Quantum ergodicity for Pauli Hamiltonians with spin 1/2

Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for non-relativistic quantum particles with spin 1/2. It is shown that quantum ergodicity holds, if a suitable combination of the classical translational dynamics and the spin dynamics along the trajectories of the translational motion is ergodic.Comment: 20 pages, no figure

Quantitative uniqueness for elliptic equations with singular lower order terms

We use a Carleman type inequality of Koch and Tataru to obtain quantitative estimates of unique continuation for solutions of second order elliptic equations with singular lower order terms. First we prove a three sphere inequality and then describe two methods of propagation of smallness from sets of positive measure.Comment: 23 pages, v2 small changes are done and some mistakes are correcte

A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization

We consider a one-dimensional model for many-electron atoms in strong magnetic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. For this model we show that the maximum number of electrons is bounded above by 2Z+1 + c sqrt{B}. We follow Lieb's strategy in which convexity plays a critical role. For the case of two electrons and fractional nuclear charge, we also discuss the critical value at which the nuclear charge becomes too weak to bind two electrons.Comment: 23 pages, 5 figures. J. Phys. A: Math and General (in press) 199

Zitterbewegung and semiclassical observables for the Dirac equation

In a semiclassical context we investigate the Zitterbewegung of relativistic particles with spin 1/2 moving in external fields. It is shown that the analogue of Zitterbewegung for general observables can be removed to arbitrary order in \hbar by projecting to dynamically almost invariant subspaces of the quantum mechanical Hilbert space which are associated with particles and anti-particles. This not only allows to identify observables with a semiclassical meaning, but also to recover combined classical dynamics for the translational and spin degrees of freedom. Finally, we discuss properties of eigenspinors of a Dirac-Hamiltonian when these are projected to the almost invariant subspaces, including the phenomenon of quantum ergodicity

A cross-national study on the antecedents of work–life balance from the fit and balance perspective

Drawing on the perceived work–family fit and balance perspective, this study investigates demands and resources as antecedents of work–life balance (WLB) across four countries (New Zealand, France, Italy and Spain), so as to provide empirical cross-national evidence. Using structural equation modelling analysis on a sample of 870 full time employees, we found that work demands, hours worked and family demands were negatively related to WLB, while job autonomy and supervisor support were positively related to WLB. We also found evidence that resources (job autonomy and supervisor support) moderated the relationships between demands and work–life balance, with high resources consistently buffering any detrimental influence of demands on WLB. Furthermore, our study identified additional predictors of WLB that were unique to some national contexts. For example, in France and Italy, overtime hours worked were negatively associated with WLB, while parental status was positively associated with WLB. Overall, the implications for theory and practice are discussed.Peer ReviewedPostprint (author's final draft

A semi-classical trace formula for Schrödinger operators

Let S ℏ =−ℏΔ+ V , with V smooth. If 0< E 2 <lim inf V(x) , the spectrum of S ℏ near E 2 consists (for ℏ small) of finitely-many eigenvalues, λ j (ℏ). We study the asymptotic distribution of these eigenvalues about E 2 as ℏ→0; we obtain semi-classical asymptotics for with , in terms of the periodic classical trajectories on the energy surface . This in turn gives Weyl-type estimates for the counting function . We make a detailed analysis of the case when the flow on B E is periodic.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46475/1/220_2005_Article_BF02099074.pd

Socioeconomic mobility and talent utilization of workers from poorer backgrounds: The overlooked importance of within-organization dynamics

Socioeconomic mobility, or the ability of individuals to improve their socioeconomic standing through merit-based contributions, is a fundamental ideal of modern societies. The key focus of societal efforts to ensure socioeconomic mobility has been on the provision of educational opportunities. We review evidence that even with the same education and job opportunities, being born into a poorer family undermines socioeconomic mobility due to processes occurring within organizations. The burden of poorer background might, ceteris paribus, be economically comparable to the gender gap. We argue that in the societal and scientific effort to promote socioeconomic mobility, the key context in which mobility is supposed to happen—organizations—as well as the key part of the life of people striving toward socioeconomic advancement—that as working adults—have been overlooked. We integrate the organizational literature pointing to key within-organizational processes impacting objective (socioeconomic) success with research, some emergent in organizational sciences and some disciplinary, on when, why, and how people from poorer backgrounds behave or are treated by others in the relevant situations. Integrating these literatures generates a novel and useful framework for identifying issues people born into poorer families face as employees, systematizes extant evidence and makes it more accessible to organizational scientists, and allows us to lay the agenda for future organizational scholarshi