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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...
Asymptotic formula for the condensate wave function of a trapped Bose gas
Asymptotic formula condensate wave function trapped Bose gas
2015/10/16
An analytical property is pointed out for the universal differential equation first derived by Dalfovo, Pitaevskii, and Stringari for the condensate wave function at the boundary of a trapped Bose gas...
Product Einstein Manifolds, Zeta-Function Regularization and the Multiplicative Anomaly
Addition multiplication Laplace symmetric Spaces the product space
2014/12/22
The global additive and multiplicative properties of Laplace type operators acting on irreducible rank 1 symmetric spaces are considered. The explicit form of the zeta function on product spaces and o...
Single-hole spectral function and spin-charge separation in the t-J model
Worm hole green's function monte carlo simulation spectral analysis spectral function thermodynamics
2014/12/22
Worm algorithm Monte Carlo simulations of the hole Green function with subsequent spectral analysis were performed for 0.1<~J/t<~0.4 on lattices with up to L×L=32×32 sites at a temperature as low as T...
Weight function in a bimaterial strip containing an interfacial crack and an imperfect interface. Application to Bloch-Floquet analysis in a thin inhomogeneous structure with cracks
Bloch-Floquet waves boundary layer crack imperfect interface weight function
2011/9/22
Abstract: We define a weight function in a bi-material strip containing a semi-infinite crack and an imperfect interface and analyse a problem of anti-plane shear. We then present an asymptotic algori...
Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
The six-vertex model Open spin chain Partition function
2011/9/22
Abstract: With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representation of ...
On the Fermi Function of Squeezed Coherent States
Fermi Function Squeezed Coherent States Quantum Physics
2011/10/9
Abstract: Fermi observed in 1930 that the state of a quantum system may be defined in two different (but equivalent) ways, namely by its wavefunction $\Psi$ or by a certain function $g_F$ on phase spa...
Elliptic gamma-function and multi-spin solutions of the Yang-Baxter equation
Elliptic gamma-function multi-spin solutions the Yang-Baxter equation
2011/7/27
Abstract: We present a generalization of the master solution to the quantum Yang-Baxter equation (obtained recently in arXiv:1006.0651) to the case of multi-component continuous spin variables taking ...
Convergence of repeated QND measurements and the wave function collapse
QND measurement the wave function collapse Quantum Physics
2011/7/26
Abstract: Motivated by recent experiments on quantum trapped fields, we give a rigorous proof that repeated indirect quantum non-demolition (QND) measurements converge to the collapse of the wave func...
Uniform asymptotics for the full moment conjecture of the Riemann zeta function
full moment conjecture the Riemann zeta function $L$-functions Number Theory
2011/7/28
Abstract: Conrey, Farmer, Keating, Rubinstein, and Snaith recently conjectured formulas for the full asymptotics of the moments of $L$-functions. In the case of the Riemann zeta function, their conjec...
Homogenization of Steklov spectral problems with indefinite density function in perforated domains
Homogenization eigenvalue problems perforated domains indefinite weight function two-scale convergence
2011/7/28
Abstract: The asymptotic behavior of second order self-adjoint elliptic Steklov eigenvalue problems with periodic rapidly oscillating coefficients and with indefinite (sign-changing) density function ...
Two-scale convergence of elliptic spectral problems with indefinite density function in perforated domains
Homogenization eigenvalue problems perforated domains indefinite weight function two-scale convergence
2011/7/28
Abstract: Spectral asymptotics of linear periodic elliptic operators with indefinite (sign-changing) density function is investigated in perforated domains with the two-scale convergence method. The l...
Fractional Trigonometric Functions in Complex-valued Space: Applications of Complex Number to Local Fractional Calculus of Complex Function
Fractional trigonometric function complex function local fractional calculus fractal space
2011/7/26
Abstract: This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.
Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial
Heun's equation generalized hypergeometric function exceptional Jacobi polynomial
2011/7/27
Abstract: We study Heun's differential equation in the case that one of the singularities is apparent. In particular we conjecture a relationship with generalized hypergeometric differential equation ...
Eigenvalue equation for a 1--D Hamilton function in deformation quantization
1--D Hamilton Eigenvalue equation deformation quantization
2011/7/25
Abstract: The choice of coordinates: time and energy as the most convenient for an eigenvalue equation for a 1--D nonrelativistic Hamiltonian in frames of deformation quantization has been proposed. A...