Transmission and Reflection of Collective Modes in Spin-1 Bose-Einstein Condensate

We study tunneling properties of collective excitations in spin-1 Bose-Einstein condensates. In the absence of magnetic fields, the total transmission in the long wavelength limit occurs in all kinds of excitations but the quadrupolar spin mode in the ferromagnetic state. The quadrupolar spin mode alone shows the total reflection. A difference between those excitations comes from whether the wavefunction of an excitation corresponds to that of the condensate in the long wavelength limit. The correspondence results in the total transmission as in the spinless BEC.Comment: 6 pages, 5 figure

Placing Entrepreneurship and Firming Small Town Economies: Manufacturing Firms, Adaptive Embeddedness, Survival and Linked Enterprise Structures

SMEs make a major contribution to the economy of cities and places. The relationship between firms and place is increasingly explained through the application of city-based externality models. Such explanations have limited validity in a number of contexts. One of these is in the economies of small- and medium-sized towns and communities (SMST). Whilst convention has sought to apply core-periphery explanations to the functioning of firms within SMSTs, the economies of SMSTs and entrepreneurial processes of SME embedding, adaptation and survival in such places are more complex. This paper explores these entrepreneurial processes in the context of manufacturing firms in five SMSTs in the West Midlands, UK. The paper uses interview data to understand the relationships between SMEs and place through the development of successive and evolving linked enterprise structures. Through these linked enterprise structures, SMEs engage in a process of adaptive embeddedness, resulting in new resource configurations through fluid iterations of structural, emotional, and circumstantial embeddedness. This paper is the first to identify and explore these different forms of embeddedness