arXiv subjects

A. A. Koulakov

Publications and source records attributed to A. A. Koulakov.

11 recordsLinked to original sources

arXiv2005

Complete structure of topographic maps in ephrin-A deficient mice

Axons of retinal ganglion cells establish orderly projections to the superior colliculus of the midbrain. Axons of neighboring cells terminate proximally in the superior colliculus thus forming a topographically precise representation of the visual world. Coordinate axes are encoded in retina and in the target through graded expression of chemical labels. Mapping based on chemical labels alone does not yield required specificity of connections. Additional sharpening is provided by electrical activity, which is correlated between neighboring axons. Here we propose a quantitative model which allows combining the effects of chemical labels and correlated activity in a single approach. Using this model we study a complete structure of two-dimensional topographic maps in mutant mice, in which one of the labels, encoding horizontal retinal coordinate (ephrin-A), is reduced/eliminated. We show that topographic maps in ephrin-A deficient mice display granular structure, with the regions of smooth mapping separated by linear discontinuities reminiscent of fractures observed in the maps of preferred orientation. We also demonstrate the presence of point singularities in topographic maps.

q-bio.NC↗

arXiv2003

A classical model for the negative dc conductivity of ac-driven 2D electrons near the cyclotron resonance

A classical model for {\em dc} transport of two dimensional electrons in a perpendicular magnetic field and under strong irradiation is considered. We demonstrate that, near the cyclotron resonance condition, and for {\em linear} polarization of the {\em ac} field, a strong change of the diagonal component, $σ_d$, of the {\em dc} conductivity occurs in the presence of a {\em weak} nonparabolicity of the electron spectrum. Small change in the electron effective mass due to irradiation can lead to negative $σ_d$, while the Hall component of the {\em dc} conductivity remains practically unchanged. Within the model considered, the sign of $σ_d$ depends on the relative orientation of the {\em dc} and {\em ac} fields, the sign of the detuning of the {\em ac} frequency from the cyclotron resonance, and the sign of nonparabolic term in the energy spectrum.

cond-mat.dis-nn↗

arXiv1999

Quasiballistic correction to the density of states in three-dimensional metal

We study the exchange correction to the density of states in the three-dimensional metal near the Fermi energy. In the ballistic limit, when the distance to the Fermi level exceeds the inverse transport relaxation time $1/τ$, we find the correction linear in the distance from the Fermi level. By a large parameter $ε_{\rm F} τ$ this ballistic correction exceeds the diffusive correction obtained earlier.

cond-mat.dis-nn↗

arXiv1999

Vortex Density of States and Absorption in Clean Layered Superconductors

We study the spectrum of the states localized in the vortex cores in the mixed state of clean layered superconductors. S-wave coupling is assumed. It is found that in a large region of parameters adjacent to the superclean case a new universal (i.e. independent of the density of impurities) class of level statistics arises. It is the circular unitary random matrix ensemble. The density of states for such conditions is calculated. The absorption resulting from the Landau-Zener transitions between these levels is different from the classical result for an isotropic three-dimensional system.

cond-mat↗

arXiv1998

Vortex mediated microwave absorption in superclean layered superconductors

In the superclean case the spectrum of vortex core excitations in the presence of disorder is not random but consists of two series of equally-spaced levels. The I-V characteristics of such superconductors displays many interesting phenomena. A series of resonances is predicted at frequencies commensurate with the spacing of the vortex excitations. These resonances reveal an even-odd anomaly. In the presence of one weak impurity the excitation levels can approach each other and almost cross. Absorption at very low frequencies is identified with the resonances arising in this case. The results of such microscopic theory coincide up to the order of magnitude with both the theory employing kinetic equation and the experiment. The non-linear effects associated with Zener transitions in such crossings are studied. These phenomena can be used as a probe of vortex core excitations.

cond-mat.supr-con↗

arXiv1997

Charging Spectrum and Configurations of a Wigner Crystal Island

Charging of a clean two-dimensional island is studied in the regime of small concentration of electrons when they form the Wigner crystal. Two forms of electron-electron interaction potential are studied: the pure Coulomb interaction and the exponential interaction corresponding to the screening by a pair of close metallic gates. The electrons are assumed to reside in a parabolic external confining potential. Due to the crystalline symmetry the center of the confinement can be situated at distinct positions with respect to the crystal. With the increasing number of electrons $N$ the center periodically hops from one such a location to another providing the lowest total energy. These events occur with the period $\sim N^{1/2}$. At these moments in the case of the pure Coulomb interaction the charging energy of the island has a negative correction $\approx 15%$. For the case of the exponential interaction at the moments of switching the capacitance becomes negative and $\sim N^{1/4}$ new electrons enter the island simultaneously. The configurations of disclinations and dislocations in the island are also studied.

cond-mat↗

arXiv1997

Charging Spectrum of a Small Wigner Crystal Island

Charging of a clean two-dimensional island is studied in the regime of small concentration of electrons when they form the Wigner crystal. The number of electrons in the island is assumed to be not too big (N < 100). It is shown that the total energy of the island as a function of N has a quasi-periodic component of a universal shape, that is independent of the form of electron-electron interactions. These oscillations are caused by the combination of the geometric effects associated with packing of the triangular lattice into the circular island. These effects are: the shell effect, associated with starting a new crystalline row, and the so-called confinement polaronic effect. In the presence of close metallic gates, which eliminate the long-range part of the electron-electron interactions, the oscillations of the energy bring about simultaneous entering of the dot by a few electrons.

cond-mat↗

arXiv1997

Statistics of the Charging Spectrum of a Two-Dimensional Coulomb Glass Island

The fluctuations of capacitance of a two-dimensional island are studied in the regime of low electron concentration and strong disorder, when electrons can be considered classical particles. The universal capacitance distribution is found, with the dispersion being of the order of the average. This distribution is shown to be closely related to the shape of the Coulomb gap in the one-electron density of states of the island. Behavior of the the capacitance fluctuations near the metal - insulator transition is discussed.

cond-mat↗

arXiv1996

The Absence of the Fractional Quantum Hall Effect at High Landau Levels

We compare the energies of the Laughlin liquid and a charge density wave in a weak magnetic field for the upper Landau level filling factors $ν_N = 1/3$ and $1/5$. The charge density wave period has been optimized and was found to be $\simeq 3R_c$, where $R_c$ is the cyclotron radius. We conclude that the optimal charge density wave is more energetically preferable than the Laughlin liquid for the Landau level numbers $N \ge 2$ at $ν_N = 1/3$ and for $N \ge 3$ at $ν_N = 1/5$. This implies that the $1/3$ fractional quantum Hall effect cannot be observed for $N \ge 2$, in agreement with the experiment.

cond-mat↗

arXiv1996

The Ground State of a Two-Dimensional Electron Liquid in a Weak Magnetic Field

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N \gg 1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factor equal to one and zero. The domains alternate with a spatial period of the order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a pseudogap linearly dependent on the magnetic field in the limit of large $N$.

cond-mat↗

arXiv1995

Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N \gg 1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factor equal to one and zero. The domains alternate with a spatial period of order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a pseudogap linearly dependent on the magnetic field in the limit of large $N$.

cond-mat↗