The Poisson Nernst-Planck equations for charge concentration and electric potential in a ball is a model of electro-diffusion of ions in the head of a neuronal dendritic spine. We study the relaxation and the steady state when an initial charge of ions is injected into the ball. The steady state equation is similar to the Liouville-Gelfand-Bratú-type equation with the difference that the bounda...

A theory of the fluctuation-induced Nernst effect is developed for a two-dimensional superconductor in a perpendicular magnetic field. First, we derive a simple phenomenological formula for the Nernst coefficient, which naturally explains the giant Nernst signal due to fluctuating Cooper pairs. The latter signal is shown to be large even far from the transition and may exceed by orders of magni...

Following the observation of an anomalous Nernst signal in cuprates, the Nernst effect has been explored in a variety of metals and superconductors during the past few years. This paper reviews the results obtained during this exploration, focusing on the Nernst response of normal quasi-particles as opposed to the one generated by superconducting vortices or by short-lived Cooper pairs. Contrar...

After a brief review of current ideas on stripe order in cuprate high-temperature superconductors, we discuss the quasiparticle Nernst effect in cuprates, with focus on its evolution in non-superconducting stripe and related nematic states. In general, we find the Nernst signal to be strongly enhanced by nearby van-Hove singularities and Lifshitz transitions in the band structure, implying that...

The Nernst effect of Pr 2−x Ce x CuO 4 (x=0.13, 0.15, and 0.17) has been measured on thin film samples between 5-120 K and 0-14 T. In comparison to recent measurements on hole-doped cuprates that showed an anomalously large Nernst effect above the resistive T c and H c2 [1–4], we find a normal Nernst effect above T c and H c2 for all dopings. The H c2 (T) determined from the Nernst effect shows...

Experiments on underdoped cuprate superconductors suggest an intricate relation between the normal-state Nernst effect and stripe order: The Nernst signal appears enhanced near 1/8 hole doping and its onset temperature scales with the stripe-ordering temperature over some range of doping. Here, we employ a phenomenological quasiparticle model to calculate the normal-state Nernst signal in the p...

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems,...

A voltammetric method has been developed for the determination of acid dissociation constant (pKa) (RfSO2)2CHR (Rf = perfluoroalkyl), which is a strongly acidic molecule that serves as an catalyst. In acetonitrile solution containing small quantity acid, reduction peak potential quinone caused by shifted to more positive side accompanied increase in acidity acid. This relationship was good agre...

The relationships of concentration gradients to electropotential gradients resulting from passive diffusion processes, after equilibration, are described by the Nernst equation. The primary criterion for the hypothesis that any given ion is actively transported is to establish that it is not diffusing passively. A test was made of how closely the Nernst equation describes the electrochemical eq...

The Nernst formulation of the third law of ordinary thermodynamics (often referred to as the “Nernst theorem”) asserts that the entropy, S, of a system must go to zero (or a “universal constant”) as its temperature, T , goes to zero. This assertion is commonly considered to be a fundamental law of thermodynamics. As such, it seems to spoil the otherwise perfect analogy between the ordinary laws...