90 research outputs found
Non-Markovian finite-temperature two-time correlation functions of system operators of a pure-dephasing model
We evaluate the non-Markovian finite-temperature two-time correlation
functions (CF's) of system operators of a pure-dephasing spin-boson model in
two different ways, one by the direct exact operator technique and the other by
the recently derived evolution equations, valid to second order in the
system-environment interaction Hamiltonian. This pure-dephasing spin-boson
model that is exactly solvable has been extensively studied as a simple
decoherence model. However, its exact non-Markovian finite-temperature two-time
system operator CF's, to our knowledge, have not been presented in the
literature. This may be mainly due to the fact, illustrated in this article,
that in contrast to the Markovian case, the time evolution of the reduced
density matrix of the system (or the reduced quantum master equation) alone is
not sufficient to calculate the two-time system operator CF's of non-Markovian
open systems. The two-time CF's obtained using the recently derived evolution
equations in the weak system-environment coupling case for this non-Markovian
pure-dephasing model happen to be the same as those obtained from the exact
evaluation. However, these results significantly differ from the non-Markovian
two-time CF's obtained by wrongly directly applying the quantum regression
theorem (QRT), a useful procedure to calculate the two-time CF's for
weak-coupling Markovian open systems. This demonstrates clearly that the
recently derived evolution equations generalize correctly the QRT to
non-Markovian finite-temperature cases. It is believed that these evolution
equations will have applications in many different branches of physics.Comment: To appear in Phys. Rev.
The Institutional Framework and Economic Development.
The compound growth rates per capita output and Farrell-type efficiency measures for 115 market economies over the period 1960-80 were compared with measures of political, civil, and economic li berty. It was found that the institutional framework has significant and large effects on the efficiency and growth rate of economies. Pol itically open societies, which subscribe to the rule of law, to priva te property, and to the market allocation of resources, grow at three times the rate and are two and one-half times as efficient as societ ies in which these freedoms are abridged. Copyright 1988 by University of Chicago Press.
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