Search results for "Mathematica"

Practical scheme from QCD to phenomena via Dyson-Schwinger equations

2019

We deliver a new scheme to compute the quark propagator and the quark-gluon interaction vertex through the coupled Dyson-Schwinger equations (DSEs) of QCD. We take the three-gluon vertex into account in our calculations, and implement the gluon propagator and the running coupling function fitted by the solutions of their respective DSEs. We obtain the momentum and current mass dependence of the quark propagator and the quark-gluon vertex, and the chiral quark condensate which agrees with previous results excellently. We also compute the quark-photon vertex within this scheme and give the anomalous chromo- and electro-magnetic moment of quark. The obtained results also agree with previous on…

Developing the Framed Standard Model

2011

The framed standard model (FSM) suggested earlier, which incorporates the Higgs field and 3 fermion generations as part of the framed gauge theory structure, is here developed further to show that it gives both quarks and leptons hierarchical masses and mixing matrices akin to what is experimentally observed. Among its many distinguishing features which lead to the above results are (i) the vacuum is degenerate under a global $su(3)$ symmetry which plays the role of fermion generations, (ii) the fermion mass matrix is "universal", rank-one and rotates (changes its orientation in generation space) with changing scale $\mu$, (iii) the metric in generation space is scale-dependent too, and in …

QCD generates the ϱ-resonance

1991

Abstract The question whether the asymptotic QCD amplitude contains potentially hadronic resonances is examined by a mathematically rigorous method, based on the theory of maximally converging sequences of polynomials and conformal mappings. It is shown that the extrapolated amplitude to the physical cut exhibits indeed a bump structure which corresponds to the ϱ-resonance.

Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states

2006

We present a novel, detailed study on the usefulness of three-mode Gaussian states states for realistic processing of continuous-variable quantum information, with a particular emphasis on the possibilities opened up by their genuine tripartite entanglement. We describe practical schemes to engineer several classes of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. In particular, we introduce a simple procedure -- based on passive optical elements -- to produce pure three-mode Gaussian states with {\em arbitrary} entanglement structure (upon availability of an initial two-mode squeezed state). We analyze in depth the properties of dist…

Multipartite entanglement in three-mode Gaussian states of continuous variable systems: Quantification, sharing structure and decoherence

2005

We present a complete analysis of multipartite entanglement of three-mode Gaussian states of continuous variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations will be quantified by a proper convex roof extension of the squared logarithmic negativity (the contangle), satisfying a monogamy relation for multimode Gaussian states, whose proof will be reviewed and elucidated. The residual contangle, emerging from the monog…

Non-Markovianity of Gaussian Channels

2015

We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated to arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.

Path Integrals in Noncommutative Geometry

2006

Dynamical Casimir-Polder force on a partially dressed atom near a conducting wall

2010

We study the time evolution of the Casimir-Polder force acting on a neutral atom in front of a perfectly conducting plate, when the system starts its unitary evolution from a partially dressed state. We solve the Heisenberg equations for both atomic and field quantum operators, exploiting a series expansion with respect to the electric charge and an iterative technique. After discussing the behaviour of the time-dependent force on an initially partially-dressed atom, we analyze a possible experimental scheme to prepare the partially dressed state and the observability of this new dynamical effect.

Non-Equilibrium Thermodynamics of Unsteady Superfluid Turbulence in Counterflow and Rotating Situations

2005

The methods of nonequilibrium thermodynamics are used in this paper to relate an evolution equation for the vortex line density $L$, describing superfluid turbulence in the simultaneous presence of counterflow and rotation, to an evolution equation for the superfluid velocity ${\mathbf{v}}_{s}$, in order to be able to describe the full evolution of ${\mathbf{v}}_{s}$ and $L$, instead of only $L$. Two alternative possibilities are analyzed, related to two possible alternative interpretations of a term coupling the effects of the counterflow and rotation on the vortex tangle, and which imply some differences between situations where counterflow and rotation vectors are parallel or orthogonal …

Algebraic quantization on a group and nonabelian constraints

1989

A generalization of a previous group manifold quantization formalism is proposed. In the new version the differential structure is circumvented, so that discrete transformations in the group are allowed, and a nonabelian group replaces the ordinary (central)U(1) subgroup of the Heisenberg-Weyl-like quantum group. As an example of the former we obtain the wave functions associated with the system of two identical particles, and the latter modification is used to account for the Virasoro constraints in string theory.