Tunneling states

Gatti F, lung C, Leforestier C and Chapuisat X 1999 Fully coupled 6D calculations of the ammonia vibration-inversion-tunneling states with a split Hamiltonian pseudospectral approach J. Chem. Phys. Ill 7236 3... 

The speed and time by which the perturbed TLS systems relax to the equilibrium thermal populations depend on the TLS characteristics and in particular on the coupling energy of tunnelling states. 

In some cases (amorphous materials as polymers or glasses), the scattering of phonons with tunnelling states is also relevant. This process leads to an approximate [40-42,94,95] dependence as T1 2 of k (see Table 3.4) and to a plateau in the 2K < T < 20K range (see Fig. 3.18). 

Coupled 6D Calculations of the Ammonia Vibration-Inversion-Tunneling States with a Split Hamiltonian Pseudospectral Approach. 

Fully Coupled Six-Dimensional Calculations of the Water Dimer Vibration-Rotation-Tunneling States with a Split Wigner Pseudo Spectral Approach. 

Tunneling rotation in the chain gives rise to tunneling states, which can be labeled by the wave vector ranging within the first Brillouin zone ... 

In contrast with the chain of coupled oscillators, the translational invariance of a chain of coupled rotors leads not to a continuous spectrum, but to two branches of tunneling states determined by Eqs. (7.83). These states are coherent, whereas the space-localized breather states (7.80) are incoherent. In this respect, the transitions between breather states are similar to thermally activated rotation of a single group, though the number of rotors lying within the breather envelope and participating in the collective motion is greater than unity ( 20). The above discussion of collective rotation, which is based on the paper of Fillaux and Carlile [1990], demonstrates that the spectrum of a chain of coupled rotors is much richer than the spectrum one can expect from the traditional band model. 

From (9.7) and (9.8) it follows that at = c, low-frequency TLS s appear with zero-point amplitude Sc — S()(D/hajn)U6. Since the tunneling splitting varies exponentially with the barrier height, as in Eq. (9.3), even a narrow distribution of R values near the critical value c results in creation of a continuous spectrum of tunneling states. 

SYMMETRY PROPERTIES OF TUNNELING STATES IN JAHN-TELLER SYSTEMS... 

Complementary studies based on measurements of US-velocity changes and Raman spectroscopy were performed on bulk single-crystalline silicon irradiated with high doses of fast neutrons and compared with the non-irradiated material this revealed the presence of tunnelling states in highly coordinated bulk silicon [59],... 

Olthof, E. H. T., van der Avoird, A, and Wormer, R E. S., Structure, internal mobility, and spectrum of the ammonia dimer Calculation of the vibration-rotation tunneling states, J. Chem. Phys. 101, 8430-8442 (1994). 

The design of the structure of the cluster composed of two SiOj tetrahedrons linked by the O atom was done elsewhere [192, 193]. A double-well potential (DWP) of the central O atom is shown in Figure 19. When R is close to equilibrium for crystal, the barrier would not emerge ( = 0), and the O atom has one equilibrium position. Tunneling states are formed at 4.2 A. According to ref. 193, the DWP energy levels are described by an approximate relation ... 

The number of tunneling ground states equals the number of wells at the lowest sheet of the APES. In the case of quadratic (g) e coupling, there are three wells and, therefore, three tunneling states (Fig. 15). 

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