Geometry of mixed states and degeneracy structure of geometric phases for multi-level quantum systems. A unitary group approach

We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study the effect of degeneracies on geometric phases for three-level systems. This is shown to lead to a highly nontrivial generalization of the result for two-level systems in which degeneracy results in a "monopole" structure in parameter space. The rich structures that arise are related to the geometry of adjoint orbits in SU(3). The limiting case of a two-level degeneracy in a three-level system is shown to lead to the known monopole structure.Comment: Latex, 27 p

A generalized Pancharatnam geometric phase formula for three level systems

We describe a generalisation of the well known Pancharatnam geometric phase formula for two level systems, to evolution of a three-level system along a geodesic triangle in state space. This is achieved by using a recently developed generalisation of the Poincare sphere method, to represent pure states of a three-level quantum system in a convenient geometrical manner. The construction depends on the properties of the group SU(3)\/ and its generators in the defining representation, and uses geometrical objects and operations in an eight dimensional real Euclidean space. Implications for an n-level system are also discussed.Comment: 12 pages, Revtex, one figure, epsf used for figure insertio

Canonical Gravity, Diffeomorphisms and Objective Histories

This paper discusses the implementation of diffeomorphism invariance in purely Hamiltonian formulations of General Relativity. We observe that, if a constrained Hamiltonian formulation derives from a manifestly covariant Lagrangian, the diffeomorphism invariance of the Lagrangian results in the following properties of the constrained Hamiltonian theory: the diffeomorphisms are generated by constraints on the phase space so that a) The algebra of the generators reflects the algebra of the diffeomorphism group. b) The Poisson brackets of the basic fields with the generators reflects the space-time transformation properties of these basic fields. This suggests that in a purely Hamiltonian approach the requirement of diffeomorphism invariance should be interpreted to include b) and not just a) as one might naively suppose. Giving up b) amounts to giving up objective histories, even at the classical level. This observation has implications for Loop Quantum Gravity which are spelled out in a companion paper. We also describe an analogy between canonical gravity and Relativistic particle dynamics to illustrate our main point.Comment: Latex 16 Pages, no figures, revised in the light of referees' comments, accepted for publication in Classical and Quantum Gravit

Geometric phase in open systems

We calculate the geometric phase associated to the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main source of decoherence are considered: dephasing and spontaneous decay. We show that the geometric phase is completely insensitive to the former, i.e. it is independent of the number of jumps determined by the dephasing operator.Comment: 4 pages, 2 figures, RevTe

Biomass gasification technology - a route to meet energy needs

The paper addresses a distributed power generation system that has evolved at the Indian Institute of Science, Bangalore. The technological and field-related experience pertaining to open top re-burn down draft biomass gasification system coupled with the internal combustion engine or thermal device are brought out. The gasifier reactor design uses dual air entry - air nozzles and open top to help in establishing a thick high temperature zone to remove the contaminants in the product gas; a gas clean-up system to further refine the gas to ultra-pure quality. These elements are integrated with other sub-systems, namely feedstock preparation, ash handling, water treatment, process automation and other accessories to form an Independent Power Producer. Based on this technology there are over 30 units operating in India and abroad, with an accumulated capacity of over 20 MW. Over 80,000 h of operation of these systems have resulted in a saving of about 350 tons of fossil fuel, implying a saving of about 1120 tons of CO2 - a promising candidate for Clean Development Mechanisms (CDMs), other than reduction in toxic gases like NOx and SOx

Generalization of geometric phase to completely positive maps

We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference effect is embodied in a set of interference patterns defined by flipping the environment state in one of the two paths. We show for the qubit that this structure gives rise to interesting additional information about the geometry of the evolution defined by the CP map.Comment: Minor revision. 2 authors added. 4 pages, 2 figures, RevTex

