A stochastic principle behind polar properties of condensed molecular matter

A statistical mechanics view leads to the conclusion that polar molecules allowed to populate a degree of freedom for orientational disorder in a condensed phase thermalize into a bi-polar state featuring zero net polarity. In cases of orientational disorder polar order of condensed molecular matter can only exist in corresponding sectors of opposite average polarities. Channel type inclusion compounds, single component molecular crystals, solid solutions, optically anomalous crystals, inorganic ionic crystals, biomimetic crystals and biological tissues investigated by scanning pyroelectric and phase sensitive second harmonic generation microscopy all showed domains of opposite polarities in their final grown state. For reported polar molecular crystal structures it is assumed that kinetic hindrance along one direction of the polar axis is preventing the formation of a bi-polar state, thus allowing for a kinetically controlled mono-domain state. In this review we summarize theoretical and experimental findings leading to far reaching conclusions on the polar state of solid molecular matter. “… no stationary state … of a system has an electrical dipole moment.” P. W. Anderson, Science, 1972, 177, 393.

Symmetry and the polar state of condensed molecular matter

Polar molecular crystals seem to contradict a quantum mechanical statement, according to which no stationary state of a system features a permanent electrical polarization. By stationary we understand here an ensemble for which thermal averaging applies. In the language of statistical mechanics we have thus to ask for the thermal expectation value of the polarization in molecular crystals. Nucleation aggregates and growing crystal surfaces can provide a single degree of freedom for polar molecules required to average the polarization. By means of group theoretical reasoning and Monte Carlo simulations we show that such systems thermalize into a bi-polar state featuring zero bulk polarity. A two domain, i.e. bipolar state is obtained because boundaries are setting up opposing effective electrical fields. Described phenomena can be understood as a process of partial ergodicity-restoring. Experimentally, a bi-polar state of molecular crystals was demonstrated using phase sensitive second harmonic generation and scanning pyroelectric microscopy

Epileptic seizures as condensed sleep: an analysis of network dynamics from electroencephalogram signals

Both deepening sleep and evolving epileptic seizures are associated with increasing slow-wave activity. Larger-scale functional networks derived from electroencephalogram indicate that in both transitions dramatic changes of communication between brain areas occur. During seizures these changes seem to be 'condensed', because they evolve more rapidly than during deepening sleep. Here we set out to assess quantitatively functional network dynamics derived from electroencephalogram signals during seizures and normal sleep. Functional networks were derived from electroencephalogram signals from wakefulness, light and deep sleep of 12 volunteers, and from pre-seizure, seizure and post-seizure time periods of 10 patients suffering from focal onset pharmaco-resistant epilepsy. Nodes of the functional network represented electrical signals recorded by single electrodes and were linked if there was non-random cross-correlation between the two corresponding electroencephalogram signals. Network dynamics were then characterized by the evolution of global efficiency, which measures ease of information transmission. Global efficiency was compared with relative delta power. Global efficiency significantly decreased both between light and deep sleep, and between pre-seizure, seizure and post-seizure time periods. The decrease of global efficiency was due to a loss of functional links. While global efficiency decreased significantly, relative delta power increased except between the time periods wakefulness and light sleep, and pre-seizure and seizure. Our results demonstrate that both epileptic seizures and deepening sleep are characterized by dramatic fragmentation of larger-scale functional networks, and further support the similarities between sleep and seizures.