Dynamic Properties and Response Theory

DYNAMIC PROPERTIES AND RESPONSE THEORY where 6(t — t ) is the Heaviside step function ... 

This edition, a completely rewritten and expanded version of the original, includes second quantization and diagrammatic perturbation theory, symmetric and unitary group methods, new forms of valence bond theory, dynamic properties and response, propagator and equation-of-motion techniques and the theory of intermolecular forces. 

Several theories were proposed in the past to describe the postglitch relaxation of pulsars angular velocity. Each physical model considers the spin-down of the superfluid in a different way. Alpar et al. [3, 4] suggest that the crustal superfluid is responsible for the glitches and postglitch relaxation they describe the dynamical properties of the crust superfluid in terms of a thermal... 

The quantum mechanical forms of the correlation function expressions for transport coefficients are well known and may be derived by invoking linear response theory [64] or the Mori-Zwanzig projection operator formalism [66,67], However, we would like to evaluate transport properties for quantum-classical systems. We thus take the quantum mechanical expression for a transport coefficient as a starting point and then consider a limit where the dynamics is approximated by quantum-classical dynamics [68-70], The advantage of this approach is that the full quantum equilibrium structure can be retained. 

MD simulation is advantageous for obtaining dynamic properties directly, since the MD technique provides not only particle positions but also particle velocities that enable us to utilize the response theory (e.g., the Kubo formula [175,176]) to calculate the transport coefficients from time-dependent correlation functions. For example, we will examine the self-diffusion process of a tagged PFPE molecular center of mass (Fig. 1.49) from the simulation to gain insight into the excitation of translational motion, specifically, spreading and replenishment. The squared displacement of the center mass of a molecule or a bead is used as a measure of translational movement. The self-diffusion coefficient D can be represented as a velocity autocorrelation function... 

Analytic response theory, which represents a particular formulation of time-dependent perturbation theory, has constituted a core technology in much of the this development. Response functions provide a universal representation of the response of a system to perturbations, and are applicable to all computational models, density-functional as well as wave-function models, and to all kinds of perturbations, dynamic as well as static, internal as well as external perturbations. The analytical character of the theory with properties evaluated from analytically derived expressions at finite frequencies, makes it applicable for a large range of experimental conditions. The theory is also model transferable in that, once the computational model has been defined, all properties are obtained on an equal footing, without further approximations. 

Calculations of analytic excited state properties for correlated methods have been reported by several groups [107-118]. Excited state dynamic properties from cubic response theory were first obtained by Norman et al. at the SCF level [55] and by Jonsson et al. at the MCSCF [56] level, and in a subsequent study a polarizable continuum model was applied to account for solvation effects [119]. Hattlg et al. presented a general theory for excited state response functions at the CC level using a quasi-energy formulation [120] which was subsequently implemented and applied at the CCSD level [121, 122]. The first ID DFT calculation of dynamic excited state polarizabilities, which we will shortly review here, was presented in [58] for pyrimidine and -tetrazine utilizing the double residue of the cubic response function derived in Section 2.7.3. 

The physical properties and chemical reactivity of molecules may be and often are drastically changed by a surrounding medium. In many cases specific complexes are formed between the solvent and solute molecules whereas in other cases only the non-bonded intermolecular interactions are responsible for the solvational effects. By one definition, the environmental effects can be divided into two principally different types, i.e. to the static and dynamic effects. The former are caused by the coulombic, exchange, electronic polarization and correlation interactions between two or more molecular species at fixed (close) distances and relative orientation in space. The dynamic interactions are due to the orientational relaxation and atomic polarization effects, which can be accounted for rigorously only by using time-dependent quantum theory. 

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