Aspects of the political economy of development and synthetic biology

What implications might synthetic biology’s potential as a wholly new method of production have for the world economy, particularly developing countries? Theories of political economy predict that synthetic biology can shift terms of trade and displace producers in developing countries. Governments, however, retain the ability to mitigate negative changes through social safety nets and to foster adaptation to some changes through research, education and investment. We consider the effects the synthetic production of otherwise naturally derived molecules are likely to have on trade and investment, particularly in developing countries. Both rubber in Malaysia and indigo dyes in India provide historical examples of natural molecules that faced market dislocations from synthetic competitors. Natural rubber was able to maintain significant market share, while natural indigo vanished from world markets. These cases demonstrate the two extremes of the impact synthetic biology might have on naturally derived products. If developing countries can cushion the pain of technological changes by providing producers support as they retool or exit, the harmful effects of synthetic biology can be mitigated while its benefits can still be captured

The Real Symplectic Groups in Quantum Mechanics and Optics

text of abstract (We present a utilitarian review of the family of matrix groups $Sp(2n,\Re)$, in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of $Sp(2n,\Re)$. Global decomposition theorems, interesting subgroups and their generators are described. Turning to $n$-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and develop a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under $Sp(2n,\Re)$ action are delineated.)Comment: Review article 43 pages, revtex, no figures, replaced because somefonts were giving problem in autometic ps generatio

Two Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed States

A general analysis of squeezing transformations for two mode systems is given based on the four dimensional real symplectic group Sp(4,\Re)\/. Within the framework of the unitary metaplectic representation of this group, a distinction between compact photon number conserving and noncompact photon number nonconserving squeezing transformations is made. We exploit the Sp(4,\Re)-SO(3,2)\/ local isomorphism and the U(2)\/ invariant squeezing criterion to divide the set of all squeezing transformations into a two parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2)\/ is emphasized, and known experimental situations where all U(2)\/ elements can be reproduced are briefly described.Comment: Revtex 37 pages, Latex figures include

Green electricity from biomass fuelled producer gas engine

In the recent times issues like the Green House Gas (GHG) emission reduction and carbon-trading through Clean Development Mechanism (CDM) have gained large prominence as a part of climate change. Biomass gasification is one such technology which is environmentally benign and holds large promise for the future. These technologies are currently being utilized for power generation applications at a number of industrial sites in India and abroad. In India there are nearly 4 MWe equivalent power plants which are based on IISc's open top reburn down draft biomass gasification technology. In the field of power generation, there has been substantial effort in the development of producer gas engine; systematic experimental and modeling studies followed by long duration field monitoring. As a part of this effort, a gas carburetor has been designed for producer gas fuel and forms a part of the power package. The essential requirements of gas conditioning equipment are packaged to meet the engine quality gas as a power plant. Currently there are more than 3.0 MWe equivalent gas engines operating in the field; of this one is deployed in an Energy Service Company (ESCO), which sells green electricity to a textile industry. The company is located at Metupalyam in South India, near the city of Coimbatore. The power plant is configured with a 150 kg/hr gasifier coupled with a turbo charged after cooled Cummins make (GTA855G) gas engine. The plant is also provided with an effluent treatment plant and an engine-waste-heat based biomass drier. The plant commissioned in September 2003 has successfully completed over 7500 hours of operation, generating about 0.7 million units, thus saving a net CO2 of about 0.7 million Tons against a fossil fuel technology. The plant operates on a continuously to meet the end use requirement over 275 hours non stop operations hours of operation. The power plant utilizes a weed namely Julifora Prosopis which is abundantly available in the southern part of India and converts into green energy; additionally generates value added product namely partially activated carbon-Iodine no. of 400-450. The paper reports specific biomass consumption and engine emission monitored over long duration. The specific biomass consumption is measured to be within 1.1 ± 0.1 kg/kWh with an overall efficiency of 22-24%. It is also found to be environmentally benign in terms of emissions; NOx and CO levels are found to be much lower than most of the existing emissions norms of various countries including the United States and European Union. The paper also highlights results from other installations using this technology. Keywords: open top gasifier, producer gas engine, CDM technology