Existence and Vanishing of the Breathing Mode in Strongly Correlated Finite Systems

One of the fundamental eigenmodes of finite interacting systems is the mode of {\em uniform radial expansion and contraction} -- the ``breathing'' mode (BM). Here we show in a general way that this mode exists only under special conditions: i) for harmonically trapped systems with interaction potentials of the form $1/r^\gamma$ $(\gamma\in\mathbb{R}_{\neq0})$ or $\log(r)$, or ii) for some systems with special symmetry such as single shell systems forming platonic bodies. Deviations from the BM are demonstrated for two examples: clusters interacting with a Lennard-Jones potential and parabolically trapped systems with Yukawa repulsion. We also show that vanishing of the BM leads to the occurence of multiple monopole oscillations which is of importance for experiments

Detection Efficiency of Lorentz and Dispersion Types of Resonance

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A Note on the Paraxial Expansion of Cylindrically Symmetric Magnetic Field

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A statistical model approximation for perovskite solid-solutions: a Raman study of lead-zirconate-titanate single crystal

Lead titanate (PbTiO3) is a classical example of a ferroelectric perovskite oxide illustrating a displacive phase transition accompanied by a softening of a symmetry-breaking mode. The underlying assumption justifying the soft-mode theory is that the crystal is macroscopically sufficiently uniform so that a meaningful free energy function can be formed. In contrast to PbTiO3, experimental studies show that the phase transition behaviour of lead-zirconate-titanate solid solution (PZT) is far more subtle. Most of the studies on the PZT system have been dedicated to ceramic or powder samples, in which case an unambiguous soft-mode study is not possible, as modes with different symmetries appear together. Our Raman scattering study on titanium-rich PZT single crystal shows that the phase transitions in PZT cannot be described by a simple soft-mode theory. In strong contrast to PbTiO3, splitting of transverse E-symmetry modes reveals that there are different locally-ordered regions. The role of crystal defects, random distribution of Ti and Zr at the B-cation site and Pb ions shifted away from their ideal positions, dictates the phase transition mechanism. A statistical model explaining the observed peak splitting and phase transformation to a complex state with spatially varying local order in the vicinity of the morphotropic phase boundary is given.Comment: Article contains four black-and-white figures, one colour figure and one Table. Symmetry analysis and details of the model are given in Appendices I and II, respectivel