A semiclassical theory of quantum noise in open chaotic systems

We consider the quantum evolution of classically chaotic systems in contact with surroundings. Based on $\hbar$-scaling of an equation for time evolution of the Wigner's quasi-probability distribution function in presence of dissipation and thermal diffusion we derive a semiclassical equation for quantum fluctuations. This identifies an early regime of evolution dominated by fluctuations in the curvature of the potential due to classical chaos and dissipation. A stochastic treatment of this classical fluctuations leads us to a Fokker-Planck equation which is reminiscent of Kramers' equation for thermally activated processes. This reveals an interplay of three aspects of evolution of quantum noise in weakly dissipative open systems; the reversible Liouville flow, the irreversible chaotic diffusion which is characteristic of the system itself, and irreversible dissipation induced by the external reservoir. It has been demonstrated that in the dissipation-free case a competition between Liouville flow in the contracting direction of phase space and chaotic diffusion sets a critical width in the Wigner function for quantum fluctuations. We also show how the initial quantum noise gets amplified by classical chaos and ultimately equilibrated under the influence of dissipation. We establish that there exists a critical limit to the expansion of phase space. The limit is determined by chaotic diffusion and dissipation. Making use of appropriate quantum-classical correspondence we verify the semiclassical analysis by the fully quantum simulation in a chaotic quartic oscillator.Comment: Plain Latex, 27 pages, 6 ps figure, To appear in Physica

Cross-Border Mergers and Market Segmentation (Replaces CentER DP 2010-096)

This paper shows that cross-border mergers are more likely to occur in industries which serve multiple segmented markets rather than a single integrated market, given that cost functions are strictly convex. The product price rises in the market where an acquisition is made but falls in the other, decreasing the acquisition price of other firms (in contrast to the results in the existing merger literature on integrated markets). Although the sum of consumer surplus across the countries may rise in response to a given acquisition, one of the countries gains at the expense of the other.cross-border mergers;endogenous mergers;competition policy;Cournot competition;economic integration

Wide-area monitoring and control of future smart grids

Application of wide-area monitoring and control for future smart grids with substantial wind penetration and advanced network control options through FACTS and HVDC (both point-to-point and multi-terminal) is the subject matter of this thesis. For wide-area monitoring, a novel technique is proposed to characterize the system dynamic response in near real-time in terms of not only damping and frequency but also mode-shape, the latter being critical for corrective control action. Real-time simulation in Opal-RT is carried out to illustrate the effectiveness and practical feasibility of the proposed approach. Potential problem with wide-area closed-loop continuous control using FACTS devices due to continuously time-varying latency is addressed through the proposed modification of the traditional phasor POD concept introduced by ABB. Adverse impact of limited bandwidth availability due to networked communication is established and a solution using an observer at the PMU location has been demonstrated. Impact of wind penetration on the system dynamic performance has been analyzed along with effectiveness of damping control through proper coordination of wind farms and HVDC links. For multi-terminal HVDC (MTDC) grids the critical issue of autonomous power sharing among the converter stations following a contingency (e.g. converter outage) is addressed. Use of a power-voltage droop in the DC link voltage control loops using remote voltage feedback is shown to yield proper distribution of power mismatch according to the converter ratings while use of local voltages turns out to be unsatisfactory. A novel scheme for adapting the droop coefficients to share the burden according to the available headroom of each converter station is also studied. The effectiveness of the proposed approaches is illustrated through detailed frequency domain analysis and extensive time-domain simulation results on different test systems

Adiabatic noise-induced escape rate for nonequilibrium open systems

We consider the motion of an overdamped particle in a force field in presence of an external, adiabatic noise, without the restriction that the noise process is Gaussian or the stochastic process is Markovian. We examine the condition for attainment of steady state for this nonequilibrium open system and calculate the adiabatic noise-induced rate of escape of the particle over a barrier.Comment: 6 pages, 3 figure

'The Voracity Effect' and Climate Change: The Impact of Clean Technologies

In the absence of a successful international cooperative agreement over the control of emissions there is a growing interest in the role that clean technologies may play to alleviate the climate change problem. Within a non-cooperative transboundary pollution game, we investigate, analytically and within a numerical example based on empirical evidence, the impact of the adoption of a cleaner technology (i.e., a decrease in the emission to output ratio). We show that countries may respond by increasing their emissions resulting in an increase in the stock of pollution that may be detrimental to welfare. This possibility is shown to arise for a signi cant and empirically relevant range of parameters. It is when the damage and/or the initial stock of pollution are relatively large and when the natural rate of decay of pollution is relatively small that the perverse e¤ect of clean technologies is strongest. Cooperation over the control of emissions is necessary to ensure that the development of cleaner technologies does not exacerbate the free riding behavior that is at the origin of the climate change problem.transboundary pollution;renewable resource;climate change;clean technolo- gies;differential games

Collusion Inducing Taxation of a Polluting Oligopoly

We show that an environmental regulation such as a tax on pollution can act as a collusive device and induce stable cartelization in an oligopolistic polluting industry. We consider a dynamic game where pollution is allowed to accumulate into a stock over time and a cartel that includes all the firms in the industry. We show that a tax on pollution emissions can make it unprofitable for any firm to leave the cartel. Moreover the cartel formation can diminish the welfare gain from environmental regulation. We provide an example where social welfare under environmental regulation and collusion of firms is below social welfare under a laisser-faire policy.pollution tax;oligopoly;cartel formation;coalition formation;differential game

International Environmental Agreements in the Presence of Adaptation

We show that adaptive measures undertaken by countries in the face of climate change, apart from directly reducing the damage caused by climate change, may also indirectly mitigate greenhouse gas emissions by increasing the stable size of international agreements on emission reductions. Moreover, we show that the more effective the adaptive measure in terms of reducing the marginal damage from emissions, the larger the stable size of the international environmental agreement. In addition, we show that larger coalitions, in the presence of adaptation, may lead to lower global emission levels and higher welfare.International Environmental Agreements, Adaptation, Coalition Formation, Climate Change