Supersymmetric quantum mechanics based on higher excited states

We generalize the formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates. The generalization is technically almost straightforward but physically quite nontrivial since it yields an infinity of new classes of susy-partner potentials, whose spectra are exactly identical except for the lowest m+1 states, if the superpotential is defined in terms of the (m+1)-st eigenfunction, with m=0 reserved for the ground state. It is shown that in case of the infinite 1-dim potential well nothing new emerges (the partner potential is still of P\"oschl-Teller type I, for all m), whilst in case of the 1-dim harmonic oscillator we get a new class of infinitely many partner potentials: for each m the partner potential is expressed as the sum of the quadratic harmonic potential plus rational function, defined as the derivative of the ratio of two consecutive Hermite polynomials. These partner potentials of course have m singularities exactly at the locations of the nodes of the generating (m+1)-st wavefunction. The susy formalism applies everywhere between the singularities. A systematic application of the formalism to other potentials with known spectra would yield an infinitely rich class of "solvable" potentials, in terms of their partner potentials. If the potentials are shape invariant they can be solved at least partially and new types of analytically obtainable spectra are expected. PACS numbers: 03.65.-w, 03.65.Ge, 03.65.SqComment: 15 pages LaTeX file, no figures, submitted to J. Phys. A: accepted for publication

Scientists as storytellers: the explanatory power of stories told about environmental crises

This paper examines how storytelling functions to share and to shape knowledge, particularly when scientific knowledge is uncertain because of rapid environmental change. Narratives or stories are the descriptive sequencing of events to make a point. In comparison with scientific deduction, the point (plot) of a story can be either implicit or explicit, and causal links between events in the story are interpretative, rendering narrative a looser inferential framework. We explore how storytelling (the process) and stories (or narratives) involving scientists can make sense of environmental crises, where conditions change rapidly and natural, social, and scientific systems collide. We use the example of the Soufrière Hills volcanic eruption (Montserrat) and scientists' experiences of the events during that time. We used 37 stories gathered from seven semi-structured interviews and one group interview (five scientists). We wanted to understand whether these stories generate or highlight knowledge and information that do not necessarily appear in more conventional scientific literature produced in relation to environmental crisis and how that knowledge explicitly or implicitly shapes future actions and views. Through our analysis of the value these stories bring to volcanic risk reduction, we argue that scientists create and transmit important knowledge about risk reduction through the stories they tell one another. In our example storytelling and stories are used in several ways: (1) evidencing the value of robust long-term monitoring strategies during crises, (2) exploring the current limits of scientific rationality and the role of instinct in a crisis, and (3) the examination of the interactions and outcomes of wide-ranging drivers of population risk. More broadly these stories allowed for the emotional intensity of these experiences to be acknowledged and discussed; the actions and outcomes of the storytelling are important. This is not about the “story” of research findings but the sharing of experience and important knowledge about how to manage and cope with volcanic crises. We suggest that storytelling frameworks could be better harnessed in both volcanic and other contexts

Conditional Allocation of Control Rights in Venture Capital Finance

When a young entrepreneurial firm matures, it is often necessary to replace the founding entrepreneur by a professional manager. This replacement decision can be affected by the private benefits of control enjoyed by the entrepreneur which gives rise to a conflict of interest between the entrepreneur and the venture capitalist. We show that a combination of convertible securities and contingent control rights can be used to resolve this conflict efficiently. This contractual arrangement is frequently observed in venture capital finance

M-Dwarf Fast Rotators and the Detection of Relatively Young Multiple M-Star Systems

We have searched the Kepler light curves of ~3900 M-star targets for evidence of periodicities that indicate, by means of the effects of starspots, rapid stellar rotation. Several analysis techniques, including Fourier transforms, inspection of folded light curves, 'sonograms', and phase tracking of individual modulation cycles, were applied in order to distinguish the periodicities due to rapid rotation from those due to stellar pulsations, eclipsing binaries, or transiting planets. We find 178 Kepler M-star targets with rotation periods, P_rot, of < 2 days, and 110 with P_rot < 1 day. Some 30 of the 178 systems exhibit two or more independent short periods within the same Kepler photometric aperture, while several have three or more short periods. Adaptive optics imaging and modeling of the Kepler pixel response function for a subset of our sample support the conclusion that the targets with multiple periods are highly likely to be relatively young physical binary, triple, and even quadruple M star systems. We explore in detail the one object with four incommensurate periods all less than 1.2 days, and show that two of the periods arise from one of a close pair of stars, while the other two arise from the second star, which itself is probably a visual binary. If most of these M-star systems with multiple periods turn out to be bound M stars, this could prove a valuable way of discovering young hierarchical M-star systems; the same approach may also be applicable to G and K stars. The ~5% occurrence rate of rapid rotation among the ~3900 M star targets is consistent with spin evolution models that include an initial contraction phase followed by magnetic braking, wherein a typical M star can spend several hundred Myr before spinning down to periods longer than 2 days.Comment: 17 pages, 12 figures, 2 tables; accepted for publication in The Astrophysical Journa