Fearless: Allan Kawala

Allan Kawala ‘13 does not stand on the sidelines. He is an agent of change and is a leader at Gettysburg College and in his home country of Malawi. He has dedicated his life to making social change a reality. [excerpt

Scottish circumvention of the English Navigation Acts in the American colonies 1660-1707

From its insular location, its limited indigenous resources and its subordinate political standing as one of three kingdoms ruled by the Stuart dynasty, Scotland was dependent on overseas trade, commercial networks and an entrepreneurial willingness to set aside international regulations for its very survival as a distinctive European nation in the later 17th century. Scotland was manifestly not a major European power, nor a significant imperial presence in the Americas. By the later 17th century, however, colonial endeavours were offering Scots the opportunity not just to break out from the mercantilist dominance of the great European powers, but also to sustain regal union under a common monarchy without recourse to political incorporation with England. By the 1690s, the clannish cohesion of their landed and commercial elite, their diligence in securing positions of influence and their collusive disregard for the Navigation Acts were perceived by English merchants, colonial officials, diplomats and ruling ministries as highly threatening. The Scots challenged the English state through their Darien Scheme to create an international entrepôt for the Pacific as well as the Atlantic on the Panama Isthmus, as through their expansion into Ireland and the Delaware Basin. If the Scots made a success of Darien, there seemed a real prospect to vested English interests that their domestic market would grow to include Ireland and that their entrepreneurial endeavours in the Delaware would lead to the secession of three counties to form a Scottish colony on the American mainland. Only political incorporation, through the Treaty of Union in 1707, seemingly put an end to Scottish flouting of English state power

Which Q-analogue of the squeezed oscillator?

The noise (variance squared) of a component of the electromagnetic field - considered as a quantum oscillator - in the vacuum is equal to one half, in appropriate units (taking Planck's constant and the mass and frequency of the oscillator all equal to 1). A practical definition of a squeezed state is one for which the noise is less than the vacuum value - and the amount of squeezing is determined by the appropriate ratio. Thus the usual coherent (Glauber) states are not squeezed, as they produce the same variance as the vacuum. However, it is not difficult to define states analogous to coherent states which do have this noise-reducing effect. In fact, they are coherent states in the more general group sense but with respect to groups other than the Heisenberg-Weyl Group which defines the Glauber states. The original, conventional squeezed state in quantum optics is that associated with the group SU(1,1). Just as the annihilation operator a of a single photon mode (and its hermitian conjugate a, the creation operator) generates the Heisenberg Weyl algebra, so the pair-photon operator a(sup 2) and its conjugate generates the algebra of the group SU(1,1). Another viewpoint, more productive from the calculational stance, is to note that the automorphism group of the Heisenberg-Weyl algebra is SU(1,1). Needless to say, each of these viewpoints generalizes differently to the quantum group context. Both are discussed. The following topics are addressed: conventional coherent and squeezed states; eigenstate definitions; exponential definitions; algebra (group) definitions; automorphism group definition; example: signal-to-noise ratio; q-coherent and q-squeezed states; M and P q-bosons; eigenstate definitions; exponential definitions; algebra (q-group) definitions; and automorphism q-group definition

Dissipative "Groups" and the Bloch Ball

We show that a quantum control procedure on a two-level system including dissipation gives rise to a semi-group corresponding to the Lie algebra semi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the action of this semi-group on a 3-vector as it moves inside the Bloch sphere, in the Bloch ball.Comment: 4 pages. Proceedings of Group 24, Paris, July, 200

Coherent States from Combinatorial Sequences

We construct coherent states using sequences of combinatorial numbers such as various binomial and trinomial numbers, and Bell and Catalan numbers. We show that these states satisfy the condition of the resolution of unity in a natural way. In each case the positive weight functions are given as solutions of associated Stieltjes or Hausdorff moment problems, where the moments are the combinatorial numbers.Comment: 4 pages, Latex; Conference 'Quantum Theory and Symmetries 2', Krakow, Poland, July 200

Dissipative Quantum Control

Nature, in the form of dissipation, inevitably intervenes in our efforts to control a quantum system. In this talk we show that although we cannot, in general, compensate for dissipation by coherent control of the system, such effects are not always counterproductive; for example, the transformation from a thermal (mixed) state to a cold condensed (pure state) can only be achieved by non-unitary effects such as population and phase relaxation.Comment: Contribution to Proceedings of \emph{ICCSUR 8} held in Puebla, Mexico, July 2003, based on talk presented by Allan Solomon (ca 8 pages, latex, 1 latex figure, 2 pdf figures converted to eps, appear to cause some trouble

Critical temperature for entanglement transition in Heisenberg models

We study thermal entanglement in some low-dimensional Heisenberg models. It is found that in each model there is a critical temperature above which thermal entanglement is absent