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Stochastic Dynamics of Electrical Membrane with Voltage-Dependent Ion Channel Fluctuations
Brownian ratchet like stochastic theory for the electrochemical membrane
system of Hodgkin-Huxley (HH) is developed. The system is characterized by a
continuous variable , representing mobile membrane charge density, and
a discrete variable representing ion channel conformational dynamics. A
Nernst-Planck-Nyquist-Johnson type equilibrium is obtained when multiple
conducting ions have a common reversal potential. Detailed balance yields a
previously unknown relation between the channel switching rates and membrane
capacitance, bypassing Eyring-type explicit treatment of gating charge
kinetics. From a molecular structural standpoint, membrane charge is a
more natural dynamic variable than potential ; our formalism treats
-dependent conformational transition rates as intrinsic
parameters. Therefore in principle, vs. is experimental
protocol dependent,e.g., different from voltage or charge clamping
measurements. For constant membrane capacitance per unit area and
neglecting membrane potential induced by gating charges, , and
HH's formalism is recovered. The presence of two types of ions, with different
channels and reversal potentials, gives rise to a nonequilibrium steady state
with positive entropy production . For rapidly fluctuating channels, an
expression for is obtained.Comment: 8 pages, two figure
Angular Momentum of Phonons and Einstein-de Haas Effect
We study angular momentum of phonons in a magnetic crystal. In the presence
of a spin-phonon interaction, we obtain a nonzero angular momentum of phonons,
which is an odd function of magnetization. At zero temperature, phonon has a
zero-point angular momentum besides a zero-point energy. With increasing
temperature, the total phonon angular momentum diminishes and approaches to
zero in the classical limit. The nonzero phonon angular momentum can have a
significant impact on the Einstein-de Haas effect. To obtain the change of
angular momentum of electrons, the change of phonon angular momentum needs to
be subtracted from the opposite change of lattice angular momentum.
Furthermore, the finding of phonon angular momentum gives a potential method to
study the spin-phonon interaction. Possible experiments on phonon angular
momentum are also discussed.Comment: Accepted by Phys. Rev. Lett. Detailed supplementary file is include
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