Interacting system perturbed Hamiltonian

Turning to the question of an interacting system, we define the perturbed Hamiltonian as... 

The Hamiltonian H of a system in a radiation field, in the absence of interaction with the field and a perturbation Hamiltonian H describing the interaction with the field, is given by... 

The noncommuting part W of the Hamiltonian takes the part of interaction or perturbation defined with respect to that part Ho of the total Hamiltonian H which is symmetric with respect to the group generators Nm 2 This perturbation must be weak in order to assure the validity of the GF approximation. The set of the operators Nm optimized with respect to this criterion yield the natural break of the system into subsystems. 

The rotational and Zeeman perturbation Hamiltonian (X) to the electronic eigenstates was given in equation (8.105). It did not, however, contain terms which describe the interaction effects arising from nuclear spin. These are of primary importance in molecular beam magnetic resonance studies, so we must now extend our treatment and, in particular, demonstrate the origin of the terms in the effective Hamiltonian already employed to analyse the spectra. Again the treatment will apply to any molecule, but we shall subsequently restrict attention to diatomic systems. 

This effective Hamiltonian will improve the taking into account of deformation vibrations [15,26,29,30], all of degrees of freedom of the system, namely vibronic effects [38,45-47]. However, the action of these factors (including stretch-bend resonance interactions, that perturb overtone part of vibrational spectra most of YCX3 molecules [15,26,29,30,48]) on vibrational... 

In the special case that the perturbation is a sum of one-particle interactions, the total Hamiltonian of the system... 

In the perturbation theory, the models of wider use consider the Hamiltonian of the interacting system, as composed of an unperturbed Hamiltonian corresponding to the Hamiltonian of the two separate partners b)... 

Some quantum systems have Hamiltonians that can be divided into two parts Ho and H, where the first one contains the main interactions and a second one that acts like a perturbation on the system and is controlled by an external agent. Examples of such systems are electrons bound by an atomic potential that can be induced to jump from an orbital to another by laser beams, and the orientation of the nuclear magnetic moment, along a strong magnetic field that can be manipulated by the weak radio-frequency pulses. These two parts should act on the system in which the simulation is to be run. The procedure only works HHs can be efficiently described by Ho and H, i.e. the simulation also depends on the system in which it is to be run. 

Nonradiative energy transfer (figure 3) occurs when there is some interaction, described by a perturbation Hamiltonian H g, between A and B. In such a case, the system ( A + B) is not a stationary state of the total Hamiltonian (H + Hg + H g). If there is an isoenergetic system (A+ B), in which the excitation now resides in the acceptor, then time-dependent perturbation theory shows that the interaction H g causes evolution of the system from ( A + B) to (A + B) and vice versa. lilH g is sufficiently small, the rate of energy transfer will be smaller than the rate of... 

The next step is to switch on the interaction between A and B. The interaction Hamiltonian W connects the dynamical variables of the two systems. It should be chosen so that the perturbed Hamiltonian be equal to the Hamiltonian of the supersystem ... 

Each electron in the system is assigned to either molecule A or B, and Hamiltonian operators and for each molecule defined in tenns of its assigned electrons. The unperturbed Hamiltonian for the system is then 0 = - A perturbation XH consists of tlie Coulomb interactions between the nuclei and... 

Ab-initio studies of surface segregation in alloys are based on the Ising-type Hamiltonian, whose parameters are the effective cluster interactions (ECI). The ECIs for alloy surfaces can be determined by various methods, e.g., by the Connolly-Williams inversion scheme , or by the generalized perturbation method (GPM) . The GPM relies on the force theorem , according to which only the band term is mapped onto the Ising Hamiltonian in the bulk case. The case of macroscopically inhomogeneous systems, like disordered surfaces is more complex. The ECIs can be determined on two levels of sophistication ... 

All discussions of transport processes currently available in the literature are based on perturbation theory methods applied to kinetic pictures of micro-scattering processes within the macrosystem of interest. These methods do involve time-dependent hamiltonians in the sense that the interaction operates only during collisions, while the wave functions are known only before and after the collision. However these interactions are purely internal, and their time-dependence is essentially implicit the over-all hamiltonian of the entire system, such as the interaction term in Eq. (8-159) is not time-dependent, and such micro-scattering processes cannot lead to irreversible changes of thermodynamic (ensemble average) properties. 

The inclusion of the S W Hamiltonian leads to a system involving a double peituibation (137), namely, the electron-electron interaction and. Thus the reference state will be expressed as a double perturbed wavefunction... 

In the DC-biased structures considered here, the dynamics are dominated by electronic states in the conduction band [1]. A simplified version of the theory assumes that the excitation occurs only at zone center. This reduces the problem to an n-level system (where n is approximately equal to the number of wells in the structure), which can be solved using conventional first-order perturbation theory and wave-packet methods. A more advanced version of the theory includes all of the hole states and electron states subsumed by the bandwidth of the excitation laser, as well as the perpendicular k states. In this case, a density-matrix picture must be used, which requires a solution of the time-dependent Liouville equation. Substituting the Hamiltonian into the Liouville equation leads to a modified version of the optical Bloch equations [13,15]. These equations can be solved readily, if the k states are not coupled (i.e., in the absence of Coulomb interactions). 

The alternative case of approximation analogous to the one mentioned above in (7.2) assumes a small magnetic perturbation and a large quadmpole interaction. This case, which is very rare and has not yet been observed in nickel systems, is expressed by the Hamiltonian [3]... 

Hamiltonian with the energy from appropriate terms in the true Hamiltonian. The latter terms include the interaction between the external field and the magnetic moment produced by the orbiting electron, the interaction between the external field and the magnetic moment due to electron spin, and the interaction between the orbital magnetic moment and the spin magnetic moment. These interactions may be expressed as a perturbation to the total Hamiltonian for the system where... 

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