我们介绍了量子谐振子的哈密顿量的另一种因式分解，它导致一个两参数的自伴算子，从标准谐振子，由Mielnik介绍的单参数振荡器，和厄米特算子的参数的某些限制。此外，本文还给出了一个不同于M. A. Reyes，H. C. Rosu和M. R. Gutierrez，Phys. Lett. A 375（2011）2145在本工作的最后部分进行了简要讨论
英文摘要：
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization which is different of the one introduced by M. A. Reyes, H. C. Rosu, and M. R. Gutierrez, Phys. Lett. A 375 (2011) 2145 is briefly discussed in the final part of this work
Using the Riesz-Feller fractional derivative, we apply the factorization algorithm to the fractional quantum harmonic oscillator along the lines previously proposed by Olivar-Romero and Rosas-Ortiz, extending their results. We solve the non-Hermitian fractional eigenvalue problem in the k space by introducing in that space a new class of Hermite `polynomials' that we call Riesz-Feller Hermite `polynomials'. Using the inverse Fourier transform in Mathematica, interesting analytic results for the same eigenvalue problem in the x space are also obtained. Additionally, a more general factorization…
The norm of the non-self-adjoint harmonic oscillator semigroup
我们确定了由非自伴谐振子作用于$L^2(\Bbb{R})$生成的半群的范数，对于它有界的所有复时。我们将这个问题的嵌入之间的高斯加权空间的全纯函数，我们表明，同样的技术适用于，在任何维度上，半群$e^{-tQ}$所产生的椭圆二次算子作用于$L^2(\Bbb{R}^n)$。所用的方法-确定Mehler公式的锐积的指数-是基本的，并受到L. Hörmander，A. Melin，and J. Sjöstrand.
In this paper we consider some aspects of tridiagonal, non self-adjoint, Hamiltonians and of their supersymmetric counterparts. In particular, the problem of factorization is discussed, and it is shown how the analysis of the eigenstates of these Hamiltonians produce interesting recursion formulas giving rise to biorthogonal families of vectors. Some examples are proposed, and a connection with bi-squeezed states is analyzed.
In this paper, we develop a factorization method to reconstruct cavities in a heat conductor by knowing the Neumann-to-Dirichlet map at the boundary of this conductor. The factorization method is a very well known reconstruction method for inverse problems described by self-adjoint elliptic equations. It enables us to reconstruct the boundaries of unknown targets such as cavities and inclusions. This method was successfully applied for examples to the inverse scattering problem by obstacles for the acoustic wave and the electrical impedance tomography problem. The forward model equations for t…
A family of non-autonomous hybrid Lienard oscillators based on a parametrically extended commutative factorization
Instituto Potosino de Investigación Científica y Tecnológica（圣路易斯波托西科学研究与技术学院）；Universidad de Guadalajara（瓜达拉哈拉大学）；Universidad Autónoma de Querétaro（克雷塔罗自治大学）
We analyze the $\ell$--weights of the evaluation and $q$-oscillator representations of the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ for $l = 1$ and $l = 2$ and prove the factorization relations for the transfer operators of the associated quantum integrable systems.
We study several natural multiplicity questions that arise in the context of the Birman-Schwinger principle applied to non-self-adjoint operators. In particular, we re-prove (and extend) a recent result by Latushkin and Sukhtyaev by employing a different technique based on factorizations of analytic operator-valued functions due to Howland. Factorizations of analytic operator-valued functions are of particular interest in themselves and again we re-derive Howland's results and subsequently extend them. Considering algebraic multiplicities of finitely meromorphic operator-valued functions, we r…
Bounds on the spectrum and reducing subspaces of a J-self-adjoint operator
给定希尔伯特空间H上的自伴对合J，考虑H上的J-自伴算子L = A + V，其中A是与J交换的可能无界自伴算子，V是有界J-自伴算子反-我们建立了L的谱相对于A的谱的位置的最优估计，并且得到了L的最大和最小算子角之间的范数界。未扰动算子A和扰动算子L的定约化子空间。所有的界都是根据V的范数和与算子L和/或算子A相关联的不相交谱集对之间的距离给出的。作为例子，讨论了PT对称微扰下的量子谐振子。得到的算子角的严格范数界将著名的Davis-Kahan三角定理推广到J-自伴扰动的情形。
We consider one-dimensional chains and multi-dimensional networks of harmonic oscillators coupled to two Langevin heat reservoirs at different temperatures. Each particle interacts with its nearest neighbors by harmonic potentials and all individual particles are confined by harmonic potentials, too. In this article, we provide, for the first time, the sharp N dependence of the spectral gap of the associated generator under various physical assumptions and for different spatial dimensions. Our method of proof relies on a new approach to analyze a non self-adjoint eigenvalue problem involving l…
We show that the theory of self-adjoint differential equations can be used to provide a satisfactory solution of the inverse variational problem in classical mechanics. A Newtonian equation when transformed to the self-adjoint form allows one to find an appropriate Lagrangian representation (direct analytic representation) for it. On the other hand, the same Newtonian equation in conjunction with its adjoint provides a basis to construct a different Lagrangian representation (indirect analytic representation) for the system. We obtain the time-dependent Lagrangian of the damped Harmonic oscill…
