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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Almost periodic function and rotation number of the Schrodinger operator
薛定谔算子 几乎周期函数 旋转数
2023/4/25
The concept of almost periodic functions is due to H. Bohr. The concept of rotation number is due to H. Poincaré. The Schr?dinger operator is named after E. Schr?dinger. I will present our work relate...
Quasi-plane waves for spin 1 field in Lobachevsky space and a generalized helicity operator
Quasi-plane waves spin 1 field Lobachevsky space generalized helicity operator Mathematical Physics
2012/5/9
Spin 1 particle is investigated in 3-dimensional curved space of constant negative curvature. An extended helicity operator is defined and the variables are separated in a tetrad-based 10-dimensional ...
Method of oscillation and spectral problem for four-order differential operator with self-similar weight
Method of oscillation spectral problem self-similar weight
2011/9/20
Abstract: Self-adjoint boundary problems for the equation $y^{(4)}-\lambda\rho y=0$ with generalized derivative $\rho\in W_2^{-1}[0,1]$ of self-similar Cantor type function as a weight are considered....
Current response, structure factor and hydrodynamic quantities of a two- and three-dimensional Fermi gas from the operator product expansion
Current response structure factor
2011/7/21
We apply the operator product expansion to determine the asymptotic form of the current response of a Fermi gas in two and three dimensions.
The two-nucleon electromagnetic charge operator in chiral effective field theory ($χ$EFT) up to one loop
electromagnetic charge operator
2011/7/20
The electromagnetic charge operator in a two-nucleon system is derived in chiral effective field theory ($\chi$EFT) up to order $e\, Q$ (or N4LO), where $Q$ denotes the low-momentum scale and $e$ is t...
Resonance theory for perturbed Hill operator
resonances scattering periodic potential S-matrix
2011/9/6
Abstract: We consider the Schr\"odinger operator $Hy=-y"+(p+q)y$ with a periodic potential $p$ plus a compactly supported potential $q$ on the real line. The spectrum of $H$ consists of an absolutely ...
The path integral representation kernel of evolution operator in Merton-Garman model
path integration evolution operator kernel option pricing Black-Scholes formula
2011/7/26
Abstract: In the framework of path integral the evolution operator kernel for the Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-...
Properties of a Polarization based Phase Operator
Properties of a Polarization Phase Operator
2011/9/14
We de ne a Hermitian phase operator for zero mass spin one particles (photons) by taking account polarization. The Hilbert space includes the positive helicity states and negative helicity states with...
Nondifferentiable variational principles in terms of a quantum operator
Holder functions quantum calculus calculus of variations Green’s theorem
2011/7/28
Abstract: We develop Cresson's nondifferentiable calculus of variations on the space of H\"{o}lder functions. Several quantum variational problems are considered: with and without constraints, with on...
Nondifferentiable variational principles in terms of a quantum operator
Holder functions quantum calculus calculus of variations Green’s theorem
2011/7/28
Abstract: We develop Cresson's nondifferentiable calculus of variations on the space of H\"{o}lder functions. Several quantum variational problems are considered: with and without constraints, with on...
Tensorial form and matrix elements of the relativistic nuclear recoil operator
Isotope shifts, mass shift, relativistic nuclear recoil
2011/8/31
Within the lowest-order relativistic approximation (∼ v2/c2) and to first order in me/M, the tensorial form of the relativistic corrections of the nuclear recoil Hamiltonian is derived, opening ...
A Blaschke-type condition for analytic functions on finitely connected domains. Applications to complex perturbations of a finite-band selfadjoint operator
Blaschke-type estimates Lieb Thirring type inequalities finite-band selfadjoint operators complex compact perturbation
2011/7/27
Abstract: This is a sequel of a recent article by Borichev-Golinskii-Kupin, where the authors obtain Blaschke-type conditions for special classes of analytic functions in the unit disk which satisfy c...
Operator algebra quantum groups of universal gauge groups
Operator algebra quantum groups universal gauge groups
2010/12/24
In this paper, we quantize universal gauge groups such as SU(\infty), in the sigma-C*-algebra setting. More precisely, we propose a concise definition of sigma-C*-quantum groups and explain the conce...
Running couplings and operator mixing in the gravitational corrections to coupling constants
Running couplings operator mixing
2010/12/23
The use of a running coupling constant in renormalizable theories is well known, but the implementation of this idea for effective field theories with a dimensional coupling constant is in general le...
A note on the vector Schwinger Model with the photon mass term: Gauge invariant reformulation, operator solution and path integral formulation
vector Schwinger Model photon mass term
2010/12/23
Vector Schwinger model is reinvestigated with the mass like term for gauge field. Phase space structure has been determined in this situation. It has been found that mass of the gauge boson acquires ...