Applications :: Math
Topology :: Math

JMP: Statistical Physics

Quantum hypothesis testing with group symmetry
Fumio Hiai, Milan Mosonyi, and Masahito Hayashi The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with the problems of the Chernoff bound, the Hoeffding bound, an ... [J. Math. Phys. 50, 103304 (2009)] published Thu Oct 22, 2009.
Nonlinear stability of boundary layer solution to the Boltzmann equation with diffusive effect at the boundary
Qianzhu Tian and Jie Sun In this paper, the stability of boundary layer solutions to the Boltzmann equation with diffusive effect at the boundary for hard sphere model is considered. When the Mach number of the far field is less than 1, the exponential decay in time is proven for linearized operator first. At last, based on ... [J. Math. Phys. 50, 103303 (2009)] published Thu Oct 8, 2009.
Computation for the canonical measures of a colored disordered lattice gas and spectral gap
Zeghdoudi Halim and Boutabia Hacene In this work we deal with spectral gap and canonical measures related to a model called colored disordered lattice gas. We consider the approach used in the work of Dermoune and Heinrich [A small step towards the hydrodynamic limit of a colored disordered lattice gas, C. R. Math. Acad. Sci. 339, 507 ... [J. Math. Phys. 50, 103302 (2009)] published Wed Oct 7, 2009.

JMP: Methods of Mathematical Physics

General decay rate estimate for a viscoelastic equation with weakly nonlinear time-dependent dissipation and source terms
Wenjun Liu A viscoelastic wave equation in canonical form with weakly nonlinear time-dependent dissipation and source terms is investigated in this paper. For a wider class of relaxation functions and without imposing any restrictive growth assumption on the damping term at the origin, we establish an explicit ... [J. Math. Phys. 50, 113506 (2009)] published Fri Nov 6, 2009.
Particle topology, braids, and braided belts
Sundance Bilson-Thompson, Jonathan Hackett, and Louis H. Kauffman Recent work [S. O. Bilson-Thompson, e-print arXiv:hep-th/0503213; Bilson-Thompson et al., Class. Quantum Grav. 24, 3975 (2007)] suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in th ... [J. Math. Phys. 50, 113505 (2009)] published Thu Nov 5, 2009.
On the Moyal deformation of Nahm equations in seven dimensions
Hugo Garcia-Compean and Aldo A. Martinez-Merino We show how the reduced (anti-)self-dual YangMills equations to seven dimensions described by the Nahm equations can be carried over to the WeylWignerMoyal formalism. In the process some new solutions for the cases of gauge groups SU(2) and SL(2,[openface R]) are explicitly obtained. ... [J. Math. Phys. 50, 113504 (2009)] published Thu Nov 5, 2009.

 

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An Introduction to Noncommutative Geometry - A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics.

404 Celestial Mechanics Research - Links, animations, references, and a brief description of research into n-body problems.
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404 Clyde Davenport's Commutative Hypercomplex Mathematics - Summary and application as it relates to electromagnetic theory and special relativity.
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Complex Geometry of Nature and General Relativity - A paper by Giampiero Esposito attempting to give a self-contained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.

Differential Equations and Oscillations - Many problems in physics are described by differential equations. As a complete discussion of differential equations is beyond the scope of this chapter we will deal only with linear first and second order ordinary differential equations.

Dimensional Analysis - A simple review of the powerful technique of dimensional analysis.

Discrete Self-trapping Equation - A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.

Doing Physics with Quaternions - A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra.

Euclidean Geometric Transforms for Physics - A new method of correlating physics formulas to derive one formula from a related formula using Euclidean geometry to represent the inter-relationship of physics formulas.

Five Lectures on Soliton Equations - A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.

Geometry and Duality - Lecture notes from the ITP miniprogram on Geometry and Duality

his Week's Finds in Mathematical Physics - This is a column written about modern topics in mathematical physics.

Holomorphic Methods in Mathematical Physics - This set of lecture notes by Brian C. Hall gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations.

Homological Methods in Mathematical Physics - These lecture notes by Joseph Krasil'shchik and Alexander Verbovetsky are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations.

500 Hyperreal World - Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.
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Inexplicable Secrets of Creation - Relationships between number theory and physics.

Intrinsic Localized Modes - Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell.

Journal on Applied Clifford Algebra - Journal devoted to the development of Geometric Analysis in particular through the use of Clifford Algebras, Quaternions, Hypercomplex Analysis and Multivector Techniques. Main emphasis en the applications to Physics.

Kinetic Theory and its Applications. - This resource is devoted to mathematical aspects of kinetic theory and its applications in physics and chemistry.

Klaus Brauer's Soliton Page - Presents a history of J.S.Russell's discovery of solitary waves, and animations of one-, two- and three-soliton solutions to the Korteweg-de Vries equation. Includes an article in PDF format on finding exact solutions to the KdV equation using the method of Backlund transform with the help of Mathematica.

Lectures on Orientifolds and Duality - Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.

Local Quantum Physics Crossroads - An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP).

Mathematical Methods I - This site contains the complete lecture notes and homework sets for PHYCS498MMA, a course of mathematical methods for physics given to entering graduate students, and senior undergraduates, at the University of Illinois at Urbana-Champaign.

Non Commutative Geometry - Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.

On the Origins of Twister Theory - A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity.

Open Problems in Mathematics and Physics - Links to open problems in mathematics, physics and other subjects.

404 Period and energy in one degree of freedom systems - An article by Jorge Rezende, University of Lisbon (PDF).

404 Radial Symmetric Fourier Transforms - Fourier transforms of radially-symmetric functions can be performed efficiently using the Hankel transform of order zero. Illustrations of the method are presented, and of the Gibbs' phenomenon.

Recent Developments in Skyrme Models - An introduction by T. Gisiger and M.B. Paranjape to recent, more mathematical developments in the Skyrme model. The aim is to render these advances accessible to mainstream nuclear and particle physicists.

Solitons - An overview of the classical and quantum theory related to solitons

Solitons - Resources at Heriot-Watt University. Meetings, local and other links.

Symplectic Geometries in Quantum Physics and Optics - A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics

The Dirac Delta Function - A brief introduction to the properties and uses of the Dirac delta function.
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Topology and Physics - An essay by C. Nash on the historical connection between topology and physics.

Twistors- What are they? - A set of notes introducing spinors and twistors.

500 Visual Mathematical Physics - Collection of animated gif pictures describing the solutions of the main partial differential equations such as Laplace, Poisson, string and membrane oscillations and heat conduction.