Search results for "Quantum Mechanic"

Polynomial method to study the entanglement of pure N-qubit states

2009

We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the number of unentangled qubits of pure N-qubit states.

Scalable Ellipsoidal Classification for Bipartite Quantum States

2008

The Separability Problem is approached from the perspective of Ellipsoidal Classification. A Density Operator of dimension N can be represented as a vector in a real vector space of dimension $N^{2}- 1$, whose components are the projections of the matrix onto some selected basis. We suggest a method to test separability, based on successive optimization programs. First, we find the Minimum Volume Covering Ellipsoid that encloses a particular set of properly vectorized bipartite separable states, and then we compute the Euclidean distance of an arbitrary vectorized bipartite Density Operator to this ellipsoid. If the vectorized Density Operator falls inside the ellipsoid, it is regarded as s…

C3v Top Data System (C3vTDS) software for spectrum simulation of XY3Z symmetric-top molecules using the group chain

2010

Abstract The C3v Top Data System (C3vTDS) program suite has been developed with the aim of studying any rovibrational band or polyad of XY3Z (C3v) symmetric-tops molecules in a singlet electronic state. It is developed in the same way as similar programs for various molecular symmetries (Td, Oh, C4v, C2v and D2h). We work in the O ( 3 ) ⊃ C ∞ v ⊃ C 3 v group chain and this choice has consequences on the method used to specify the input parameters for Hamiltonian and transition moment calculations. One example concerning the ν 2 band of the CH 3 12 D symmetric-top molecule is presented. This package consists in a series of FORTRAN programs called by scripts. The whole package is freely acces…

QCD sum rule calculation ofK ℓ3 form factors

1992

We present a combined finite energy sum rule (FESR) and analytic continuation by duality (ACD) calculation of the (neutral)K l3 decay. We confirm the Callan-Treiman relation and investigate the validity of a linear fit for the form factors. Furthermore, we obtain ζ=−0.1...−0.3, consistent with the mean experimental value ζ=−0.1±0.09.

An Interlude: Writing the Hamiltonian

2012

Modulational instability and two-dimensional dynamical structures

2008

A process of nonlinear structure formation on a two-dimensional lattice is proposed. The basic model consists of a two-dimensional lattice equipped at each node with a molecule or dipole rotating in the lattice plane. The interactions involved in the model are reduced to a periodic lattice. Such a discrete system can be applied to the problem of molecule adsorption on a substrate crystal surface, for instance. The continuum approximation of the model leads to a 2-D sine-Gordon system including nonlinear couplings, which itself can be reduced to a 2-D nonlinear Schrodinger equation in the low amplitude limit. Spatio-temporal structure formation is investigated by means of numerical simulatio…

Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling

2014

In this paper we study how to preserve entanglement and nonlocality under dephasing produced by classical noise with large low-frequency components, as $1/f$ noise, by Dynamical Decoupling techniques. We first show that quantifiers of entanglement and nonlocality satisfy a closed relation valid for two independent qubits locally coupled to a generic environment under pure dephasing and starting from a general class of initial states. This result allows to assess the efficiency of pulse-based dynamical decoupling for protecting nonlocal quantum correlations between two qubits subject to pure-dephasing local random telegraph and $1/f$-noise. We investigate the efficiency of an "entanglement m…

Time-dependent density-functional theory in the projector augmented-wave method

2008

We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born–Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear e…

Quantum field theory of dilute homogeneous Bose-Fermi mixtures at zero temperature: General formalism and beyond mean-field corrections

2002

We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We introduce a new relevant object, the renormalized boson-fermion T-matrix which we determine to second order in the boson-fermion s-wave scattering length. We also discuss how to incorporate the usual boson-boson T-matrix in mean-field approximation to obtain the total ground state properties of the system. The next order term beyond mean-field stems from the boson-fermion interaction and is proportional to $a_{\scriptsize BF}k_{\scriptsize F}$. The total groun…

Beam-normal single-spin asymmetry in elastic scattering of electrons from a spin-0 nucleus

2021

We study the beam-normal single-spin asymmetry (BNSSA) in high-energy elastic electron scattering from several spin-0 nuclei. Existing theoretical approaches work in the plane-wave formalism and predict the BNSSA to scale as $\ensuremath{\sim}A/Z$ with the atomic number $Z$ and nuclear mass number $A$. While this prediction holds for light and intermediate nuclei, a striking disagreement in both the sign and the magnitude of BNSSA was observed by the PREX collaboration for $^{208}\mathrm{Pb}$, coined the ``PREX puzzle.'' To shed light on this disagreement, we go beyond the plane-wave approach which neglects Coulomb distortions known to be significant for heavy nuclei. We explicitly investig…