Related papers: Matrices, Fermi Operators and Applications
Determinants and symmetric functions of the eigenvalues of matrices characterizing stochastic processes with indepedent increments. Relationships with Fibonacci numbers are derived.
We study a Fermi Hamilton operator $\hat K$ which does not commute with the number operator $\hat N$. The eigenvalue problem and the Schr\"odinger equation is solved. Entanglement is also discussed. Furthermore the Lie algebra generated by…
A Grassmann functional phase space is formulated for the definition of fermionic Wigner functionals by identifying suitable fermionic operators that are analogues to boson quadrature operators. Instead of the Majorana operators, we use…
We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…
We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…
In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…
This note deals with two topics of linear algebra. We give a simple and short proof of the multiplicative property of the determinant and provide a constructive formula for rotations. The derivation of the rotation matrix relies on simple…
Riemann surfaces with nodes can be described by introducing simple composite operators in matrix models. In the case of the Kontsevich model, it is sufficient to add the quadratic, but ``non-propagating'', term (tr[X])^2 to the Lagrangian.…
In this paper we investigate weighted composition operators between weak and strong vector valued weighted Bergman spaces and Hardy spaces.
To be able to solve operator equations numerically a discretization of those operators is necessary. In the Galerkin approach bases are used to achieve discretized versions of operators. In a more general set-up, frames can be used to…
Several examples of Jacobi matrices with an explicitly solvable spectral problem are worked out in detail. In all discussed cases the spectrum is discrete and coincides with the set of zeros of a special function. Moreover, the components…
This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…
A review of recent lattice calculations of nucleon structure and matrix elements of operators in nucleons is presented. It primarily covers developments in the calculation of the matrix elements of the scalar, tensor, pseudo-scalar,…
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
For lattice operators that are relevant to the calculation of moments of nucleon structure functions we investigate the transformation properties under the hypercubic group. We give explicit bases of irreducible subspaces for tensors of…
Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is…
After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in…
Family of replica matrices, related to general ultrametric spaces, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed.