Time-optimal control of a 3-level quantum system and its generalization

peer reviewedWe solve the problem of steering a three-level quantum system from one eigen- state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three-level system we find all optimal controls by finding two types of symmetry in the problems: Z2 ×S3 discrete sym- metry and S1 continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system

Identifikasi Masalah Aplikasi Teknologi Pengolahan Air Payau dengan Sistem Ro di Kabupaten Rembang dan Cara Mengatasinya

A brackish water treatment process technology based on reverse osmosis principle has been applied in an Islamic school community “Raudlatuttalibin”, Rembang, since July 2008. Production capacity of the water treatment plant was designed 10M3 of drinking water per day. After running the system for one and a half years, a lot of problems were consecutively appearing untill the end of March 2010. This identification activity clarified all problems in detail and explained how to solve them. They are not only technical problems, but also social and cultural problems of the community. To solve them it must be started from increasing the capability of operators and applying the clean production concept. Finally by changing all the technically broken spareparts and running the RO unit system properly, they will be guaranteed to be able to produce good quality of drinking water

The SL(K+3,C) Symmetry of the Bosonic String Scattering Amplitudes

We discover that the exact string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory can be expressed in terms of the basis functions in the infinite dimensional representation space of the SL(K+3,C) group. In addition, we find that the K+2 recurrence relations among the LSSA discovered by the present authors previously can be used to reproduce the Cartan subalgebra and simple root system of the SL(K+3,C) group with rank K+2. As a result, the SL(K+3,C) group can be used to solve all the LSSA and express them in terms of one amplitude. As an application in the hard scattering limit, the SL(K+3,C) group can be used to directly prove Gross conjecture [1-3], which was previously corrected and proved by the method of decoupling of zero norm states [4-10].Comment: 19 pages, no figure. v2: 20 pages, typos corrected and Eqs. added. v3: 24 pages, Examples in sec. II added,"Discussion" added, to be published in Nucl.Phys.

Economic Incentives Versus Command and Control: What's the Best Approach for Solving Environmental Problems?

Now, decades after the first environmental laws were passed in this country, policymakers face many choices when seeking to solve environmental problems. Will taxing polluters for their discharges be more effective than fining them for not meeting certain emissions standards? Will a regulatory agency find it less costly to enforce a ban or oversee a system of tradable permits? Which strategy will reduce a pollutant the quickest? Clearly, there are no "one-size-fits-all" answers. Many factors enter into the decision to favor either policies that lean more toward economic incentives (EI) and toward direct regulation, commonly referred to as command-and-control (CAC) policy. Underlying determinants include a country's governmental and regulatory infrastructure, along with the nature of the environmental problem itself. Even with these contextual factors to consider, we thought it would be useful to compare EI and CAC policies and their outcomes in a real-world setting. To do this, we looked at six environmental problems that the United States and at least one European country dealt with differently (see box on page 14.) For each problem, one approach was more of an EI measure, while the other relied more on CAC. For example, to reduce point-source industrial water pollution, the Netherlands implemented a system of fees for organic pollutants (EI), while the United States established a system of guidelines and permits (CAC). It turned out, in fact, that most policies had at least some elements of both approaches, but we categorized them as EI or CAC based on their dominant features. We then asked researchers who had previously studied these policies on either side of the Atlantic to update or prepare new case studies. We analyzed the 12 case studies (two for each of the six environmental problems) against a list of hypotheses frequently made for or against EI and CAC, such as which instrument is more effective or imposes less administrative burden

The power of quantum systems on a line

We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with 9 states per particle). This might have practical implications for experimentalists interested in constructing an adiabatic quantum computer. Building on the same construction, but with some additional technical effort and 12 states per particle, we show that the problem of approximating the ground state energy of a system composed of a line of quantum particles is QMA-complete; QMA is a quantum analogue of NP. This is in striking contrast to the fact that the analogous classical problem, namely, one-dimensional MAX-2-SAT with nearest neighbor constraints, is in P. The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Not all illegal configurations can be ruled out by local checks, so instead we rule out such illegal configurations because they would, in the future, evolve into a state which can be seen locally to be illegal. Our construction implies (assuming the quantum Church-Turing thesis and that quantum computers cannot efficiently solve QMA-complete problems) that there are one-dimensional systems which take an exponential time to relax to their ground states at any temperature, making them candidates for being one-dimensional spin glasses.Comment: 21 pages. v2 has numerous corrections and clarifications, and most importantly a new author, merged from arXiv:0705.4067. v3 is the published version, with additional clarifications, publisher's version available at http://www.springerlink.co