Related papers: Quasideterminants and q-commuting minors
For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…
We describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these…
Let U^+ be the plus part of the quantized enveloping algebra of a simple Lie algebra and let B^* be the dual canonical basis of U^+. Let b,b' be in B* and suppose that one of the two elements is a q-commuting product of quantum flag minors.…
We give a new determinant expression for the characteristic polynomial of the bond scattering matrix of a quantum graph G. Also, we give a decomposition formula for the characteristic polynomial of the bond scattering matrix of a regular…
The transition matrix elements between the correlated $N$ and $N\!+\!1$ electron states of a quantum dot are calculated by numerical diagonalization. They are the central ingredient for the linear and non--linear transport properties which…
For any homogeneous identity between $q$-minors, we provide an identity between $P,Q$-minors.
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…
We study, from a combinatorial viewpoint, the quantized coordinate ring of mxn matrices over an infinite field K (also called quantum matrices) and its torus-invariant prime ideals. The first part of this paper shows that this algebra,…
In this paper, we proceed on determining the minimum $q_{min}$ among the connected nonbipartite graphs on $n\geq 5$ vertices and with domination number $\frac{n+1}{3}<\gamma\leq \frac{n-1}{2}$. Further results obtained are as follows:…
Uniformly quasiconformally homogeneous domains in $\mathbb{R}^n$ carry a transitive collection of $K$-quasiconformal maps for a fixed $K\geq 1.$ In this paper, we study two questions in this setting. The first is to show that…
We present a one-parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards. Our central result is the evaluation of the spectral two-point correlation form factor…
A mixed graph is obtained from an unoriented graph by orienting a subset of its edges. Yu, Liu, and Qu in 2017 have established the expression for the determinant of Hermitian (quasi-) Laplacian matrix of a mixed graph. Here we find general…
In this paper a systematic study of unitary asymptotes of commuting $n$-tuples of general Hilbert space operators is initiated. Special emphasis is put on the study of the quasianalicity property.
In this paper we compute explicit formulas for the commutation relations among quantum minors in the quantum matrix bialgebra $\cO_q(M_n(k))$.
This paper investigates continuous-time quantum walks on directed bipartite graphs based on a graph's adjacency matrix. We prove that on bipartite graphs, probability transport between the two node partitions can be completely suppressed by…
Complete sets of commutation relations for arbitrary pairs of quantum minors are computed, with explicit coefficients in closed form.
We review some of the recent developments in two dimensional statistical mechanics in which corner transfer matrices provide the vital link between the physical system and the representation theory of quantum affine algebras. This opens…
We present an explicit formula for the characteristic polynomial of the transition matrix of the discrete-time quantum walk on a graph via the second weighted zeta function. As applications, we obtain new proofs for the results on spectra…
We study the ring of quasisymmetric polynomials in $n$ anticommuting (fermionic) variables. Let $R_n$ denote the polynomials in $n$ anticommuting variables. The main results of this paper show the following interesting facts about…
Mathematical tools related to coherence theory and classical-quantum equivalence, due to Wigner and Glauber, are essential to modern, practical and empirical understanding of electromagnetics in areas like quantum optics and…