Explicit energy expansion for general odd degree polynomial potentials

In this paper we derive an almost explicit analytic formula for asymptotic eigenenergy expansion of arbitrary odd degree polynomial potentials of the form $V(x)=(ix)^{2N+1}+\beta _{1}x^{2N}+\beta _{2}x^{2N-1}+\cdot \cdot \cdot \cdot \cdot +\beta _{2N}x$ where $\beta _{k}^{\prime }$s are real or complex for $1\leq k\leq 2N$. The formula can be used to find semiclassical analytic expressions for eigenenergies up to any order very efficiently. Each term of the expansion is given explicitly as a multinomial of the parameters $\beta _{1},\beta _{2}....$ and $\beta _{2N}$ of the potential. Unlike in the even degree polynomial case, the highest order term in the potential is pure imaginary and hence the system is non-Hermitian. Therefore all the integrations have been carried out along a contour enclosing two complex turning points which lies within a wedge in the complex plane. With the help of some examples we demonstrate the accuracy of the method for both real and complex eigenspectra.Comment: 10 page

Sri Lanka’s water policy: themes and issues

Fresh water resources in Sri Lanka remain a free public good with the State acting as the trustee and custodian of the resource. Although the country is blessed with a seemingly plentiful supply of water, it encounters severe problems of temporal and spatial scarcity. Nearly five decades of efforts at formulating a national water policy with a view to introducing a bulk water allocation system have failed mainly due to a lack of understanding of the basic issues confronting certain elements that constitute the basic policy. This paper presents selected key themes and issues which help stimulate the formulation and adoption of an improved water resource policy statement. The author argues that what is important in the case of water is not the question of ‘ownership’ of water but regulating the user rights of this common property resource, particularly since such use is always in a state of flux. In the course of its movement in the hydrological cycle, it can only be owned when it is captured in a receptacle or in an impounding tank or as treated water in a reservoir and water conveyed in an irrigation channel. But, it is this very right to abstraction of bulk water from its natural state that is not defined and left to the will of individuals and agencies – virtually resulting in the creation of a ‘free for all’ situation. While the domain of water is characterized by over 50 legislative enactments and a plethora of agencies numbering over 40, there isn’t a single neutral agency to determine the appropriate balance between the demands for off stream consumption and the volume of water flows needed by the river system. The objectives of this paper are: to clarify the meaning of the terms ‘ownership’, ‘user rights’, ‘common property rights’, and ‘right to water’; to analyze and suggest refinements to several water policy themes and issues such as ‘bulk water entitlements’, ‘groundwater management’ and ‘user conflicts’; to outline the roles of institutions for clarity in implementation; to suggest elements that should constitute a future water policy. A better understanding of the issues relating to this finite and vulnerable resource will help clarify the policy concerns that are constantly overlooked – intentionally or unintentionally - in the domain of water. Does Sri Lanka have the right water resource policies for the twenty-first century? Such concerns prompted policyholders to attempt several policy reforms in Sri Lanka’s water domain during the last five decades. Several United State Agency for International Development (USAID) and Asian Development Bank (ADB) efforts culminated in producing a ‘national water resources policy and institutional arrangement’ document with a water policy approved by the Cabinet of the Government of Sri Lanka in March 2000. Yet, public concerns expressed on certain sensitive issues, and the lack of consensus due to the changing hands of the subject of policy development among various successor ministries, resulted in the demise of this water policy formulation effort.Length: pp.113-126Water policyOwnershipGroundwater managementInstitutionsWater use

Effects of complex parameters on classical trajectories of Hamiltonian systems

Anderson $\textit{et al}$ have shown that for complex energies, the classical trajectories of $\textit{real}$ quartic potentials are closed and periodic only on a discrete set of eigencurves. Moreover, recently it was revealed that, when time is complex $t$ $(t=t_{r}e^{i\theta _{\tau }}),$ certain real hermitian systems possess close periodic trajectories only for a discrete set of values of $\theta _{\tau }$. On the other hand it is generally true that even for real energies, classical trajectories of non $\mathcal{PT}$- symmetric Hamiltonians with complex parameters are mostly non-periodic and open. In this paper we show that for given real energy, the classical trajectories of $\textit{complex}$ quartic Hamiltonians $H=p^{2}+ax^{4}+bx^{k}$, (where $a$ is real, $b$ is complex and $k=1$ $or$ $2$) are closed and periodic only for a discrete set of parameter curves in the complex $b$-plane. It was further found that given complex parameter $b$, the classical trajectories are periodic for a discrete set of real energies (i.e. classical energy get discretized or quantized by imposing the condition that trajectories are periodic and closed). Moreover, we show that for real and positive energies (continuous), the classical trajectories of $\textit{complex}$ Hamiltonian $H=p^{2}+\mu x^{4}, (\mu=\mu _{r}e^{i\theta })$ are periodic when $\theta =4 tan^{-1}[(n/(2m+n))]$ for $\forall$ $n$ and $m\in \mathbb{Z}$.Comment: 9 pages, 2 tables, 6 figure

Level Crossings in Complex Two-Dimensional Potentials

Two-dimensional PT-symmetric quantum-mechanical systems with the complex cubic potential V_{12}=x^2+y^2+igxy^2 and the complex Henon-Heiles potential V_{HH}=x^2+y^2+ig(xy^2-x^3/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both potentials respect the PT symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.Comment: 9 pages, 4 figures. Submitted as a conference proceeding of PHHQP

Digital processing system for developing countries

An effort was undertaken to perform simple digital processing tasks using pre-existing general purpose digital computers. An experimental software package, LIGMALS, was obtained and modified for this purpose. The resulting software permits basic processing tasks to be performed including level slicing, gray mapping and ratio processing. The experience gained in this project indicates a possible direction which may be used by other developing countries to obtain digital processing capabilities

Mimesis, cover versions and the commercial vocalists’ dilemma; Sri Lankan perspective

Nanda Malini is a renowned songster, known as the nightingale of the Sri Lankan music industry. A few years ago, a young boy band who called themselves ‘Promises’ published a cassette mimicking Malini and appropriating a number of her very popular songs. Nanda sought relief from the Courts with the assistance of the authors of the songs i.e. lyricists and composers, for the purpose of making a sustainable case against the perpetrators. Making cover versions is a significantly contested issue in the Sri Lankan music industry. Although the Sri Lankan commercial music industry in its initial stages was predominantly reliant on covering Indian melodies, the attitude towards cover versions in the contemporary music industry seems to be varied. The introduction of Performers’ Rights under Sri Lankan Intellectual Property Act was intended to address inter alia this issue of cover versions in the music industry. Accordingly, this article will examine and problematize the various artistic and cultural concerns surrounding cover versions in the Sri Lankan music industry and the impact (or lack of it) of the National Intellectual Property Law on this contemporary issue