Search results for "QUANTUM MECHANICS"
showing 10 items of 2468 documents
Bi-coherent states as generalized eigenstates of the position and the momentum operators
2022
AbstractIn this paper, we show that the position and the derivative operators, $${{\hat{q}}}$$ q ^ and $${{\hat{D}}}$$ D ^ , can be treated as ladder operators connecting various vectors of two biorthonormal families, $${{{\mathcal {F}}}}_\varphi $$ F φ and $${{{\mathcal {F}}}}_\psi $$ F ψ . In particular, the vectors in $${{{\mathcal {F}}}}_\varphi $$ F φ are essentially monomials in x, $$x^k$$ x k , while those in $${{{\mathcal {F}}}}_\psi $$ F ψ are weak derivatives of the Dirac delta distribution, $$\delta ^{(m)}(x)$$ δ ( m ) ( x ) , times some normalization factor. We also show how bi-coherent states can be constructed for these $${{\hat{q}}}$$ q ^ and $${{\hat{D}}}$$ D ^ , both as con…
Construction of pseudo-bosons systems
2010
In a recent paper we have considered an explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. We have introduced the so-called {\em pseudo-bosons}, and the role of Riesz bases in this context has been analyzed in detail. In this paper we consider a general construction of pseudo-bosons based on an explicit {coordinate-representation}, extending what is usually done in ordinary supersymmetric quantum mechanics. We also discuss an example arising from a linear modification of standard creation and annihilation operators, and we analyze its connection with coherent states.
An algebraic approach to the study of multipartite entanglement
2012
A simple algebraic approach to the study of multipartite entanglement for pure states is introduced together with a class of suitable functionals able to detect entanglement. On this basis, some known results are reproduced. Indeed, by investigating the properties of the introduced functionals, it is shown that a subset of such class is strictly connected to the purity. Moreover, a direct and basic solution to the problem of the simultaneous maximization of three appropriate functionals for three-qubit states is provided, confirming that the simultaneous maximization of the entanglement for all possible bipartitions is compatible only with the structure of GHZ-states.
Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well
2014
This paper is a direct offspring of Ref. [J. Math. Phys. 54, 072103, (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions was maid with respect to various inconsistencies and faulty statements omnipresent in the literature devoted to so-called fractional quantum mechanics spectral problems. Presently, we give a decisive computer-assisted proof, for an exemplary finite and ultimately infinite Cauchy well problem, that spectral solutions proposed so far were plainly wrong. As a constructive input, we provide an explicit spectral solution of the finite Cauchy well. The infinite well emerges as a limiting case in a sequence of deep…
General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles
2017
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, which is the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. H…
QCD analysis of the tau hadronic width
1992
32 páginas, 1 figura, 4 tablas.-- CERN-TH-6070-91 ; NUHEP-TH-91-8 ; PM-91-8.
and the electroweak penguin contribution
2003
Abstract Our dispersive sum rule calculation of the electroweak penguin contribution to ϵ′ ϵ is reviewed. A more recent analysis based on the finite-energy sum rule approach is described. Finally, a new determination of the electroweak penguin contribution to ϵ′ ϵ is presented.
The spin-dependent structure function of the proton g1p and a test of the Bjorken sum rule
2010
Abstract The inclusive double-spin asymmetry, A 1 p , has been measured at COMPASS in deep-inelastic polarised muon scattering off a large polarised NH3 target. The data, collected in the year 2007, cover the range Q 2 > 1 ( GeV / c ) 2 , 0.004 x 0.7 and improve the statistical precision of g 1 p ( x ) by a factor of two in the region x 0.02 . The new proton asymmetries are combined with those previously published for the deuteron to extract the non-singlet spin-dependent structure function g 1 NS ( x , Q 2 ) . The isovector quark density, Δ q 3 ( x , Q 2 ) , is evaluated from a NLO QCD fit of g 1 NS . The first moment of Δ q 3 is in good agreement with the value predicted by the Bjorken su…
Neutrinoless double beta decay and QCD running at low energy scales
2018
There is a common belief that the main uncertainties in the theoretical analysis of neutrinoless double beta ($0\nu\beta\beta$) decay originate from the nuclear matrix elements. Here, we uncover another previously overlooked source of potentially large uncertainties stemming from non-perturbative QCD effects. Recently perturbative QCD corrections have been calculated for all dimension 6 and 9 effective operators describing $0\nu\beta\beta$-decay and their importance for a reliable treatment of $0\nu\beta\beta$-decay has been demonstrated. However, these perturbative results are valid at energy scales above $\sim 1$ GeV, while the typical $0\nu\beta\beta$-scale is about $\sim 100$ MeV. In vi…
W+W−Production at Hadron Colliders in Next to Next to Leading Order QCD
2014
Charged gauge boson pair production at the Large Hadron Collider allows detailed probes of the fundamental structure of electroweak interactions. We present precise theoretical predictions for on-shell W+ W- production that include, for the first time, QCD effects up to next to next to leading order in perturbation theory. As compared to next to leading order, the inclusive W+ W- cross section is enhanced by 9% at 7 TeV and 12% at 14 TeV. The residual perturbative uncertainty is at the 3% level. The severe contamination of the W+ W- cross section due to top-quark resonances is discussed in detail. Comparing different definitions of top-free W+ W- production in the four and five flavor numbe…