Related papers: Diagonal Representation for a Generic Matrix Value…
We establish a q-generalization of Gordon's theorem that the space of diagonal coinvariants has a quotient identified with a perfect representation of the rational double affine Hecke algebra. It leads to a simple proof of his theorem and…
It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of…
In this paper we give a new and simple algorithm to put any multivariate polynomial into a normal determinant form in which each entry has the form , and in each column the same variable appears. We also apply the algorithm to obtain a…
Hamiltonians whose symbols are not simply real valued, but matrix or, more generally, endomorphism valued functions appear in many places in physics, examples being the Dirac equation, multicomponent wave equations like electrodynamics in…
Recent innovations on the differential calculus for functions of non-commuting variables, begun for a quaternionic variable, are now extended to the case of a general matrix over the complex numbers. The expansion of F(X+Delta) is given to…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…
Barbero recently suggested a modification of Ashtekar's choice of canonical variables for general relativity. Although leading to a more complicated Hamiltonian constraint this modified version, in which the configuration variable still is…
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
Diagonal matrix elements of pseudodifferential operators are needed in order to compute effective Lagrangians and currents. For this purpose the method of symbols is often used, which however lacks manifest covariance. In this work the…
General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
The similarity renormalization group is used to transform a general Dirac Hamiltonian into diagonal form. The diagonal Dirac operator consists of the nonrelativistic term, the spin-orbit term, the dynamical term, and the relativistic…
The multivariate quantum $q$-Krawtchouk polynomials are shown to arise as matrix elements of "$q$-rotations" acting on the state vectors of many $q$-oscillators. The focus is put on the two-variable case. The algebraic interpretation is…
We consider infinite dimensional port-Hamiltonian systems. Based on a power balance relation we introduce the port-Hamiltonian system representation where we pay attention to two different scenarios, namely the non-differential operator…
In this paper, we study the opening of a spectral gap for a class of 2-dimensional periodic Hamiltonians which include those modelling multilayer graphene. The kinetic part of the Hamiltonian is given by $\sigma \cdot F(-i\nabla)$, where…
Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple…
In this paper a generalization of Weyl quantization which maps a dynamical operator in a function space to a dynamical superoperator in an operator space is suggested. Quantization of dynamical operator, which cannot be represented as…
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.
The paper presents a new generalized integer orthogonal transformation which consists of a well known orthogonal transform followed by stretching the basis vectors maintaining the asymptotic behavior of the number of integer solutions for…
In this paper we study the $(2+1)$-dimensional Dirac-Dunkl oscillator coupled to an external magnetic field. Our Hamiltonian is obtained from the standard Dirac oscillator coupled to an external magnetic field by changing the partial…