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Spectroscopy of Biological Molecules at Very Low Temperatures: Theoretical Studies
Published in Leonid Khriachtchev, Physics and Chemistry at Low Temperatures, 2019
The anharmonic interactions in the potential energy can be classified into two types. The first and simplest is the intrinsic anharmonicity of each mode: consider displacing the molecule away from equilibrium along a single normal mode. The deviation from harmonic behavior in such a displacement reveals the intrinsic anharmonicity of that mode. All other anharmonic interactions are due to coupling between different normal modes. We adhere in this part to the pairwise coupling approximation for the potential in terms of the normal modes, discussed in Section 1,42 In this framework, the second type of anharmonicity is due to mode–mode coupling. Though both types of anharmonicity contribute to the vibrational spectrum, the difference between the two is important. Only the anharmonic coupling between modes can cause, in dynamics, intramolecular vibrational energy flow.
Isotope Separation with Infrared Laser Beams
Published in Fred M. Dickey, Scott C. Holswade, David L. Shealy, Laser Beam Shaping Applications, 2018
The excitation of the lower vibrational levels is of particular interest in isotope separation since this stage of the process determines the isotope selectivity of the multiple photon process. A nonselective process would imply that both isotopes have been excited. This could occur if the bandwidth of the source was too large and overlapped with the absorption bands of both isotopes. The excitation of these lower levels is through multistep resonant multiple photon excitations of successive vibrational levels. Anharmonicity causes a frequency detuning of successive vibrational levels, and this prevents resonant excitation beyond one or two vibrational levels. This is compensated for by the rotational levels of the molecule and the anharmonic splitting of the higher vibrational levels. Thus the same photon frequency can be used to excite the molecule.
Laser Isotope Separation with Shaped Light
Published in Fred M. Dickey, Todd E. Lizotte, Laser Beam Shaping Applications, 2017
The excitation of the lower vibrational levels is of particular interest in isotope separation since this stage of the process determines the isotope selectivity of the multiple-photon process. A nonselective process would imply that both isotopes have been excited. This could happen if the bandwidth of the source is too large, overlapping with the absorption bands of both isotopes. The excitation of these lower levels is through multistep resonant multiple-photon excitations of successive vibrational levels. Anharmonicity causes a frequency detuning of successive vibrational levels, which would prevent resonant excitation beyond one or two vibrational levels. This is compensated for by the rotational levels of the molecule, and the anharmonic splitting of the higher vibrational levels. Thus, the same photon frequency can be used to excite the molecule.
Interaction of obliquely incident lasers with anharmonic CNTs acting as dipole antenna to generate resonant THz radiation
Published in Waves in Random and Complex Media, 2022
Sandeep Kumar, Shivani Vij, Niti Kant, Vishal Thakur
Therefore, the expression of the x-component of self-field can be derived from Equation (3), One can find the restoring force for each electron of CNTs, by using the relation, , The plasma electrons of the CNTs do not experience the same restoration force. Instead, some of the electrons experience a weak, and others experience a strong restoration force. It results in anharmonicity in the CNTs. The anharmonicity plays a significant role in the enhancement of THz amplitude. The anharmonic behavior of the electrons of CNTs compels us to find the (average) and the r (average) of the restoration force to obtain its linear and nonlinear components . Following Kumar et al. [15], one can calculate these linear and nonlinear components and . By using these components, the net average restoration force is given as where, is the characteristic parameter and is known as the anharmonicity factor. Both terms are responsible for nonlinear mixing in the response of the electrons of CNTs. The numerical values of both depend upon the inner and outer radii of CNTs.
Non-equilibrium solvation dynamics: results beyond linear response theory
Published in Molecular Physics, 2020
Sayantani Choudhury, Aniket Patra, Arup Kumar Pathak, Alok Kumar Samanta
The sequential steps to evaluate the explicit expression for (Equation 15) are as follows: (i) solve Equation (11) with the initial condition defined in Equation (12) to obtain the expression for , (ii) Substitute the same into Equation (15) and obtain the analytical expression for and (iii) obtain S(t) through Equation (3). In contrast to the harmonic case, the analytical form of is not known for an anharmonic potential, . It is difficult to develop a systematic perturbation theory for over the entire a space and time domain as a power series of the anharmonicity parameter, γ. Therefore, we first derive a kinetic equation for non-equilibrium solvation which removes the need for the knowledge of .
Investigation of temperature and pressure effects on thermodynamic parameters of intermetallic alloy in EXAFS
Published in Cogent Engineering, 2020
The second cumulant contributes to the anharmonic EXAFS amplitude, while and contribute to the phase shift of the EXAFS due to anharmonicity. Note that , , and contain the anharmonicity parameter k3eff and exist only when this parameter is included, which is why , , and must be considered when calculating the anharmonic effects in EXAFS. Under ambient pressure, the factor is proportional to the temperature and inversely proportional to the shell radius, which is consistent with the anharmonicity obtained in experimental research into catalysis (Clausen et al., 1993), and R is considered as the particle radius. In Equations (9)–(13), is the heat and pressure function, which describes how the cumulants, the thermal expansion coefficient, and the anharmonic factor depend on the absolute temperature T and pressure applied to the intermetallic alloy.