On Dielectric Constants and Magnetic Susceptibilities in the New Quantum Mechanics Part III—Application to Dia- and Paramagnetism

1928 ◽  
Vol 31 (4) ◽  
pp. 587-613 ◽  
Author(s):  
J. H. Van Vleck
Keyword(s):  
Quantum Mechanics ◽  
Dielectric Constants ◽  
Magnetic Susceptibilities

scholarly journals Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 125
Author(s):  
Tobias Gulden ◽  
Alex Kamenev
Keyword(s):  
Quantum Mechanics ◽  
Algebraic Topology ◽  
Riemann Surfaces ◽  
Surrounding Medium ◽  
Coulomb Systems ◽  
Dielectric Constants ◽  
Ion Interactions ◽  
Multivalent Ions ◽  
Electric Filed ◽  
Entropic Effects

We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.

scholarly journals The rotation of molecules in fields of octahedral symmetry

1936 ◽  
Vol 153 (880) ◽  
pp. 601-621 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Potential Energy ◽  
Potential Field ◽  
Rotational Energy ◽  
Dielectric Constants ◽  
Mathematical Treatment ◽  
Octahedral Symmetry ◽  
Specific Heats ◽  
Angular Coordinate ◽  
Energy States

A problem in quantum mechanics which has important applications in the theory of specific heats and dielectric constants of solids, is that of determining the rotational energy states of a molecule in a potential field, such as occurs in a crystal. A mathematical treatment of the rotation of molecules in crystals was first given by Pauling, and the theory has since been extended by several other authors. In these discussions, however, either the potential energy has been assumed to depend only on one angular coordinate or the term involving the second angular coordinate has been supposed to be sufficiently small to be treated as a perturbation.

Electron microscopy studies of PZT ferroelectric film capacitor structures

1992 ◽  
Vol 50 (2) ◽  
pp. 1364-1365
Author(s):  
V. Kaushik ◽  
P. Maniar ◽  
J. Olowolafe ◽  
R. Jones ◽  
A. Campbell ◽  
...  
Keyword(s):  
Electric Fields ◽  
Sol Gel ◽  
Ferroelectric Material ◽  
Dielectric Constants ◽  
Dielectric Films ◽  
Lead Zirconium Titanate ◽  
Si Substrate ◽  
Film Capacitor ◽  
Pzt Films ◽  
High Dielectric

Lead zirconium titanate films (Pb (Zr,Ti) O3 or PZT) are being considered for potential application as dielectric films in memory technology due to their high dielectric constants. PZT is a ferroelectric material which shows spontaneous polarizability, reversible under applied electric fields. We report herein some results of TEM studies on thin film capacitor structures containing PZT films with platinum-titanium electrodes.The wafers had a stacked structure consisting of PZT/Pt/Ti/SiO2/Si substrate as shown in Figure 1. Platinum acts as electrode material and titanium is used to overcome the problem of platinum adhesion to the oxide layer. The PZT (0/20/80) films were deposited using a sol-gel method and the structure was annealed at 650°C and 800°C for 30 min in an oxygen ambient. XTEM imaging was done at 200KV with the electron beam parallel to <110> zone axis of silicon.Figure 2 shows the PZT and Pt layers only, since the structure had a tendency to peel off at the Ti-Pt interface during TEM sample preparation.

The need of electron microscopy in the study of domains and domain walls in ferroelectrics

1994 ◽  
Vol 52 ◽  
pp. 550-551
Author(s):  
Wenwu Cao
Keyword(s):  
Domain Wall ◽  
Domain Walls ◽  
High Mobility ◽  
Continuum Theory ◽  
Polarization Vector ◽  
Ferroelectric Materials ◽  
Dielectric Constants ◽  
Nonlocal Coupling ◽  
Cubic Symmetry ◽  
Gradient Energy

Domain structures play a key role in determining the physical properties of ferroelectric materials. The formation of these ferroelectric domains and domain walls are determined by the intrinsic nonlinearity and the nonlocal coupling of the polarization. Analogous to soliton excitations, domain walls can have high mobility when the domain wall energy is high. The domain wall can be describes by a continuum theory owning to the long range nature of the dipole-dipole interactions in ferroelectrics. The simplest form for the Landau energy is the so called ϕ model which can be used to describe a second order phase transition from a cubic prototype,where Pi (i =1, 2, 3) are the components of polarization vector, α's are the linear and nonlinear dielectric constants. In order to take into account the nonlocal coupling, a gradient energy should be included, for cubic symmetry the gradient energy is given by,

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