Search results for "Mathematical physics"
showing 10 items of 2687 documents
Quasi-Modes and Spectral Instability in One Dimension
2019
In this section we describe the general WKB construction of approximate “asymptotic” solutions to the ordinary differential equation $$\displaystyle P(x,hD_x)u=\sum _{k=0}^m b_k(x)(hD_x)^ku=0, $$ on an interval α < x < β, where we assume that the coefficients bk ∈ C∞(]α, β[). Here h ∈ ]0, h0] is a small parameter and we wish to solve (above equation) up to any power of h. We look for u in the form $$\displaystyle u(x;h)=a(x;h)e^{i\phi (x)/h}, $$ where ϕ ∈ C∞(]α, β[) is independent of h. The exponential factor describes the oscillations of u, and when ϕ is complex valued it also describes the exponential growth or decay; a(x;h) is the amplitude and should be of the form $$\displaystyle a(x;h…
Module categories of finite Hopf algebroids, and self-duality
2017
International audience; We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.
Double β Decay and the Axial Strength
2019
Quenching of the weak axial strength gA is discussed and relations of this quenching to the nuclear matrix elements of double beta decays are highlighted. An analysis of Gamow-Teller transitions in the mass range A = 62 − 142 is presented and its results are compared with those of many previous works. The enhancement of the axial charge is discussed for first-forbidden pseudoscalar β transitions. Higher-forbidden β transitions are introduced and their role in determining the effective value of gA is examined, in particular from the point of view of the β-decay half-lives and the shapes of electron spectra of forbidden non-unique β transitions. peerReviewed
Value of the Axial-Vector Coupling Strength in β and ββ Decays : A Review
2017
In this review the quenching of the weak axial-vector coupling constant, $g_{\rm A}$, is discussed in nuclear $\beta$ and double-$\beta$ decays. On one hand, the nuclear-medium and nuclear many-body effects are separated, and on the other hand the quenching is discussed from the points of view of different many-body methods and different $\beta$-decay and double-$\beta$-decay processes. Both the historical background and the present status are reviewed and contrasted against each other. The theoretical considerations are tied to performed and planned measurements, and possible new measurements are urged, whenever relevant and doable. Relation of the quenching problem to the measurements of …
The Isgur-Wise function from the lattice
1995
We calculate the Isgur-Wise function by measuring the elastic scattering amplitude of a $D$ meson in the quenched approximation on a $24^3\times48$ lattice at $\beta=6.2$, using an $O(a)$-improved fermion action. Fitting the resulting chirally-extrapolated Isgur-Wise function to Stech's relativistic-oscillator parametrization, we obtain a slope parameter $\rho^2=1.2+7-3. We then use this result, in conjunction with heavy-quark symmetry, to extract $V_{cb}$\ from the experimentally measured $\bar B\to D^*l\bar\nu\,$\ differential decay width. We find $|V_{cb}|\sqrt{\tau_B/1.48{\mathrm ps}}= 0.038 +2-2 +8-3, where the first set of errors is due to experimental uncertainties, while the second …
An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications
2020
Author's accepted manuscript. This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Bergelson, V., Knutson, I. J. H. & Son, Y. (2020). An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications. International Mathematics Research Notices, 2021(19), 14965-15018 is available online at: https://academic.oup.com/imrn/article/2021/19/14965/5775499 and https://doi.org/10.1093/imrn/rnaa035. Generalized polynomials are mappings obtained from the conventional polynomials by the use of the operations of addition and multiplication and taking th…
Space of signatures as inverse limits of Carnot groups
2021
We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.
Mutual nonlinear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: Comparison among different strategie…
2008
We compare the different existing strategies of mutual nonlinear prediction regarding their ability to assess the coupling strength and directionality of the interactions in bivariate time series. Under the common framework of $k$-nearest neighbor local linear prediction, we test three approaches based on cross prediction, mixed prediction, and predictability improvement. The measures of interdependence provided by these approaches are first evaluated on short realizations of bivariate time series generated by coupled Henon models, investigating also the effects of noise. The usefulness of the three mutual nonlinear prediction schemes is then assessed in a common physiological application d…
Nonlinear pseudo-bosons
2011
In a series of recent papers the author has introduced the notion of (regular) pseudo-bosons showing, in particular, that two number-like operators, whose spectra are ${\Bbb N}_0:={\Bbb N}\cup\{0\}$, can be naturally introduced. Here we extend this construction to operators with rather more general spectra. Of course, this generalization can be applied to many more physical systems. We discuss several examples of our framework.
On the existence of the exponential solution of linear differential systems
1999
The existence of an exponential representation for the fundamental solutions of a linear differential system is approached from a novel point of view. A sufficient condition is obtained in terms of the norm of the coefficient operator defining the system. The condition turns out to coincide with a previously published one concerning convergence of the Magnus series expansion. Direct analysis of the general evolution equations in the SU(N) Lie group illustrates how the estimate for the domain of existence/convergence becomes larger. Eventually, an application is done for the Baker-Campbell-Hausdorff series.