Effects of the finite pulse widths on solid echo signals

Simple two-pulse time-reversal sequence for dipolar and quadrupolar-coupled spin systems

We demonstrate, both theoretically and experimentally, that two-pulse sequence (2n+1) X 90 degrees(Y) - 90 degrees(X) -Acq(t) without delay between pulses, yields the reverse of time evolution of spin system with dipolar and quadrupole interactions. This process results in refocusing of the spin magnetization into magic echo at te = t1/2 after the second pulse, where t1 is the length of the first pulse.

Solid echo in the slow-motion region. Effects of the finite pulse widths

The effects of nonzero radio-frequency pulse widths on the echo signals in solids with molecular motions have been investigated. It has been shown that in the slow-motion region a time position and an amplitude of the echo signal depend not only on the width of the pulse, but also on the shape of potential wells and the correlation time, describing the molecular motion. A comparison of the developed theory with experimental results obtained for polycrystalline NH4Cl demonstrates a good agreement between them.

Generalized langevin equation and recurrence relations

The generalized Langevin equation (GLE) is a reformulation of the Heisenberg equation of motion, and hence, an exact equation. It is the basis of the memory function approach, a very widely used method for studying dynamics of classical and quantum fluids. The GLE was first derived by Mori in a very formal way. A much simpler and more physically motivated derivation was given by us some years later. In this work we provide perhaps the simplest possible derivation of the GLE. The simplicity of the derivation helps to bring out the subtleties present in this important dynamical relationship.

Heisenberg, langevin, and current equations via the recurrence relations approach

Some years ago the Heisenberg equation of motion was formally solved by the recurrence relations approach. It is shown here that the Langevin equation represents a structural property of the recurrence relations. The Langevin equation is useful for studying the time evolution of the current. The resulting current-current correlation function is compared with Luttinger's phenomenological theory. Geometric interpretations are made for the conductivity and the dielectric function.