Rotational quantum

Here we review the properties of the model in the mean field theory [328] of the system with the quantum APR Hamiltonian (41). This consists of considering a single quantum rotator in the mean field of its six nearest neighbors and finding a self-consistent condition for the order parameter. Solving the latter condition, the phase boundary and also the order of the transition can be obtained. The mean-field approximation is similar in spirit to that used in Refs. 340,341 for the case of 3D rotators. 

Fig. 0.2. (a) The comb spectrum of N2 considered as a quantum rotator. The envelope of the rotational structure of the Q-branch slightly split by the rotovibra-tional interaction is shaded, (b) The depolarized rotovibrational spectrum of N2 at corpuscular density n = 92 amagat, T = 296 K and pressure p = 100 atm. The central peak, reported in a reduced (x30) scale is due to a polarized component [5] (V) experimental (—) best fit. 

Orlova N. D., Pozdniakova L. A. Profiles of infrared absorption bands and rotational motion of molecules in liquids. Quantum rotation of hydrogen-chloride molecules, Opt. Spectr. 35, 624-7 (1973). [Optika i Spectr. 35, 1074-7 (1973)]. 

The classical continuum approximation (13.80) becomes questionable for light nuclei, where inertial moments are reduced and quantum rotational spacings proportionally increased, and in this case the quantum sum over angular momentum states may be substituted. Furthermore, the treatment assumes sufficient free volume for unhindered rotations, and is therefore only appropriate at the lower-density conditions of gaseous reactions. 

To place these results in context it should be reaffirmed that microwave heating is a completely distinct phenomenon operating in an entirely different way from microwave spectroscopy. This latter process involves the direct interaction of photons of a particular energy in order to excite the quantum rotational levels of gas-phase sample. Although in microwave heating, the absorption of microwave irradiation by a sample has been shown to be frequency dependent, it is not a requirement of the system for the energy to be quantised. As a result the heating process does not depend upon the direct absorption of microwave photons, instead the sample is heated via... 

Analysis of the fluorescence from electronically excited molecules in a conventional static gas system21 provides a way of investigating vibrational relaxation of such molecules, and is also a means of studying selection rules for rotational relaxation22. It is now well established that multiple quantum rotational jumps can occur with high probability (see Section 6). 

Brown, C.M., Yildrim, T., Neumann, D.A., et al. (2000). Quantum rotation of hydrogen in single-wall carbon nanotubes. Chem. Phys. Lett., 329, 311—16. 

Additional thanks are expressed with pleasure to Prof. Eduardo Pina, Universidad Autonoma Metropolitana - Iztapalapa, for sharing his expertise on classical and quantum rotations to Prof. Hans Volkmer, Universify of Wisconsin - Milwaukee, for discussions on how fo evaluafe Lam6 functions and to Prof. Jocele Allegra Wild Wolf for proof reading and susfained encouragement. 

AJ. Ramirez-Cuesta, P.C.H. Mitchell S.F. Parker (2001). J. Mol. Cat. A Chemical, 167, 217-224. An inelastic neutron scattering study of the interaction of dihydrogen with the cobalt site of a cobalt aluminophosphate catalyst. Two-dimensional quantum rotation of adsorbed dihydrogen. 

Gutt, C., Asmussen, B., Press, W., Merkl, C., Casalta, H., Greinert, J., Bohrmann, G, Tse, J., and Hiiller, A., 1999. Quantum rotations in natural methane-clathrates from the Pacific sea-floor. Europhysics... 

Colmenero. J. Mudkhopadhyay. R. Alegria, A. Frick. B. Quantum rotational tunneling of methyl groups in polymers. Phys. Rev. Lett. 1998. 93(11), 2350-2353. 

Quantum Rotational Dynamics for Pairs of Coupled Rotors... 

The quantum rotational partition function for a diatomic or linear polyatomic molecule is equal to the classical version divided by and also divided by the symmetry number a, equal to 1 for a heteronuclear diatomic molecule and equal to 2 for a homonuclear diatomic molecule. 

The quantum rotational partition function of a nonlinear polyatomic gas is related to the classical version as follows ... 

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