We propose a new frustrated Heisenberg antiferromagnetic model with spatially anisotropic exchange parameters J c , J a , and J ac , extending along the c, a, and a ± c (c-a-ca model) lattice directions, and apply it to describe the fascinating physics of copper carbodiimide, CuNCN, assuming the resonating valence bond (RVB) type of its phases. This explains within a unified picture the intriguing absence of magnetic order in CuNCN. We further present a parameters-temperature phase diagram of the c-a-ca-RVB model in the high-temperature approximation. Eight different phases including Curie and Pauli paramagnets (respectively, in disordered and 1D-or Q1D-RVB phases) and (pseudo)gapped (quasi-Arrhenius) paramagnets (2D-RVB phases) are possible. By adding magnetostriction and elastic terms to the model, we derive possible structural manifestations of RVB phase transitions. Assuming a sequence of RVB phase transitions to occur in CuNCN with decreasing temperature, several anomalies observed in the temperature course of the lattice constants are explained.

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We review three-and four-level schemes of inversionless amplification with different types of coherent pumping. We show that amplification without inversion between the "bare" states is a result of population inversion between eigenstates of the density matrix. In particular, it can be achieved due to the coherent population trapping, i.e. effective removal from the interaction with the field a fraction of atoms at lower levels.

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