Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs

The classical Hodgkin--Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. We study slow dynamics in an extended HH framework that includes time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. Ion gain and loss of the system is identified as a bifurcation parameter whose essential importance was not realized in earlier studies. Our systematic study of the bifurcation structure and thus the phase space structure helps to understand activation and inhibition of a new excitability in ion homeostasis which emerges in such extended models. Also modulatory mechanisms that regulate the spiking rate can be explained by bifurcations. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.Comment: 18 pages, 11 figure

Three-color Sagnac source of polarization-entangled photon pairs

We demonstrate a compact and stable source of polarization-entangled pairs of photons, one at 810 nm wavelength for high detection efficiency and the other at 1550 nm for long-distance fiber communication networks. Due to a novel Sagnac-based design of the interferometer no active stabilization is needed. Using only one 30 mm ppKTP bulk crystal the source produces photons with a spectral brightness of 1.13x10^6 pairs/s/mW/THz with an entanglement fidelity of 98.2%. Both photons are single-mode fiber coupled and ready to be used in quantum key distribution (QKD) or transmission of photonic quantum states over large distances.Comment: 7 pages, 4 figure

Bistable dynamics underlying excitability of ion homeostasis in neuron models

When neurons fire action potentials, dissipation of free energy is usually not directly considered, because the change in free energy is often negligible compared to the immense reservoir stored in neural transmembrane ion gradients and the long-term energy requirements are met through chemical energy, i.e., metabolism. However, these gradients can temporarily nearly vanish in neurological diseases, such as migraine and stroke, and in traumatic brain injury from concussions to severe injuries. We study biophysical neuron models based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent ion concentrations inside and outside the cell and metabolic energy-driven pumps. We reveal the basic mechanism of a state of free energy-starvation (FES) with bifurcation analyses showing that ion dynamics is for a large range of pump rates bistable without contact to an ion bath. This is interpreted as a threshold reduction of a new fundamental mechanism of 'ionic excitability' that causes a long-lasting but transient FES as observed in pathological states. We can in particular conclude that a coupling of extracellular ion concentrations to a large glial-vascular bath can take a role as an inhibitory mechanism crucial in ion homeostasis, while the Na$^+$/K$^+$ pumps alone are insufficient to recover from FES. Our results provide the missing link between the HH formalism and activator-inhibitor models that have been successfully used for modeling migraine phenotypes, and therefore will allow us to validate the hypothesis that migraine symptoms are explained by disturbed function in ion channel subunits, Na$^+$/K$^+$ pumps, and other proteins that regulate ion homeostasis.Comment: 14 pages, 8 figures, 4 table

On the optimality of individual entangling-probe attacks against BB84 quantum key distribution

It is shown that an existing method to study ideal individual attacks on the BB84 QKD protocol using error discard can be adapted to reconciliation with error correction, and that an optimal attack can be explicitly found. Moreover, this attack fills Luetkenhaus bound, independently of whether error positions are leaked to Eve, proving that it is tight. In addition, we clarify why the existence of such optimal attacks is not in contradiction with the established ``old-style'' theory of BB84 individual attacks, as incorrectly suggested recently in a news feature.Comment: 12 pages, 3 figure

Superdeformation and hyperdeformation in the 108^{108}Cd nucleus

The superdeformation and hyperdeformation in $^{108}$Cd have been studied for the first time within the framework of the fully self-consistent cranked mean field theory, namely, cranked relativistic mean field theory. The structure of observed superdeformed bands 1 and 2 have been analyzed in detail. The bumps seen in their dynamic moments of inertia are explained as arising from unpaired band crossings. This is contrary to an explanation given earlier within the framework of projected shell model. It was also concluded that this nucleus is not doubly magic SD nucleus

Correlated electron tunneling through two separate quantum dot systems with strong capacitive interdot coupling

A system consisting of two independently contacted quantum dots with strong electrostatic interaction shows interdot Coulomb blockade when the dots are weakly tunnel coupled to their leads. It is studied experimentally how the blockade can be overcome by correlated tunneling when tunnel coupling to the leads increases. The experimental results are compared with numerical renormalization group calculations using predefined (measured) parameters. Our results indicate Kondo correlations due to the electrostatic interaction in this double quantum dot system.Comment: 5 pages, 3 figures, published in Phys. Rev. Lett. Oct. 30t