Optimized Perturbation Theory for Wave Functions of Quantum Systems

The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings.Comment: 11 pages, RevTeX, three ps figure

Direct observation of frozen moments in the NiFe/FeMn exchange bias system

We detect the presence of frozen magnetic moments in an exchange biased NiFe ferromagnet at the NiFe/FeMn ferromagnet/antiferromagnet interface by magnetic circular dichroism in x-ray absorption and resonant reflectivity experiments. Frozen moments are detected by means of the element-specific hysteresis loops. A weak dichroic absorption with unidirectional anisotropy can be linked to frozen magnetic moments in the ferromagnet. A more pronounced exchange bias for increasing the thickness of the FeMn layer correlates with an increase in orbital moment for interface Ni atoms carrying a frozen moment. These atoms compose about a single monolayer, but only a fraction of the atoms contributes by means of a strongly enhanced orbital moment to the macroscopic exchange bias phenomenon. The microscopic spin-orbit energy associated with these few interface frozen moment atoms appears to be sufficient to account for the macroscopic exchange bias energ

Direct observation of frozen moments in the NiFe/FeMn exchange bias system

We detect the presence of frozen magnetic moments in an exchange biased NiFe ferromagnet at the NiFe/FeMn ferromagnet/antiferromagnet interface by magnetic circular dichroism in x-ray absorption and resonant reflectivity experiments. Frozen moments are detected by means of the element-specific hysteresis loops. A weak dichroic absorption with unidirectional anisotropy can be linked to frozen magnetic moments in the ferromagnet. A more pronounced exchange bias for increasing the thickness of the FeMn layer correlates with an increase in orbital moment for interface Ni atoms carrying a frozen moment. These atoms compose about a single monolayer, but only a fraction of the atoms contributes by means of a strongly enhanced orbital moment to the macroscopic exchange bias phenomenon. The microscopic spin-orbit energy associated with these few interface frozen moment atoms appears to be sufficient to account for the macroscopic exchange bias energ

Dynamical mass generation by source inversion: Calculating the mass gap of the Gross-Neveu model

We probe the U(N) Gross-Neveu model with a source-term $J\bar{\Psi}\Psi$. We find an expression for the renormalization scheme and scale invariant source $\hat{J}$, as a function of the generated mass gap. The expansion of this function is organized in such a way that all scheme and scale dependence is reduced to one single parameter d. We get a non-perturbative mass gap as the solution of $\hat{J}=0$. In one loop we find that any physical choice for d gives good results for high values of N. In two loops we can determine d self-consistently by the principle of minimal sensitivity and find remarkably accurate results for N>2.Comment: 13 pages, 3 figures, added referenc

The Lantern Vol. 16, No. 2, December 1947

• A Little Light • Traitor\u27s Son • The Comeback • Wolf-Dog • Lucky Harry • Security or Progress • To Tell a Story • Endless • What Purpose, Life? • I Would Not Say • Adult Farewell • Springtime Fields • M.W. Armstronghttps://digitalcommons.ursinus.edu/lantern/1044/thumbnail.jp

Variational Quark Mass Expansion and the Order Parameters of Chiral Symmetry Breaking

We investigate in some detail a "variational mass" expansion approach, generalized from a similar construction developed in the Gross-Neveu model, to evaluate the basic order parameters of the dynamical breaking of the $SU(2)_L \times SU(2)_R$ and $SU(3)_L \times SU(3)_R$ chiral symmetries in QCD. The method starts with a reorganization of the ordinary perturbation theory with the addition of an arbitrary quark mass $m$. The new perturbative series can be summed to all orders thanks to renormalization group properties, with specific boundary conditions, and advocated analytic continuation in $m$ properties. In the approximation where the explicit breakdown of the chiral symmetries due to small current quark masses is neglected, we derive ansatzes for the dynamical contribution to the "constituent" masses $M_q$ of the $u,d,s$ quarks; the pion decay constant $F_\pi$; and the quark condensate $$ in terms of the basic QCD scale $\Lambda_{\bar{MS}}$. Those ansatzes are then optimized, in a sense to be specified, and also explicit symmetry breaking mass terms can be consistently introduced in the framework. The obtained values of $F_\pi$ and $M_q$ are roughly in agreement with what is expected from other non-perturbative methods. In contrast we obtain quite a small value of $|< \bar q q >|$ within our approach. The possible interpretation of the latter results is briefly discussed.Comment: 40 pages, LaTex, 2 PS figures. Additions in section 2.2 to better explain the relation between the current mass and the dynamical mass ansatz. Minor misprints corrected. Version to appear in Phys. Rev.

(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in 1/F, where $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for m \lsim \Lambda, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, which can define certain "non-perturbative" quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by re-evaluating, from purely perturbative informations, the O(N) Gross-Neveu model mass gap, known for arbitrary $N$ from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording corrections, 2 references added. To appear in Phys. Rev.

Firms' Strategies for Knowledge and Technology Transfer With Public Research Organisations and Their Impact on Firms' Performance: An Empirical Analysis Based on Firm-Level Data

Based on a representative firm sample for Switzerland we empirically investigated strategic approaches for knowledge and technology transfer (KTT) activities between business firms and public research organisations. Based on cluster analysis of 19 different forms for KTT, three types of KTT strategies were identified, each of them correspond with a specific combination of some of the 19 different forms for KTT activities. It was found that they are determined mainly by variables related (a) to the absorptive capacity of a firm and (b) to the degree of appropriability of the returns of innovation, indicating that the followed strategy reflects the resource base of a firm. Further, it was shown that a firm's obstacle profile with respect to KTT activities is related to the applied strategy. Firms with more intensive contacts emphasise risk-related factors and financial restrictions, while firms with less intensive contacts emphasise a mismatch between firm and university requirements with respect to KTT. Furthermore and most importantly, it was found that strategy matters for the impact of KTT on the innovation performance of a firm. In fact, KTT strategies related to the core R&D activities of a firm showed a greater impact compared to strategies related to softer forms of transfer activities, e.g. informal contacts or education related contacts

Three-points interfacial quadrature for geometrical source terms on nonuniform grids

International audienceThis paper deals with numerical (finite volume) approximations, on nonuniform meshes, for ordinary differential equations with parameter-dependent fields. Appropriate discretizations are constructed over the space of parameters, in order to guarantee the consistency in presence of variable cells' size, for which $L^p$-error estimates, $1\le p < +\infty$, are proven. Besides, a suitable notion of (weak) regularity for nonuniform meshes is introduced in the most general case, to compensate possibly reduced consistency conditions, and the optimality of the convergence rates with respect to the regularity assumptions on the problem's data is precisely discussed. This analysis attempts to provide a basic theoretical framework for the numerical simulation on unstructured grids (also generated by adaptive algorithms) of a wide class of mathematical models for real systems (geophysical flows, biological and chemical processes, population dynamics)