Related papers: Weak coupling asymptotics for the Pauli operator i…
We study the asymptotic behaviour of the eigenvalues of the Laplace-Beltrami operator on a compact hypersurface in \mathds{R}^{n+1} as it is flattened into a singular double-sided flat hypersurface. We show that the limit spectral problem…
We analyse the asymptotic symmetries of electromagnetism non-minimally coupled to scalar fields, with non-minimal couplings of the Fermi type that occur in extended supergravity models. Our study is carried out at spatial infinity where…
We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave…
We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the…
The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and…
We consider the Laplace operator with Dirichlet boundary conditions on a domain in R^d and study the effect that performing a scaling in one direction has on the eigenvalues and corresponding eigenfunctions as a function of the scaling…
An experimental proposal is presented in which dark port post-selection together with weak measurements are used to enlarge the radiation pressure effect of a single photon on a mechanical oscillator placed in the middle of a Fabry-Perot…
Chiral Magnetic Effect and Chiral Vortical Effect are parity odd transport phenomena originating from chiral anomaly, and have generalizations to all even dimensional space-time higher than four dimensions. We attempt to compute the…
Simple asymptotic expansions for the Jacobi functions $P_\nu^{(\alpha, \beta)}(z)$ and $Q_\nu^{(\alpha, \beta)}(z)$ for large degree $\nu$, with fixed parameters $\alpha$ and $\beta$, are surprisingly rare in the literature, with only a few…
Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional fractional Laplace operator (-d^2/dx^2)^(alpha/2) (0 < alpha < 2) in the interval (-1,1) is given: the n-th eigenvalue is equal to (n pi/2 - (2 - alpha) pi/8)^alpha +…
I propose an approximation scheme for asymptotically free field theories combining both weak coupling and strong coupling series. The weak coupling expansion is used to integrate the high frequency modes and the resulting low energy…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
We consider a class of pseudodifferential operators defined on the product of two closed manifolds, with crossed vector valued symbols. We study the asymptotic expansion of Weyl counting function of positive selfadjoint operators in this…
We describe a perturbation expansion for the energy and wave function of a weakly bound particle in a short-range potential in one space dimension.
We consider a pentadiagonal matrix which will be described in the text. We demonstrate practical methods for obtaining weak coupling expressions for the lowest eigenvector in terms of the parameters in the matrix, v and w. It is found that…
Sequential weak measurements of non-commuting observables is not only fundamentally interesting in quantum measurement but also shown potential in various applications. The previous reported methods, however, can only realize limited…
We study asymptotic distribution of eigen-values $\omega$ of a quadratic operator polynomial of the following form $(\omega^2-L(\omega))\phi_\omega=0$, where $L(\omega)$ is a second order differential positive elliptic operator with…
We prove a two-term Weyl-type asymptotic law, with error term O(1/n), for the eigenvalues of the operator psi(-Delta) in an interval, with zero exterior condition, for complete Bernstein functions psi such that x psi'(x) converges to…
This text is a survey of recent results obtained by the author and collaborators on different problems for non-self-adjoint operators. The topics are: Kramers-Fokker-Planck type operators, spectral asymptotics in two dimensions and Weyl…
The correlation functions of open Wilson line operators in two-dimensional Yang-Mills theory on the noncommutative torus are computed exactly. The correlators are expressed in two equivalent forms. An instanton expansion involves only…