arXiv subjects

L. S. Borkowski

Publications and source records attributed to L. S. Borkowski.

14 recordsLinked to original sources

arXiv2013

Response of the Hodgkin-Huxley neuron to a periodic sequence of biphasic pulses

We study the response of the Hodgkin-Huxley neuron stimulated periodically by biphasic rectangular current pulses. The optimal response for charge-balanced input is obtained for cathodic-first pulses with an inter-phase gap (IPG) approximately equal 5 ms. For short pulses the topology of the global bifurcation diagram in the period-amplitude plane is approximately invariant with respect to the pulse polarity and shape details. If stimuli are delivered at neuron's resonant frequencies the firing rate is a continuous function of pulse amplitude. At nonresonant frequencies the quiescent state and the firing state coexist over a range of amplitude values and the transition to excitability is a discontinuous one. There is a multimodal odd-all transition between the 2:1 and 3:1 locked-in states. A strong antiresonant effect is found between the states 3:1 and 4:1, where the modes (2+3n):1, $n=0,1,2,...$, are entirely absent. At high frequencies the excitation threshold is a nonmonotonic function of the stimulus and the perithreshold region is bistable, with the quiescent state coexisting with either a regular or chaotic firing.

physics.bio-ph↗

arXiv2012

Multimodal transition and excitability of a neural oscillator

We analyze the response of the Morris-Lecar model to a periodic train of short current pulses in the period-amplitude plane. For a wide parameter range encompassing both class 2 and class 3 behavior in Hodgkin's classification there is a multimodal transition between the set of odd modes and the set of all modes. It is located between the 2:1 and 3:1 locked-in regions. It is the same dynamic instability as the one discovered earlier in the Hodgkin-Huxley model and observed experimentally in squid giant axons. It appears simultaneously with the bistability of the states 2:1 and 3:1 in the perithreshold regime. These results imply that the multimodal transition may be a universal property of resonant neurons.

physics.bio-ph↗

arXiv2011

Bistability and resonance in the periodically stimulated Hodgkin-Huxley model with noise

We describe general characteristics of the Hodgkin-Huxley neuron's response to a periodic train of short current pulses with Gaussian noise. The deterministic neuron is bistable for antiresonant frequencies. When the stimuli arrive at the resonant frequency the firing rate is a continuous function of the current amplitude $I_0$ and scales as $(I_0-I_{th})^{1/2}$, where $I_{th}$ is an approximate threshold. Intervals of continuous irregular response alternate with integer mode-locked regions with bistable excitation edge. There is an even-all multimodal transition between the 2:1 and 3:1 states in the vicinity of the main resonance, which is analogous to the odd-all transition discovered earlier in the high-frequency regime. For $I_0<I_{th}$ and small noise the firing rate has a maximum at the resonant frequency. For larger noise and subthreshold stimulation the maximum firing rate initially shifts towards lower frequencies, then returns to higher frequencies in the limit of large noise. The stochastic coherence antiresonance, defined as the maximum of the coefficient of variation as a function of noise intensity, occurs over a wide range of parameter values, including monostable regions.

physics.bio-ph↗

arXiv2010

Multimodal transition and stochastic antiresonance in squid giant axons

The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G. Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude $I_0$ in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is highly sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs. $I_0$ for above the transition is also confirmed.

physics.bio-ph↗

arXiv2010

Response of a Hodgkin-Huxley neuron to a high-frequency input

We study the response of a Hodgkin-Huxley neuron stimulated by a periodic sequence of conductance pulses arriving through the synapse in the high frequency regime. In addition to the usual excitation threshold there is a smooth crossover from the firing to the silent regime for increasing pulse amplitude $g_{syn}$. The amplitude of the voltage spikes decreases approximately linearly with $g_{syn}$. In some regions of parameter space the response is irregular, probably chaotic. In the chaotic regime between the mode-locked regions 3:1 and 2:1 near the lower excitation threshold the output interspike interval histogram (ISIH) undergoes a sharp transition. If the driving period is below the critical value, $T_i < T^*$, the output histogram contains only odd multiples of $T_i$. For $T_i > T^*$ even multiples of $T_i$ also appear in the histogram, starting from the largest values. Near $T^*$ the ISIH scales logarithmically on both sides of the transition. The coefficient of variation of ISIH has a cusp singularity at $T^*$. The average response period has a maximum slightly above $T^*$. Near the excitation threshold in the chaotic regime the average firing rate rises sublinearly from frequencies of order 1 Hz.

physics.bio-ph↗

arXiv2010

Distinguishing d-wave from highly anisotropic s-wave superconductors

Systematic impurity doping in the Cu-O plane of the hole-doped cuprate superconductors may allow one to decide between unconvention al ("d-wave") and anisotropic conventional ("s-wave") states as possible candidates for the order parameter in these materials. We show that potential scattering of any strength always increases the gap minima of such s-wave states, leading to activated behavior in temperature with characteristic impurity concentration dependence in observable quantities such as the penetration depth. A magnetic component to the scattering may destroy the energy gap and give rise to conventional gapless behavior, or lead to a nonmonotonic dependence of the gap on impurity concentration. We discuss how experiments constrain this analysis.

