量子代数$SU_q(2)$在对角基$"J_x"$ generator中的表示

一类 WCLT 非退化 GKSL 生成元的渐近等价性

Asymptotic equivalence of a subclass of WCLT non degenerate GKSL generator

本文证明了具有 Toeplitz 块的块对角矩阵序列的渐近等价性，并利用 circulant 和 WCLT 量子 Markov 半群的 GKSL 生成元的算子子空间不变性，在适当假设下证明了这些族的渐近等价性。

GL型对角约化代数的结构常数

Structure constants of diagonal reduction algebras of gl type

我们描述，在发电机和关系，减少代数，有关的对角嵌入的李代数$\gl_n$到$\gl_n\oplus\gl_n$。它的表示论与$\gl_n$ -模的张量积分解理论有关。

GKSL Generators and Digraphs: Computing Invariant States

In recent years, digraph induced generators of quantum dynamical semigroups have been introduced and studied, particularly in the context of unique relaxation and invariance. In this article we define the class of pair block diagonal generators, which allows for additional interaction coefficients but preserves the main structural properties. Namely, when the basis of the underlying Hilbert space is given by the eigenbasis of the Hamiltonian (for example the generic semigroups), then the action of the semigroup leaves invariant the diagonal and off-diagonal matrix spaces. In this case, we expl…

Addition of SU(3) generators and its Singlet Hilbert space

We construct the singlet Hilbert space associated with addition of SU(3) generators. This corresponds to the solution of Gauss law in lattice QCD. The normalized basis states are explicitly constructed using Schwinger Bosons. Further, we compute the action of basic singlet operators on these basis states.

Bi-orthogonal Polynomials and the Five parameter Asymmetric Simple Exclusion Process

We apply the bi-moment determinant method to compute a representation of the matrix product algebra -- a quadratic algebra satisfied by the operators $\mathbf{d}$ and $\mathbf{e}$ -- for the five parameter ($α$, $β$, $γ$, $δ$ and $q$) Asymmetric Simple Exclusion Process. This method requires an $LDU$ decomposition of the ``bi-moment matrix''. The decomposition defines a new pair of basis vectors sets, the `boundary basis'. This basis is defined by the action of polynomials $\{P_n\}$ and $\{Q_n\}$ on the quantum oscillator basis (and its dual). Theses polynomials are orthogonal to themselves (i…

On Poincaré-Birkhoff-Witt basis of quantum general linear superalgebra

We give a detailed derivation of the commutation relations for the Poincaré--Birkhoff--Witt generators of the quantum superalgebra $\mathrm U_q(\mathfrak{gl}_{M|N})$.