arXiv subjects

A. Verçin

Publications and source records attributed to A. Verçin.

4 recordsLinked to original sources

arXiv2016

Reduced quantum dynamics with initial system-environment correlations characterized by pure Markov states

Any tripartite state which saturates the strong subadditivity relation for the quantum entropy is defined as the Markov state.A tripartite pure state describing an open system, its environment and their purifying system isa pure Markov state iff the bipartite marginal state of purifying system and environment is a product state. It has been shown that as long as the purification of the input system-environment state is a pure Markov state the reduced dynamics of the open system can be described, on the support of initial system state, by a quantum channel for every joint unitary evolution of the system-environment composite even in the presence of initial correlations. Entanglement, discord and classical correlations of the initial system-environment states implied by the pure Markov state are analyzed and it has been shown that all these correlations are entirely specified by the entropy of the environment. Some implications concerning perfect quantum error correction procedure and quantum Markovian dynamics are presented.

quant-ph↗

arXiv2009

First-order symmetries of Dirac equation in curved background: a unified dynamical symmetry condition

It has been shown that, for all dimensions and signatures, the most general first-order linear symmetry operators for the Dirac equation including interaction with Maxwell field in curved background are given in terms of Killing-Yano (KY) forms. As a general gauge invariant condition it is found that among all KY-forms of the underlying (pseudo) Riemannian manifold, only those which Clifford commute with the Maxwell field take part in the symmetry operator. It is also proved that associated with each KY-form taking part in the symmetry operator, one can define a quadratic function of velocities which is a geodesic invariant as well as a constant of motion for the classical trajectory. Some geometrical and physical implications of the existence of KY-forms are also elucidated.

gr-qc↗

arXiv2008

Basic Gravitational Currents and Killing-Yano Forms

It has been shown that for each Killing-Yano (KY)-form accepted by an $n$-dimensional (pseudo)Riemannian manifold of arbitrary signature, two basic gravitational currents can be defined. Conservation of the currents are explicitly proved by showing co-exactness of the one and co-closedness of the other. Some general geometrical facts implied by these conservation laws are also elucidated. In particular, the conservation of the one-form currents implies that the scalar curvature of the manifold is a flow invariant for all of its Killing vector fields. It also directly follows that, while all KY-forms and their Hodge duals on a constant curvature manifold are the eigenforms of the Laplace-Beltrami operator, for an Einstein manifold this is certain only for KY 1-forms, $(n-1)$-forms and their Hodge duals.

gr-qc↗

arXiv1997

Ordered Products, $W_{\infty}$-Algebra, and Two-Variable, Definite-Parity, Orthogonal Polynomials

It has been shown that the Cartan subalgebra of $W_{\infty}$- algebra is the space of the two-variable, definite-parity polynomials. Explicit expressions of these polynomials, and their basic properties are presented. Also has been shown that they carry the infinite dimensional irreducible representation of the $su(1,1)$ algebra having the spectrum bounded from below. A realization of this algebra in terms of difference operators is also obtained. For particular values of the ordering parameter $s$ they are identified with the classical orthogonal polynomials of a discrete variable, such as the Meixner, Meixner-Pollaczek, and Askey-Wilson polynomials. With respect to variable $s$ they satisfy a second order eigenvalue equation of hypergeometric type. Exact scattering states with zero energy for a family of potentials are expressed in terms of these polynomials. It has been put forward that it is the İnönü-Wigner contraction and its inverse that form bridge between the difference and differential calculus.

quant-ph↗