cond-mat↗

arXiv2009

Magnetic impurity transition in a 'd+s'-wave superconductor

We consider the superconducting state of $d+s$ symmetry with finite concentration of Anderson impurities in the limit $Δ_s/Δ_d \ll 1$. The model consists of a BCS-like term in the Hamiltonian and the Anderson impurity treated in the self-consistent large-$N$ mean field approximation. Increasing impurity concentration or lowering the ratio $Δ_s/Δ_d$ drives the system through a transition from a state with two sharp peaks at low energies and exponentially small density of states at the Fermi level to one with $N(0) \simeq (Δ_s/Δ_d)^2$. This transition is discontinuous if the energy of the impurity resonance is the smallest energy scale in the problem.

cond-mat.supr-con↗

arXiv2009

Spatial distribution of Gaussian fluctuations of the molecular field and magnetization in the pyramid-like Ising nanoscopic system interacting with the substrate

We study thermodynamic properties of an Ising model of a ferromagnetic nanoscopic pyramid deposited onto a ferromagnetic bulk substrate. The influence of the interaction between the pyramid and the substrate is calculated in terms of the equilibrium reduced-state (density) operator used for description of thermodynamic properties of nanoscopic systems. The spatial distribution of the fluctuations of molecular field and magnetization in the nanoscopic pyramid is obtained in the Gaussian fluctuations approximation. Experimental consequences for the magnetic force measurements are briefly discussed.

cond-mat.other↗

arXiv2008

Zero temperature phase diagram of a d-wave superconductor with Anderson impurities

We study the model of a d-wave superconductor interacting with finite concentration of Anderson impurities at zero temperature. The interaction between impurity and conduction electrons is taken into account within the large-$N$ approximation. We discuss the obtained phase diagram and its dependence on the main energy scales.

cond-mat.supr-con↗

arXiv1998

From BCS to BEC Superconductivity: Spectroscopic Consequences

The evolution from BCS to BEC superconductivity in the s-wave and d-wave channels is analyzed at zero temperature for a two-dimensional superconductor. Spectroscopic quantities for s-wave and d-wave systems present fundamental differences when particle density and attraction strength are varied. A detailed analysis of single quasiparticle properties (excitation spectrum, momentum distribution, spectral function and density of states) indicates that the evolution of these spectroscopic quantities in the d-wave case is not smooth, unlike the situation encountered for the s-wave system.

cond-mat.supr-con↗

arXiv1996

On Magnetic Impurities in Gapless Fermi Systems

In ordinary metals, antiferromagnetic exchange between conduction electrons and a magnetic impurity leads to screening of the impurity spin below the Kondo temperature, $T_K$. In systems such as semimetals, small-gap semiconductors and unconventional superconductors, a reduction in available conduction states near the chemical potential can greatly depress $T_K$. The behavior of an Anderson impurity in a model with a power-law density of states, $N(ε) \sim |ε|^r$, $r>0$, for $|ε| < Δ$, where $Δ\ll D$, is studied using the non-crossing approximation. The transition from the Kondo singlet to the magnetic ground state can be seen in the behavior of the impurity magnetic susceptibility $χ$. The product $Tχ$ saturates at a finite value at low temperature for coupling smaller than the critical one. For sufficiently large coupling $Tχ\to 0$, as $T \to 0$, indicating complete screening of the impurity spin.

cond-mat↗

arXiv1995

Transport Properties of "Extended-s" State Superconductors

Superconducting states with "extended s-wave" symmetry have been suggested in connection with recent ARPES experiments on BSCCO. In the presence of impurities, thermodynamic properties of such states reflect a residual density of states $N(0)$ for a range of concentrations. While properties reflecting $N(ω)$ alone will be similar to those of d-wave states, transport measurements may be shown to qualitatively distinguish between the two. In contrast to the d-wave case with unitarity limit scattering, limiting low-temperature residual conductivities in the s-wave state are large and scale inversely with impurity concentration.

cond-mat↗

arXiv1994

Multichannel Kondo impurities in superconductors

We discuss the effect of multichannel Kondo impurities on superconductivity. In the strong coupling regime such impurities are pairbreakers, in contrast to the ordinary Kondo effect. Measurements of $T_c$-suppression may help in identifying impurities displaying this more exotic exchange coupling to the conduction band.

cond-mat↗

arXiv1994

Low Temperature Properties of Anisotropic Superconductors with Kondo Impurities

We present a self-consistent theory of superconductors in the presence of Kondo impurities, using large-$N$ slave-boson methods to treat the impurity dynamics. The technique is tested on the s-wave case and shown to give good results compared to other methods for $T_K > T_c$. We calculate low temperature thermodynamic and transport properties for various superconducting states, including isotropic s-wave and representative anisotropic model states with line and point nodes on the Fermi surface.

cond-mat↗