Lyapunov exponents, entropy production and decoherence

We establish that the entropy production rate of a classically chaotic Hamiltonian system coupled to the environment settles, after a transient, to a meta-stable value given by the sum of positive generalized Lyapunov exponents. A meta-stable steady state is generated in this process. This behavior also occurs in quantum systems close to the classical limit where it leads to the restoration of quantum-classical correspondence in chaotic systems coupled to the environment.Comment: 4 ReVTeX pages + 3 postscript figures. PRL (to appear

Calculation of eigenvalues of a strongly chaotic system using Gaussian wavepacket dynamics

We apply the approximate dynamics derived from the Gaussian time-dependent variational principle to the Hamiltonian $\hat H= {1/2}(\hat p_x ^2+ \hat p_y ^2)+ {1/2}\hat x^2\hat y^2$, which is strongly chaotic in the classical limit. We are able to calculate, essentially analytically, low-lying eigenvalues for this system. These approximate eigenvalues agree within a few percent with the numerical results. We believe that this is the first example of the use of TDVP dynamics to compute individual eigenvalues in a non-trivial system and one of the few such computations in a chaotic system by any method. There is a short self-contained discussion on the validity of Gaussian approximations in the paper.Comment: 19 pages, Revtex + 1 ps fig , Phys. Rev. E, to appear (1997

Chaos and Lyapunov exponents in classical and quantal distribution dynamics

We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions $\rho(p,q)$. Of particular interest is $\lambda_2$, an exponent which quantifies the rate at which chaotically evolving distributions acquire structure at increasingly smaller scales and which is generally larger than the maximal Lyapunov exponent $\lambda$ for trajectories. The approach is trajectory-independent and is therefore applicable to both classical and quantum mechanics. In the latter case we show that the $\hbar\to 0$ limit yields the classical, fully chaotic, result for the quantum cat map.Comment: 5 RevTeX pages + 2 ps figs. Phys. Rev. E (to appear,'97

Non-hermiticity in a kicked model: Decoherence and the semiclassical limit

We study the effects of non-hermitian perturbation on a quantum kicked model exhibiting a localization transition. Using an exact renormalization scheme, we show that the critical line separating the extended and localized phases approaches its semiclassical limit as the imaginary part of the kicking parameter is steadily increased. Further, the metastability of the quantum states appears to be directly correlated with the deviation between the semi-classical and quantum results. This direct evidence of quantum-classical correspondence suggests that non-hermitian perturbations may be used to model decoherence

Does Openness Promote Competition? A Case Study of Indian Manufacturing

This paper uses firm level data for the period 1989-2001 to analyse the working of competition in India’s manufacturing sector. It examines the impact of greater competition on profit mark-up over the last decade. The econometric analysis of the factors determining markup indicates that, contrary to received wisdom, trade openness by itself does not act to reduce the profit mark-up. The paper also investigates the degree of competitiveness defined as the Lerner price-cost margin. The analysis indicates that the estimated margins are in general high over the 1990s across all industries and in most of the industries considered these margins have been increasing over the second-half of the 1990s. The market by itself does not bring about competitive outcomes. The regulatory agencies probably have a crucial role to ensure a level playing field.Competition; Indian Manufacturing

Exponentially rapid decoherence of quantum chaotic systems

We use a recent result to show that the rate of loss of coherence of a quantum system increases with increasing system phase space structure and that a chaotic quantal system in the semiclassical limit decoheres exponentially with rate $2 \lambda_2$, where $\lambda_2$ is a generalized Lyapunov exponent. As a result, for example, the dephasing time for classically chaotic systems goes to infinity logarithmically with the temperature, in accord with recent experimental results.Comment: 4 ReVTeX pages + 1 postscript figure. PRL (to appear

Corporate governance and Competition: A Case Study of India.

The aim of this paper is to show the interaction effect of product market competition and corporate governance variables on firm performance. While the linkage between internal governance mechanism and firm performance is well established in several studies, the interaction between internal and external governance mechanism has received very little attention in emerging market economies. Here we have shown the independent and interaction effect of ownership and competition variable on firm level productivity. Contrary to conventional wisdom, we document that competition has in reality become a discernible force in developing economies. The econometric modeling result confirms while the standalone effect of ownership variable on productivity is mostly insignificant, there is a strong positive interaction effect with competition variables.