I am interested in the condensed matter theory and in the theoretical neuroscience with applications to real biological systems.

My recent work in condensed matter is focused on magnetic impurities in superconductors of mixed order parameter symmetry. The most interesting behavior occurs in the case when the s-wave component of the order parameter is subdominant, as may occur e.g. in some high-temperature superconductors. At very low temperature the density of states near the Fermi level undergoes a discontinuous transition as a function of some parameter other than temperature. This has a strong effect on all low energy properties.

I also study the nonlinear dynamics of neurons and neural systems. These are strongly nonlinear systems with rich internal dynamics, chaos, multimodal response, resonance and the ability to perform nontrivial transformations of incoming signals. Even seemingly simple models lead to surprising outcomes. One of such surprises is a **multimodal transition** involving the change of parity of response modes in a periodically stimulated resonant neuron. I discovered the transition, Phys. Rev. E 80, 051914 (2009), and analyzed it in a subsequent series of papers. I also showed by comparing results of theoretical calculations to experimental data of a Japanese group *N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G. Matsumoto, P hysica D 43, 318 (1990),*

L. S. Borkowski

Magnetic impurity-induced states in the gap of an s± superconductor
Phys. Stat. Sol. B **250**, 615 (2013)

L. S. Borkowski

Acta Phys. Pol. A **122**, 776 (2012)

L. S. Borkowski

L. S. Borkowski

Phys. Rev. E **83**, 051901 (2011)

L. S. Borkowski

Multimodal transition and stochastic antiresonance in squid giant axons

Phys. Rev. E

URL:

DOI:

10.1103/PhysRevE.82.041909

Abstract

L. S. Borkowski

Magnetic impurity transition in a (d+s)-wave superconductor

Phys. Status Solidi B**247**, 602–604 (2010)

L. S. Borkowski

Magnetic impurity transition in a (d+s)-wave superconductor

Phys. Status Solidi B

Abstract

*This monograph describes the dynamics of the Hodgkin-Huxley neurons stimulated by periodic and stochastic stimuli. In the high frequency regime there is a multimodal transition between the odd-only modes and the state with both odd and even modes. This singularity appears in the presence of noise as a stochastic anti-resonance. The competition of different parity modes is reflected also in the structure of the resonances, where even and odd phase-locked states are separated by crossover regimes. The boundaries between various mode-locked states form complicated patterns. The relation between the output frequency and stimulus amplitude near the excitation threshold is often continuous even in the absence of noise. Models of regular spiking excitatory and inhibitory cells of mammalian cortex are also studied within this framework. The obtained high variability of response agrees with experiments in vivo.*

Title page

Table of contents

pages 1-70

pages 71-78
**DOI**:10.1186/1471-2202-10-S1-P250
L. S. Borkowski

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

Phys. Rev. E 80, 051914 (2009)
**DOI**: 10.1088/1742-6596/150/5/052023

L. S. Borkowski and Z. Jacyna-Onyszkiewicz

Spatial distribution of Gaussian fluctuations of the molecular field and magnetization in the pyramid-like Ising nanoscopic system interacting with the substrate**DOI**:10.1016/j.susc.2008.10.028

L. S. Borkowski and Z. Jacyna-Onyszkiewicz

Spatial distribution of magnetization in the pyramid-like Ising nanoscopic system interacting with the substrate

Acta Phys. Pol. A**112**, 1223-1230 (2007)

L. S. Borkowski

Nonlinear dynamics of Hodgkin-Huxley neurons

Wydawnictwo Naukowe UAM, Poznan (2010) (*Adam Mickiewicz University Press*)

ISBN 978-83-232-2106-7

78 pages, 71 figures

Title page

Table of contents

pages 1-70

pages 71-78

Color version of Fig. 3.9 from the monograph.

The blue color refers to k=5:2, yellow refers to k=3, red refers to k=4.

L. S. Borkowski

BMC Neuroscience 2009, **10**(Suppl 1):P250

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

Phys. Rev. E 80, 051914 (2009)

DOI:

10.1103/PhysRevE.80.051914

Abstract

L. S. Borkowski

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

Acta Phys. Pol. A**115**, 120-122 (2009)

L. S. Borkowski

Density of states of s+d-wave superconductor with Anderson impurities

Journal of Physics: Conference Series**150** (2009) 052023

L. S. Borkowski

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

Acta Phys. Pol. A

L. S. Borkowski

Density of states of s+d-wave superconductor with Anderson impurities

Journal of Physics: Conference Series

L. S. Borkowski and Z. Jacyna-Onyszkiewicz

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

Surf. Sci. **603**, 27-32 (2009)

L. S. Borkowski

Phase diagram of a d-wave superconductor with Anderson impurities

Phys. Rev. B**78**, 020507(R) (2008)

Phase diagram of a d-wave superconductor with Anderson impurities

Phys. Rev. B

DOI:

10.1103/PhysRevB.78.020507

L. S. Borkowski and Z. Jacyna-Onyszkiewicz

Spatial distribution of magnetization in the pyramid-like Ising nanoscopic system interacting with the substrate

Acta Phys. Pol. A