Quantum analysis

As we discussed in the Introduction, we assume that the noise is weak and short-correlated, i.e., that considerable dissipative contributions to the spin dynamics arise on time scales much longer than the typical correlation time rc of the noise. Below we discuss the influence of the low- and high-frequency fluctuations on the (classical) spin dynamics and recover the results of the quantum analysis above. Further, using the result for the low-frequency contribution we obtain the correction to the Berry phase from the environmental fluctuations at all frequencies. 

Engel, V., Metiu, H., Almeida, R., Marcus, R.A., and Zewail, A.H. (1988). Molecular state evolution after excitation with an ultra-short laser pulse A quantum analysis of Nal and NaBr dissociation, Chem. Phys. Lett. 152, 1-7. 

To summarize, we have studied the interaction of two weak quantum fields with an optically dense medium of coherently driven four-level atoms in tripod configuration. We have presented a detailed semiclassical as well as quantum analysis of the system. The main conclusion that has emerged from this study is that optically dense vapors of tripod atoms are capable of realizing a novel regime of symmetric, extremely efficient nonlinear interaction of two multimode single-photon pulses, whereby the combined state of the system acquires a large conditional phase shift that can easily exceed 1r. Thus our scheme may pave the way to photon-based quantum information applications, such as deterministic all-optical quantum computation, dense coding and teleportation [Nielsen 2000]. We have also analyzed the behavior of the multimode coherent state and shown that the restriction on the classical correspondence of the coherent states severely limits their usefulness for QI applications. 

This result should be contrasted with expectations founded on the classical equipartition theorem which asserts that an oscillator should have a mean energy of kT. Here we note two ideas. First, in the low-temperature limit, the mean energy approaches a constant value that is just the zero point energy observed earlier in our quantum analysis of the same problem. Secondly, it is seen that in the high-temperature limit, the mean energy approaches the classical equipartition result E) = kT. This can be seen by expanding the exponential in the denominator of the second term to leading order in the inverse temperature (i.e. — 1 ... 

By analogy with our quantum analysis, we calculate the semiclassical Fano factor, defined by Eq. (1.4), and quadrature squeezing variance... 

Owing to the metal-metal distances between adjacent dimers (> 4.8 A), they are expected to behave as isolated binuclear species whose behavior may accurately be discussed from rigorous quantum analysis. 

The four thermodynamically stable forms of carbon are diamond, graphite, Cgo, Buckminster fullerene, and carbon nanotubes. It would be a challenge to extend the experience gained in CNT to nanotubes made of other material than carbon. It would also be interesting to form stable spherical structures in the nanoscale dimensions without agglomeration. At what scale would the quantum analysis for atoms be applicable when compared with the Newtonian mechanics used to describe macro... 

Thermodynamic equilibrium and stability are important considerations in the formation of nanocomposites. LCST and UCST behavior can be seen in polymeric systems. The four thermodynamically stable forms of carbon are diamond, graphite, Cgo Buckminister fullerenes, and carbon nanotubes. At some point dnring miniaturization, atom-by-atom quantum analysis would be more applicable compared with macroscale Newtonian mechanical treatment. Layer rearrangement can happen due to Marongoni instability. 

Thus in the quantum analysis of a beam experiment it is necessary to obtain an expression for the scattering amplitude out of the Pm=0 state, under the constraint that the axis to which the projection quantum number refers may differ fiom the collision frame z-axis. The appropriate expression is [51-53]... 

This analysis is conceptually and pictorially appealing. It has to be used to provide a qualitatively satisfactory interpretation of the experimental results of Leone, Zare, and their co-workers. Despite this apparent success, it is necessary to ask whether this model is justified on the basis of the exact quantum analysis of the collision dynamics presented here. 

By performing the above algorithm, either by Schrodinger and Dirac quantum analysis, one obtains the working expression for the bondonic mass [63] ... 

This quantum analysis was systematized within the vibrationally enhanced ground-state tunneling theory (VEGST) (Bruno Bialek, 1992), experimentally verified on reactions catalyzed by the bacterial enzyme methylamine dehydrogenase (Basran et al., 1999), despite some limitations for those enzyme in which the tunneling process acts so close... 

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