Coherent states tunneling

Such a tunnel switching of the magnetization can be described by the so-called one-domain approximation, when the total magnetization vector M is taken as a main dynamic variable with fixed absolute value M. Then the total energy density, or the anisotropy energy E, is obtained from the spin-Hamiltonian H using a spin coherent state n) chosen along the direction n [332,333] ... 

In condensed matter, there are only few examples of coherent states (with the exception of superconductors and superfluids), but certain tunnelling states of protons [Wipf 1987] or positive muons [Karlsson 1998] in metals have been... 

Related studies have made use of 2H NMR spectroscopy in the solid state. The theoretical foundation for the study of dynamics in dihydrogen complexes was developed by Buntkowsky and coworkers.124 Solid-state 2H NMR spectroscopy has been used to study the dynamics of bound D2 in tntns- Ru( D2)CI(dppe)2 PI>, where evidence was found for coherent rotational tunneling, with a barrier of 6.2kcal/ mol.125 In more recent work, solid-state 2H NMR spectroscopy has been used to determine the structure and dynamics of several dihydrogen Ru complexes.126... 

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

This question is closely related to the coherent-incoherent transition problem absent from the standard situation in the gas phase namely, a true rate constant can be defined only when the tunneling dynamics is incoherent, i.e., once prepared in the initial state (reactant valley), the system... 

Segal D, Nitzan A, Davis WB, Wasielewski MR, Ratner MA (2000) Electron transfer rates in bridged molecular systems 2. A steady-state analysis of coherent tunneling and thermal transitions. J Phys Chem B 104( 16) 3817—3829... 

Symmetry of superconducting state. No Hebel-Slichter coherence peak was observed in either k -(ET)2Cu(NCS)2 or c-(ET)2Cu[N(CN)2]Br in NMR measurements, ruling out a BCS s-wave state. The symmetry of the superconducting state of c-(ET)2Cu(NCS)2 had been controversially described as normal BCS-type or non-BCS type however, scanning tunneling spectroscopy showed f-wave symmetry with line nodes along the direction near ti/4 from k - and Kc-axes [228, 229], and thermal conductivity measurements were consistent with this result [230]. c-(ET)2Cu [N(CN)2]Br showed the same symmetry [231]. 

We observe the coherent excitation of an optically inactive mode proving that the reactive process itself and not only the optical excitation drives the observed vibrational motions. Further we demonstrate that during the ESIPT the proton is adiabatically shifted from one site to the other and tunneling of the proton is not rate determining. The dynamics is entirely controlled by the skeletal modes. Interestingly, this is quite similar to ground state proton transfer of HC1, where the fluctuations of the water environment enable the adiabatic process [8]. 

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