Related papers: n-ary star product: construction and integral repr…
An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An…
Using coherent states of the Weyl-Heisenberg algebra $h_N$, extended Voros products and Moyal brakets are derived. The covariance of Voros product under canonical transformations is discussed. Star product related to Barut-Girardello…
This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…
The structural control of silicon nanocrystals is an important technological problem. Typically a distribution of nanocrystal sizes and shapes emerges under the uncontrolled aggregation of smaller clusters. The aim of this computational…
This paper provides a product integration rule for highly oscillating integrands, based on equally spaced nodes. The stability and the error estimate are proven in the space of continuous functions, and some numerical tests which confirm…
We prove the existence of a deformation quantization for integrable Poisson structures on R^3 and give a generalization for a special class of three dimensional manifolds.
An new eigenvalue $\mathbb R$-linear problem arisen in the theory of metamaterials is stated and constructively investigated for circular non-overlapping inclusions. An asymptotic formula for eigenvalues is deduced when the radii of…
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using…
Factorization of an $n\times n$ unitary matrix as a product of $n$ diagonal matrices containing only phases interlaced with $n-1$ orthogonal matrices each one generated by a real vector as well as an explicit form for the Weyl factorization…
In this paper, we deal with a q-Dirac system. We investigate some spectral properties and the asymptotic behavior of the eigenvalues and the eigenfunctions of this q-Dirac system.
We prove that the pointwise product of two holomorphic functions of the upper half-plane, one in the Hardy space $\mathcal H^1$, the other one in its dual, belongs to a Hardy type space. Conversely, every holomorphic function in this space…
We consider the geometric and non-geometric faces of closed string vacua arising by T-duality from principal torus bundles with constant H-flux and pay attention to their double phase space description encompassing all toroidal coordinates,…
By means of a modified hypervirial theorem we derive simple expressions for the integrals of products of Airy functions. Present results contain earlier ones as particular cases.
In this paper we outline the construction of semiclassical eigenfunctions of integrable models in terms of the semiclassical path integral for the Poisson sigma model with the target space being the phase space of the integrable system. The…
In this paper we address the relation between the star exponentials emerging within the Deformation Quantization formalism and Feynman's path integrals associated with propagators in quantum dynamics. In order to obtain such a relation, we…
Based on the conventional energy band theory, an approach is presented to describe the electronic structure of crystalline insulators in the presence of a finite homogeneous electric field. The expression of polarization is derived which…
The nanocrystallite have the finite number of the oscillation modes. Their number increases proportionally to a cube of the characteristic size. Thus the oscillation spectrum of nanocrystal becomes discrete, and the separate modes of…
In the present paper we construct the star products concerning scalar fields in the covariant case from a new approach. We construct the star products at three levels, which are levels of functions on Rd, fields and functionals…
In this study, the properties of an oscillating system composed of a pendulum connected to a seesaw and placed on a moving platform with a certain slope are analyzed. Using complex numbers to collect the information contained in the system…
Calculating the structure of white dwarf and neutron stars would be a suitable topic for an undergraduate thesis or an advanced special topics or independent study course. The subject is rich in many different areas of physics accessible to…