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1
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Zero Temperature Phase Diagram of a d-Wave Superconductor with Anderson Impurities

100%
Borkowski L.
Acta Physica Polonica A
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2009
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vol. 115
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issue 1
120-122
EN
We study the model of a d-wave superconductor interacting with finite concentration of the 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.
2
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Response of the Hodgkin-Huxley Neuron to a Periodic Sequence of Biphasic Pulses

100%
Borkowski L.
|
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vol. 125
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issue 1
145-154
EN
Electric stimulation of various parts of the nervous system is a widely used therapeutic method and a principle of operation of prosthetic devices. Its usefulness has been proven in areas such as treatment of neurological disorders and cochlear prostheses. However the dynamic mechanisms underlying these applications are not well understood. In order to shed some light on this problem we study the response of the Hodgkin-Huxley neuron subject to periodic train of biphasic rectangular current pulses. One of the simpler ways to understand the behavior of such a nonlinear system is the analysis of the global bifurcation diagram in the period-amplitude plane. For short pulses the topology of this diagram is approximately invariant with respect to the pulse polarity and shape details. The lowest excitation threshold for charge-balanced input was obtained for cathodic-first pulses with an inter-phase gap approximately equal to 5 ms. The firing rate of the Hodgkin-Huxley neuron stimulated at the frequency of its natural resonance is a square root function of the pulse amplitude. At nonresonant frequencies the quiescent state and the firing state coexist and transition to firing is a discontinuous one. We found a multimodal transition in the regime of irregular firing between the 2:1 and 3:1 locked-in states. This transition separates the regime of odd-only multiples of the stimulus period from the regime where modes of both parities participate in the response. A strong antiresonant effect was found between the states 3:1 and 4:1, where the modes (2 + 3n) : 1, where n=0,1,2,..., were entirely absent. The antiresonant effects at high stimulation frequency, such as multimodal transition, may provide an explanation for the therapeutic mechanism of deep brain stimulation.
3
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Multimodal Transition and Excitability of a Neural Oscillator

100%
Borkowski L.
Acta Physica Polonica A
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2012
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vol. 122
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issue 4
776-780
EN
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 the Hodgkin 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.
4
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Thin Film of a Superfluid Fermi System in a Magnetic Field

63%
Harań G., Borkowski L.
Acta Physica Polonica A
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1991
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vol. 80
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issue 1
47-60
EN
We study the problem of a thin film of neutral fermions in the presence of a magnetic field and scattering on random, uncorrelated irregularities at the boundaries of the film. An attractive interaction of s-wave type is assumed. We solve the equation for the energy gap and demonstrate its dependence on both the field and the scattering strength. The phase diagram is found. There exists a critical point (T_{c}^{*}, H_{c}^{*}). For temperatures below T_{c}^{*} the phase transition is of the first order and of the second order above it. As expected, the surface scattering significantly reduces the values of the critical field and temperature T_{c}. The critical point changes its position with increasing scattering rate but is not removed from the phase diagram until superfluidity is destroyed.
5
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Spatial Dependence of Magnetization and Gaussian Fluctuations of Molecular Field in an Ising Nanopyramid Interacting with the Substrate

63%
Borkowski L., Jacyna-Onyszkiewicz Z.
Acta Physica Polonica A
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2009
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vol. 115
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issue 1
375-377
EN
We study thermodynamic properties of an Ising model of a ferromagnetic nanoscopic pyramid deposited on a ferromagnetic bulk substrate. The influence of the interaction between the pyramid and the substrate is calculated in terms of the reduced-state (density) operator used for description of thermodynamic properties of nanoscopic systems. The spatial distribution of magnetization in the nanopyramid is obtained in the Gaussian fluctuations approximation.
6
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Evolution from the BCS to the Bose-Einstein Limit in a d-Wave Superconductor at T=0

63%
Borkowski L., Sá de Melo C.
Acta Physica Polonica A
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2001
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vol. 99
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issue 6
691-698
EN
We study the evolution from BCS to Bose limit in a two-dimensional d-wave superconductor at zero temperature and low density of charge carriers within the mean-field theory. We examine single quasiparticle properties when particle density and attraction strength are varied. For sufficiently high interaction strength there is a critical density below which the system has a gap. The spectral and thermodynamic properties of the system do not evolve smoothly from the BCS-like to the Bose-like regime.
7
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Spatial Distribution of Magnetization in the Pyramid-Like Ising Nanoscopic System Interacting with the Substrate

63%
Borkowski L., Jacyna-Onyszkiewicz Z.
Acta Physica Polonica A
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2007
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vol. 112
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issue 6
1223-1230
EN
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 substrateis calculated in terms of the reduced-state (density) operator used for description of thermodynamic properties of nanoscopic systems. The spatial distribution of the magnetization in the nanoscopic pyramid is obtained in the molecular field approximation.
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