Electron—phonon system

The OOA, also known as Kugel-Khomskii approach, is based on the partitioning of a coupled electron-phonon system into an electron spin-orbital system and crystal lattice vibrations. Correspondingly, Hilbert space of vibronic wave functions is partitioned into two subspaces, spin-orbital electron states and crystal-lattice phonon states. A similar partitioning procedure has been applied in many areas of atomic, molecular, and nuclear physics with widespread success. It s most important advantage is the limited (finite) manifold of orbital and spin electron states in which the effective Hamiltonian operates. For the complex problem of cooperative JT effect, this partitioning simplifies its solution a lot. 

The commutator and anticommutator operations in Hilbert space can thus be implemented with a single multiplication by a and + superoperator, respectively. We further introduce the Liouville space-time ordering operator T. This is a key ingredient for extending NEGFT to superoperators when applied to a product of superoperators it reorders them so that time increases from right to left. We define (A(t)) = Tr A(f)Peq where peq = p(t = 0) represents the equilibrium density matrix of the electron-phonon system. It is straightforward to see that for any two operators A and B we have... 

Hirsch, J.E. and Fradkin, E., Phase diagram of one-dimensional electron-phonon systems. 11. The molecular-crystal model, Pfiys. Rev. fi, 27,4302,1983 Niyaz, R, Scalettar, R.T., Fong, C.Y., and Batrouni, G.G., Phase transitions in an interacting boson model with near-neighbor repulsion, Phys. Rev. B, 50, 362,1994. 

Recent calculations involving all kinds of optical phonons or based on the nonadi-abaticity of the electron-phonon system resulted in an increasing overtone/fundamental ratio with decreasing dot radius in accordance with experiments on CdSe and CuBr QDs [264,265]. 

The total wave function of the complete (electron-phonon) system can be written using the above-mentioned method as a linear combination of the instantaneous local atomic wave functions ... 

The explanation for this two-peak structure near cp lies not in a new surface state but in a complex line shape because of many-body effects in the electron-phonon system. In order to see behind these effects, we need to take a closer look at the spectral function A(k, E) for a coupled electron-phonon system. In general, A(k, E) is related to the self-energy E(k, E) of a quasi particle by the equation... 

For example in copper, a metal used in nuclear adiabatic demagnetization (see Section 7.4), electron and phonon systems are decoupled the power transferred between the two systems is [18] ... 

However, for the dendrimer nanocomposite metallic systems this change in shape was not observed. Again, due to the high stability to intense laser pulses, the anisotropy value of the gold dendrimer nanocomposite, which can be viewed as a measure of the symmetry of the particle, did not change after several repeated cycles of measurements. It is possible that the initial optical pumping of the electron-phonon modes of the metal particles is partially absorbed by the encapsulating PAMAM dendrimer. 

Meanwhile there is overwhelming evidence that the basic assumptions of the SSH model are not applicable to 7i-bonded conjugated polymers. Coulombic and electron-electron correlation effects are large while electron-phonon coupling is moderately weak. As a consequence, the spectroscopic features in this class of materials are characteristic of molecular rather than of inorganic crystalline semiconductor systems. There are a number of key experimental and theoretical results that support this assignment ... 

Consider now the equality Hoj> n Jm=8j>j. Thus, in this model, preparing the system in the ground state of the Coulomb Hamiltonian, no time evolution can be expected if we do not switch on the kinematic couplings. We take a simple case where the electron-phonon coupling is on. The matrix elements of H in this base set look like ... 

The electron-phonon operator is a tensor product between the electronic dipole and the nuclear dipole operators. A mixing between the AA and BB via the singlet-spin diradical AB state is possible now. A linear superposition of identical vibration states in AA and BB is performed by the excited state diradical AB. If the system started at cis state, after coupling may decohere by emission of a vibration photon in the trans state furthermore, relaxation to the trans... 

As was mentioned above, the motion of one electron in these systems affects the motion of other electrons in the system. Therefore, the electron - phonon interaction can be said to mediate electron... 

Tunneling Spectroscopy has revealed electron - phonon coupling strengths for optical phonons in Ba K BiOg which suggest that phonon mediated coupling is responsible for superconductivity in this system (59). 

Besides electron-phonon coupling, the shape of the Fermi surface is important in deciding CDW formation. Fermi surfaces of systems containing linear or planar arrays of atoms reflect their one- or two-dimensional character. Since the Fermi surfaces connect many states with the same wave vector, Q, a periodic distortion having the wave vector Q will produce gaps at those portions connected by Q. The energy gained... 

When a polaron can move between two sites of equal energy, the state of the system (electron+phonons) will split into two states of even and odd parity, separated by an energy AE fc27t2/mpa2, which, when mp is large, may be quite small. The polarizability of this system will lead to the formation of a moment in a field F of order... 

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