Gebhard Grübl

Determination of cell membrane resistance in cultured renal epithelioid (MDCK) cells: effects of cadmium and mercury ions

Previous studies have indicated that the cell membrane of Madin Darby Canine Kidney (MDCK) cells is hyperpolarized by a number of hormones and trace elements, in parallel with an enhancement of potassium selectivity. Without knowledge of the cell membrane resistance (Rm), however, any translation of potassium selectivity into potassium conductance remains equivocal. The present study was performed to determine the Rm of MDCK cells by cellular cable analysis. To this end, three microelectrodes were impaled into three different cells of a cell cluster; current was injected via one microelectrode and the corresponding voltage deflections measured by the other two microelectrodes. In order to extract the required specific resistances, the experimental data were analysed mathematically in terms of an electrodynamical model derived from Maxwells equations. As a result, a mean Rm of 2.0±0.2 kΩcm2 and an intercellular coupling resistance (Rc) of 6.1±0.8 MΩ were obtained at a mean potential difference across the cell membrane of -47.0±0.6 mV. An increase of the extracellular K+ concentration from 5.4 to 20 mmol/l depolarized the cell membrane by 16.2±0.5 mV and decreased Rm by 30.6±3.0%; 1 mmol/l barium depolarized the cell membrane by 20.1±1.1 mV and increased Rm by 75.9±14.3%. Omission of extracellular bicarbonate and carbon dioxide at constant extracellular pH caused a transient hyperpolarization (up to −60.4±1.4 mV), a decrease of Rm (by 75±4.5%) and a decrease of Rc (by 23.1±8.4%). The changes in Rm and Rc were probably the result of intracellular alkalosis. Cadmium ions (1 μmol/l) led to a sustained, reversible hyperpolarization (to −64.8±1.3 mV) and to a decrease of Rm (by 77.0±2.7%); mercury ions (1 μmol/l) cause a sustained hyperpolarization (to −60.1±1.2 mV) and a decrease of Rm (by 76.3±3.9%). Neither manoeuvre significantly altered Rc. We have previously shown that both cadmium and mercury hyperpolarize the cell membrane potential and increase its potassium selectivity; the decrease of the Rm observed in the present study indicates that these effects are due to an increase of the potassium-selective conductance of the cell membrane.

Time of arrival from Bohmian flow

We develop a new conception for the quantum mechanical arrival time distribution from the perspective of Bohmian mechanics. A detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated. Basic positivity and monotonicity properties are established. We show that our detection probability improves and generalizes an earlier proposal by Leavens and McKinnon. The difference between the two notions is illustrated through application to a free wavepacket.

Fock space construction of the massless dipole field

Abstract We construct the Fock space representation of the free massless scalar dipole field in terms of creation and annihilation operators for the eigenvectors of the momentum operator. The Poincare group is implemented unitarily only on a subspace of the full (positive metric) Hilbert space. The subspace possesses a hermitean, local, irreducible scalar field constructed out of the (non-hermitean) dipole field. Thus this subspace is a perfect candidate for a physical subspace of observable particles. We show that this possibility is however excluded by the fact that these particles interact with an external c-number source in a manner that violates unitarity. We illustrate our construction by applying it to the linearized Higgs model with external c-number source and examine the (non-trivial) dynamics of the dipole degrees of freedom in this case. An explicit separation of the physical degrees of freedom from the unphysical ones is presented for this interacting model.

A new approach to quantum backflow

We derive some rigorous results concerning the backflow operator introduced by Bracken and Melloy. We show that it is linear bounded, self-adjoint and non-compact. Thus the question is underlined whether the backflow constant is an eigenvalue of the backflow operator. From the position representation of the backflow operator, we obtain a more efficient method to determine the backflow constant. Finally, detailed position probability flow properties of a numerical approximation to the (perhaps improper) wavefunction of maximal backflow are displayed.

The quantum measurement problem enhanced

The quantum measurement problem as formalised by Bassi and Ghirardi [Phys. Lett. A 275 (2000) 373] without taking recourse to sharp apparatus observables is extended to cover impure initial states.

Bohmian trajectories and Klein's paradox

We compute the Bohmian trajectories of the incoming scattering plane waves for Kleins potential step in explicit form. For finite norm incoming scattering solutions we derive their asymptotic space-time localization and we compute some Bohmian trajectories numerically. The paradox, which appears in the traditional treatments of the problem based on the outgoing scattering asymptotics, is absent.

Fleming's bound for the decay of mixed states

Flemings inequality is generalized to the decay function of mixed states. We show that for any symmetric Hamiltonian h and for any density operator ρ on a finite-dimensional Hilbert space with the orthogonal projection Π onto the range of ρ the estimate holds for all t with (Δh)ρ|t| ≤ π/2. We show that equality either holds for all or it does not hold for a single t with 0 < (Δh)ρ|t| ≤ π/2. All the density operators saturating the bound for all , i.e. the mixed intelligent states, are determined.

Bohmian arrival time without trajectories

The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wavefunction Ψ and its spatial derivative ∂xΨ, both restricted to the boundary of the detectors spacetime volume, is derived for the general case, where the probability current at the detectors boundary may vary its sign.

Dynamical squeezing in quantum mechanics

The time evolution orbits of Gaussian vectors under a harmonic oscillator dynamics are computed and discussed. The generic case is shown to be this: a minimum uncertainty vector which is coherent with respect to a harmonic oscillator Hamiltonian with smaller frequency than the one of the driving Hamiltonian, evolves into a minimum uncertainty vector with reduced position variance for exactly two discrete instants of time per period. The results are applied to the case of a perturbing frequency jump in the driving harmonic oscillator Hamiltonian. The total transition probability to the excited (unperturbed) oscillator levels from the ground-state vector is computed.

Times of arrival: Bohm beats Kijowski

We prove that the Bohmian arrival time of the one-dimensional Schrodinger evolution violates the quadratic form structure on which Kijowskis axiomatic treatment of arrival times is based. Within Kijowskis framework, for a free right moving wave packet Ψ, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time . We derive the inequality relating the average Bohmian arrival time to that of Kijowksi. We prove that if and only if Ψ leads to position probability backflow through x.