Caldeira

If all the PES coordinates are split off in this way, the original multidimensional problem reduces to that of one-dimensional tunneling in the effective barrier (1.10) of a particle which is coupled to the heat bath. This problem is known as the dissipative tunneling problem, which has been intensively studied for the past 15 years, primarily in connection with tunneling phenomena in solid state physics [Caldeira and Leggett 1983]. Interaction with the heat bath leads to the friction force that acts on the particle moving in the one-dimensional potential (1.10), and, as a consequence, a> is replaced by the Kramers frequency [Kramers 1940] defined by... 

As first shown by Caldeira and Leggett [1981], in the tunneling regime friction reduces the transition probability by the factor... 

According to (2.29), dissipation reduces the spread of the harmonic oscillator making it smaller than the quantum uncertainty of the position of the undamped oscillator (de Broglie wavelength). Within exponential accuracy (2.27) agrees with the Caldeira-Leggett formula (2.26), and similar expressions may be obtained for more realistic potentials. 

That is, Ci 2(t + P) = Ci,2Wexp( j3e). In fact, when the temperature is less than the separation between the two lowest energy levels of the bath, the latter can be approximated by a set of two-level systems [Caldeira and Leggett 1983 Mermin 1991],... 

Two most appealing features of this model draw so much attention to it. First, although microscopically one has very little information about the parameters entering into (5.24), it is known [Caldeira and Leggett 1983] that when the bath responds linearly to the particle motion, the operators q and p satisfying (5.24) can always be constructed, and the only quantity entering into the various observables obtained from the model (5.24) is the spectral density... 

Substituting (5.34) and (5.35) for (5.8) and dropping in Z the constant partition function of unperturbed harmonic oscillator we get the nonlocal effective action derived by Feynman (see also Caldeira and Leggett [1983]),... 

Caldeira J, R Feicht, H White, M Teixeira, JJG Moura, H Simon, I Moura (1996) EPR and Mdssbauer spectroscopic studies on enoate reductase. J Biol Chem 271 18743-18748. 

Caldeira, K. and Rampino, M.R. (1991) The mid-Cretaceous super-plume, carbon dioxide and global warming. Geophys. Res. Lett., 18, 987-990. 

Kerrick, D.M. and Caldeira, K. (1993) Paleoatmospheric consequences of CO2 released during early Cenozoic regional metamorphism in the Tethyan orogen. Chem. Geol., 108, 205-230. 

Bala G, Caldeira K, Wickett M, Phillips T, Lobell D, Delires C, Mirin A. Combined climate and carbon-cycle effects of large-scale deforestation. Proceedings of the National Academy of Sciences of the United States of America, 2007.104(16) pp. 6550-6555. doi 10.1073/pnas.0608998104... 

Herzog, H., Caldeira, K., and Adams, E., Carbon Sequestration via Direct Injection. Workshop on Carbon Sequestration Science, NETL Publication, Pittsburgh, PA, 2001. 

Caldeira, K., Forests, climate, and silicate rock weathering, /. Geochem. Exploration, 88(1-3), 419 (Special Issue), 2006. 

Hector A, Schmid B, Beierkuhnlein C, Caldeira MC, Diemer M, Dimitrakopoulos PG, Finn JA, Freitas H, Giller PS, Good J, Harris R, Hogberg P, Huss-Danell K, Joshi J, Jumpponen A, Komer C, Leadley PW, Loreau M, Minns A, Mulder CPH, O Donovan G, Otway SJ, Pereira... 

K. Caldeira, A.K. Jain, M.I. Hoffert, Climate sensitivity uncertainty and the need for energy without C02 emission, Science 299 (2003) 2052-2054. 

Guilderson, T.P., K. Caldeira, and P.B. Duffy. 2000. Radiocarbon as a diagnostic tracer in ocean and carbon cycle modeling. Global Biogeochemical Cycles 14(3) 887-902. 

Caldeira JC, Wu Y, Mameli M, Purdy RH, Li P-K, Akwa Y, Savage DD, Engen JR, Valenzuela CF. 2004. Fetal alcohol exposure alters neurosteroid levels in the developing rat brain. J Neurochem 90 1530-1539. 

Hoffert MI, Caldeira K, Jain AK, Haites EE, Harvey LDD, Potter SD, Schlesinger ME, Schneider SH, Watts RG, Wigley TML, Wuebbles DJ (1998) Energy implications of future stabilization of atmospheric CO2 content. Nature 395 881... 

Hector, A. Schmid, B. Bei kuhnlein, C. Caldeira, M.C. Dianra-, M. (1999) Plant diversity and productivity experiments in European grassland. Scioice, 286, 1123-7. 

Caldeira and Kasting (1993) show that these two factors largely cancel each other so that using C02 as the reference gas is still useful. 

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