We develop a theoretical framework to describe the dielectric response of live cells in suspensions when placed in low external electric fields. The treatment takes into account the presence of the cell's membrane and of the charge movement at the membrane's surfaces. For spherical cells suspended in aqueous solutions, we give an analytic solution for the dielectric function, which is shown to account for the alpha- and beta-plateaus seen in many experimental data. The effect of different physical parameters on the dielectric curves is methodically analyzed.

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We have developed a dielectric spectroscopy technique for low-frequencies and low-electric field amplitudes. The excellent sensitivity of this method enables us to apply field amplitudes that are below the linear threshold. The dielectric constants of inorganic and organic liquids are found to be consistent with the previously reported experimental data and theoretical predictions.

One of the major challenges in electrochemistry is to properly account for polarization of the electrical double layer that forms at an electrode-electrolyte interface, especially when interpreting the impedance spectra of biological molecules, electrolytes, or live cell suspensions. This double layer, which affects the measured impedance, is also known as the electrode polarization effect. Various methods of correcting for its effects on impedance data have been reported, including varying the spacing between electrodes, four-electrode techniques, and electrodeless methods. Here we discuss the use of a constant phase element in a recently proposed circuit model, which can be thought of as a measure of the fractal nature of the interface. We also report on the conductivity spectra of several saline solutions over the frequency range 1 Hz-1 MHz, in which we observe Debye-like relaxation behavior that changes with ion concentration and type. Good agreement is obtained with an alternative model that treats the cations and anions as overdamped oscillators in harmonic restoring potentials.

Recently observed Aharonov-Bohm quantum interference of the period h/2e in charge density wave rings strongly suggests that correlated density wave electron transport is a cooperative quantum phenomenon. The picture discussed here posits that quantum solitons nucleate and transport current above a Coulomb blockade threshold field. We propose a field-dependent tunneling matrix element and use the Schrödinger equation, viewed as an emergent classical equation as in Feynman's treatment of Josephson tunneling, to compute the evolving macrostate amplitudes, finding excellent quantitative agreement with voltage oscillations and current-voltage characteristics in NbSe(3). A proposed phase diagram shows the conditions favoring soliton nucleation versus classical depinning.