Dynamic spin Jahn-Teller effect in small magnetic clusters

We study the effect of spin-phonon coupling in small magnetic clusters, concentrating on a S=1/2 ring of 4 spins coupled antiferromagnetically. If the phonons are treated as classical variables, there is a critical value of the spin-phonon coupling above which a static distortion occurs. This is a good approximation if the zero point energy is small compared to the energy gain due to the distortion, which is true for large exchange interactions compared to the phonons energy ($J\gg\hbar\omega$). In the opposite limit, one can integrate out the phonon degrees of freedom and get an effective spin hamiltonian. Using exact diagonalizations to include the quantum nature of both spins and phonons, we obtain the spectrum in the whole range of parameters and explicit the crossover between the classical and quantum regimes. We then establish quantitatively the limits of validity of two widely used approaches (one in the quantum and one in the classical limits) and show that they are quite poor for small magnetic clusters. We also show that upon reducing $\hbar\omega/J$ the first excitation of a 4-site cluster becomes a singlet, a result that could be relevant for Cu$_2$Te$_2$O$_5$Br$_2$

The resilient entrepreneur: the use of successful coping behaviours to experience relief from emotional intensity by entrepreneurs in Canada

There is a lack of qualitative research demonstrating the emotional processes that entrepreneurs experience after they first start their businesses. This dissertation analyzed the emotional processes experienced by ten entrepreneurs during their venture’s start-up phase. A constructivist grounded theory research design was used to collect and analyze data in this investigation. Research findings showed entrepreneurs experienced simultaneous emotions that were of an intense nature during their early stages of business. These emotions included some combination of: excitement, anxiety/fear, disappointment, pressure/self-doubt, isolation, and relief. In addition, entrepreneurs identified entrepreneurial distress related to the constant need for action in their ventures and the use of technology, including cellular phones, email, and social media. Entrepreneurs described a gradual reduction in emotional intensity as they gained experience and learned how to cope. Coping behaviours used by entrepreneurs to counteract the overwhelming nature of emotions were: (a) developing improved entrepreneurial social networks, (b) gaining experience/learning from mistakes, and (c) changing their perspective on life as a whole. Coping behaviours aided in the reduction and fluctuation of entrepreneurial emotions

Topological Phases near a Triple Degeneracy

We study the pattern of three state topological phases that appear in systems with real Hamiltonians and wave functions. We give a simple geometric construction for representing these phases. We then apply our results to understand previous work on three state phases. We point out that the ``mirror symmetry'' of wave functions noticed in microwave experiments can be simply understood in our framework.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Economic and social condition of England on the eve of the industrial revolution, with special reference to Lancashire

The economic and social condition of England on the eve of the industrial revolution, with special reference to LancashireIt is the purpose of this thesis to discuss some phases of this period of preparation, and to show how, in the spheres of agriculture and of industry, the highway had been made straight for the entry of the new methods and organisation that were to create and dominate the new age. An endeavour will he made to show how far the abandonment of the old economic organisation had proceeded, and to what extent the lines of the new had begun to emerge. While special attention is paid throughout to Lancashire, it has not been the intention to confine the scope of discussion to that county* but rather to use it to illustrate the broader sweep of the principles involved. Any description of England is liable to be partial , and thus make generalisations difficult. Industry was expanding in the north, while in the south and west,, it tended to decline. The worsted industry of Norfolk and Essex had already begun to move northward into Yorkshire. The cotton industry bin Lancashire was already beginning to cause uneasiness amongst the woollen manufacturers and merchants, lest the new fabrics should spoil their trade. With industry, population was moving northward. While the date 1760 is adopted as roughly marking the limit of the present enquiry, it stands rather as a landmark than as a goal post. In the woollen industry particularly, it is possible to take facts from a later period without invalidating the main contention of the thesis.There will he an attempt to show how the new movements, which were to dominate the modern, economic world were already groping through to the light. During the first half of the eighteenth century. the systems and organisation of a former age were passing away, and when the new order gained, entrance, it found the "room more or less swept and garnished. There were still many survivals of the former system, but the great landmarks, which had so strongly characterized the Tudor and Stuart regimes were gone, and their places were waiting to be filled by the ideas and institutions of a new world