) [pdf, ps, other]
Title: T-duality of singular spacetime compactifications in an H-flux
Authors: Andrew Linshaw (1), Varghese Mathai (2) ((1) Denver, (2) Adelaide)
Comments: 13 pages. Free access in 2018
Journal-ref: J. Geom. Phys., vol. 129, no. 7 (2018) 269-278
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Differential Geometry (math.DG)
[15]  arXiv:1711.09132 (replaced) [pdf, other]
Title: Multiparameter Gaussian Quantum Metrology
Comments: 14 pages, 3 figures; expanded and updated; to appear in Physical Review A
Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Instrumentation and Detectors (physics.ins-det); Optics (physics.optics)
[16]  arXiv:1801.00396 (replaced) [pdf, ps, other]
Title: Towards multifractional calculus
Journal-ref: Front. Phys. 6 (2018) 58
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th)
[17]  arXiv:1803.07319 (replaced) [pdf, ps, other]
Title: Wigner measures and effective mass theorems
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
[18]  arXiv:1803.11120 (replaced) [pdf, other]
Title: Hyperbolic vortices and Dirac fields in 2+1 dimensions
Comments: 27 pages, 5 figures, J Phys A accepted version
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
[19]  arXiv:1806.00876 (replaced) [pdf, ps, other]
Title: A modular-invariant modified Weierstrass sigma-function as a building block for lowest-Landau-level wavefunctions on the torus
Authors: F. D. M. Haldane
Comments: 5 pages, no figures. Revised to reference and describe a connection to Eisenstein's "periodic completion"of the Weierstrass zeta function
Subjects: Mathematical Physics (math-ph); Strongly Correlated Electrons (cond-mat.str-el)
[ total of 19 entries: 1-19 ]
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