Resurgent Analysis of the Witten Laplacian in One Dimension

نویسنده

  • Alexander GETMANENKO
چکیده

The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the low-lying eigenvalues of the Witten Laplacian are resurgent.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Witten Laplacians and Brascamp-Lieb’s inequality on manifolds with boundary

In this paper, we derive from the supersymmetry of the Witten Laplacian Brascamp-Lieb’s type inequalities for general differential forms on compact Riemannian manifolds with boundary. In addition to the supersymmetry, our results essentially follow from suitable decompositions of the quadratic forms associated with the Neumann and Dirichlet self-adjoint realizations of the Witten Laplacian. The...

متن کامل

Uniform bounds and exponential time decay results for the Vlasov-Poisson-Fokker-Planck system

We consider the non-linear VPFP system with a coulombian repulsive interaction potential and a generic confining potential in space dimension d ≥ 3. Using spectral and kinetic methods we prove the existence and uniqueness of a mild solution with bounds uniform in time in weighted spaces, and for small total charge we find an explicit exponential rate of convergence toward the equilibrium in ter...

متن کامل

Small eigenvalues of the Witten Laplacian acting on p-forms on a surface

In this article, we are interested in the exponentially small eigenvalues of the self adjoint realization of the semiclassical Witten Laplacian ∆ f,h, in the general framework of p-forms, on a connected compact Riemannian manifold without boundary. Our purpose is to notice that the knowledge of (the asymptotic formulas for) the smallest non zero eigenvalues of the self adjoint realization of ∆ ...

متن کامل

Multiplicity of Positive Solutions of laplacian systems with sign-changing weight functions

In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.

متن کامل

Existence of at least one nontrivial solution for a class of problems involving both p(x)-Laplacian and p(x)-Biharmonic

We investigate the existence of a weak nontrivial solution for the following problem. Our analysis is generally bathed on discussions of variational based on the Mountain Pass theorem and some recent theories one the generalized Lebesgue-Sobolev space. This paper guarantees the existence of at least one weak nontrivial solution for our problem. More precisely, by applying Ambrosetti and Rabinow...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008