Quantum processes

Schulten, K. Curve crossing in a protein coupling of the elementary quantum process to motions of the protein. In Quantum mechanical simulation methods for studying biological systems, D. Bicout and M. Field, eds. Springer, Berlin (1996) 85-118. 

An interesting feature of the energy diagram is that there are two transitions that involve the simultaneous flip of both spins. These are the transitions aa )3j8 (a double-quantum process, Wf) and a/3 )8a (a zero-... 

Since the equilibrium state has been disturbed, the system tries to restore equilibrium. For this it can use as the predominant relaxation pathways the double-quantum process (in fast-tumbling, smaller molecules), leading to a positive nOe, or the zero-quantum process 1% (in slower-tumbling macromolecules), leading to a negative nOe. 

Chandler, D. Quantum processes in liquids. In Liquids, Freezing and Glass Transition, Levesque, D. Hansen, J. Zinn-Justin, J., Eds. Elsevier New York, 1990, pp. 195-285... 

Since the early days of quantum mechanics, the wave function theory has proven to be very successful in describing many different quantum processes and phenomena. However, in many problems of quantum chemistry and solid-state physics, where the dimensionality of the systems studied is relatively high, ab initio calculations of the structure of atoms, molecules, clusters, and crystals, and their interactions are very often prohibitive. Hence, alternative formulations based on the direct use of the probability density, gathered under what is generally known as the density matrix theory [1], were also developed since the very beginning of the new mechanics. The independent electron approximation or Thomas-Fermi model, and the Hartree and Hartree-Fock approaches are former statistical models developed in that direction [2]. These models can be considered direct predecessors of the more recent density functional theory (DFT) [3], whose principles were established by Hohenberg,... 

Due to the development of efficient initial-value representations of the semiclassical propagator, recently there has been considerable progress in the semiclassical description of multidimensional quantum processes [104—111,... 

The photochemical conversion of the st/n-phenylhydrazone of pyri-dine-2-carboxaldehyde to the antz-isomer has been shown to be a first order and 1-quantum process.266,256... 

Therefore it should be possible to decompose water with two quantum photochemical process with the input of at least 237 kJ or 2.46 eV per molecule. For a one quantum process, the light of wavelength shorter than 500 nm can only be effective, which means poor utilization of solar spectrum. Semiconductor electrodes with suitable band gaps can act as-... 

Since the absorption of light by an organic molecule is, in general, a one-quantum process, we may also write Eq. 15-7 as ... 

It is true that there exist situations (corresponding to statistical ensembles) where Eq. (11) would be true in classical mechanics. Examples are given in the Feynman lectures.8 However, in general Eq. (11) is incorrect in both quantum and classical mechanics. Indeed, the type of interference of probabilities which we derive in our theory (see Section IX) is qualitatively similar for classical and quantum processes. 

No instance is known in which the rate of reaction is proportional to a power of the light intensity greater than the first. It is, indeed, very improbable that a molecule would remain in a condition where it possessed so large an excess of energy as a quantum of visible light long enough to acquire a second quantum, since all the time it would be subject to collisions which would rapidly deprive it of its first quantum. Probably all photochemical transformations are one-quantum processes. 

This, moreover, makes it easy to understand the exclusive prevalence of one-quantum processes in photochemical reactions. 

The basis for the semiclassical description of kinetics is the existence of two well separated time scales, one of which describes a slow classical evolution of the system and the other describes fast quantum processes. For example, the collision integral in the Boltzmann equation may be written as local in time because quantum-mechanical scattering is assumed to be fast as compared to the evolution of the distribution function. 

The resulting rate can be estimated as logT 4>q(G/Gq)x If o < 1, this reduces to log T 4>o(G/Go)Ith/If- In the opposite limit, the estimation for the rate reads log r 4>o(G/Gq ) l< (It J h), F being a dimensionless function 1. It is important to note that these expressions match the quantum tunneling rate log Jr Uqt/K (G/Gq)< provided eVr h. Therefore the quasi-stationary approximation is valid when the quantum tunneling rate is negligible and the third factor mentioned in the introduction is not relevant. For equilibrium systems, the situation corresponds to the well-known crossover between thermally activated and quantum processes at k Tr h [9]. 

It is now known that the quantum process of photodesorption does occur and that it is surface-material sensitive. For clean metals it is an extremely inefficient process if it occurs at all99-101). Quantum efficiencies appear to be of the order of < 10 9 molecules/photon, with corresponding cross sections of the order of < 10"27 m2. Photodesorption from semiconductors appears to be a very efficient process with quantum efficiencies approaching 10-2 molecules/photon and cross sections as high as 10-21 m2. Photodesorption is material dependent and therefore the material must be specified as well as the photon flux as a function of wavelength before estimates of the contribution to overall desorption processes can be made. Additionally the gaseous species present in the system which may adsorb and contribute to photodesorption must also be known. 

Swanson, M.S. (1992). Path Integrals and Quantum Processes (Academic Press, New York). 

Ayao Okiji, Yoshitada Murata, and Kenji Makoshi, Proceedings of the International Symposium on Dynamical Quantum Processes on Solid Surfaces (DQPSS 95). Proceedings of a conference held in Osaka, Japan, 20-22 September 1995, in Surf. Sci., 363 (1-3), Elsevier, Amsterdam, The Netherlands, 1996. 

When studying the limits of solar energy conversion, either by thermal or quantum processes, the sun has traditionally been treated as a blackbody (thermal equilibrium) radiator with surface temperature 5 800 K and distance 1.5 x 1011 m from Earth. A blackbody absorbs all incident radiation irrespective of its wavelength and direction of incidence and is represented classically by a hole in a cavity. 

D. Trivich, P. Flinn Maximum Efficiency of Solar Energy Conversion by Quantum Processes, in Solar Energy Research, ed. by F. Daniels, J. Duffie (Thames Hudson, London 1955) pp. 143-147... 

Additional insight into the quantum processes that are involved may be obtained from Fig. 8.3, which shows the energy levels for a two-spin system, each of spin V2.The spin operators are denoted / and S. We shall assume no spin-spin... 

An exciplex may degrade in the continued presence of the excitating radiation. There are two routes to exciplex formation excitation of either donor or acceptor followed by complexation, or excitation of the preformed complex. The excitation energies are often quite low, even only a few kT, but must be supplied in a one-quantum process involving a virtual photon. Thus excitation may be produced by nonradiative means, especially elec-trochemically. Exciplexes are rather weak adducts. The electronic transi-... 

A. Yogev, Quantum Processes for Solar Energy Conversion, Weizmann Sun Symp. Proc., Rehovot, Israel, 1996. 

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