Melvin Models and Diophantine Approximation
نویسندگان
چکیده
منابع مشابه
Melvin Models and Diophantine Approximation
Melvin models with irrational twist parameter provide an interesting example of conformal field theories with non-compact target space, and localized states which are arbitrarily close to being delocalized. We study the torus partition sum of these models, focusing on the properties of the regularized dimension of the space of localized states. We show that its behavior is related to interestin...
متن کاملDiophantine approximation and Diophantine equations
The first course is devoted to the basic setup of Diophantine approximation: we start with rational approximation to a single real number. Firstly, positive results tell us that a real number x has “good” rational approximation p/q, where “good” is when one compares |x − p/q| and q. We discuss Dirichlet’s result in 1842 (see [6] Course N◦2 §2.1) and the Markoff–Lagrange spectrum ([6] Course N◦1...
متن کاملDiophantine Approximation and Coloring
We demonstrate how connections between graph theory and Diophantine approximation can be used in conjunction to give simple and accessible proofs of seemingly difficult results in both subjects.
متن کاملDislocation Defects and Diophantine Approximation
In this paper we consider a Schrödinger eigenvalue problem with a potential consisting of a periodic part together with a compactly supported defect potential. Such problems arise as models in condensed matter to describe color in crystals as well as in engineering to describe optical photonic structures. We are interested in studying the existence of point eigenvalues in gaps in the essential ...
متن کاملHausdorff dimension and Diophantine approximation
In the present survey paper, we explain how the theory of Hausdorff dimension and Hausdorff measure is used to answer certain questions in Diophantine approximation. The final section is devoted to a discussion around the Diophantine properties of the points lying in the middle third Cantor set.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2005
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-005-1306-9