arXiv subjects

D. L. Shepelyansky

Publications and source records attributed to D. L. Shepelyansky.

At least 55 records · Page 3Linked to original sources

arXiv2010

Towards Google matrix of brain

We apply the approach of the Google matrix, used in computer science and World Wide Web, to description of properties of neuronal networks. The Google matrix ${\bf G}$ is constructed on the basis of neuronal network of a brain model discussed in PNAS {\bf 105}, 3593 (2008). We show that the spectrum of eigenvalues of ${\bf G}$ has a gapless structure with long living relaxation modes. The PageRank of the network becomes delocalized for certain values of the Google damping factor $α$. The properties of other eigenstates are also analyzed. We discuss further parallels and similarities between the World Wide Web and neuronal networks.

cond-mat.dis-nn↗

arXiv2010

Spectral properties of the Google matrix of the World Wide Web and other directed networks

We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure in the vicinity of the maximal eigenvalue for Google damping parameter $α$ equal to unity. The vocabulary networks have relatively homogeneous spectral density, while university networks have pronounced spectral structures which change from one university to another, reflecting specific properties of the networks. We also determine specific properties of eigenstates of the Google matrix, including the PageRank. The fidelity of the PageRank is proposed as a new characterization of its stability.

cs.IR↗

arXiv2010

Theory of resonant photon drag in monolayer graphene

Photon drag current in monolayer graphene with degenerate electron gas is studied under interband excitation near the threshold of fundamental transitions. Two main mechanisms generate an emergence of electron current. Non-resonant drag effect (NDE) results from direct transfer of in-plane photon momentum ${\bf q}$ to electron and dependence of matrix elements of transitions on ${\bf q}$. Resonant drag effect (RDE) originates from ${\bf q}$-dependent selection of transitions due to a sharp form of the Fermi distribution in energy. The drag current essentially depends on the polarization of radiation and, in general, is not parallel to ${\bf q}$. The perpendicular current component appears if the in-plain electric field is tilted towards ${\bf q}$. The RDE has no smallness connected with $q$ and exists in a narrow region of photon frequency $ω$: $|\hbarω-2ε_F|< \hbar sq$, where $s$ is the electron velocity.

cond-mat.mes-hall↗

arXiv2009

Google matrix, dynamical attractors and Ulam networks

We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite size matrix approximant of this operator is constructed by the Ulam method. This method applied to the simple dynamical model creates the directed Ulam networks with approximate scale-free scaling and characteristics being rather similar to those of the World Wide Web. The simple dynamical attractors play here the role of popular web sites with a strong concentration of PageRank. A variation of the Google parameter $α$ or other parameters of the dynamical map can drive the PageRank of the Google matrix to a delocalized phase with a strange attractor where the Google search becomes inefficient.

cs.IR↗

arXiv2009

Capture of dark matter by the Solar System

We study the capture of galactic dark matter by the Solar System. The effect is due to the gravitational three-body interaction between the Sun, one of the planets, and a dark matter particle. The analytical estimate for the capture cross-section is derived and the upper and lower bounds for the total mass of the captured dark matter particles are found. The estimates for their density are less reliable. The most optimistic of them give an enhancement of dark matter density by about three orders of magnitudes compared to its value in our Galaxy. However, even this optimistic value remains below the best present observational upper limits by about two orders of magnitude.

astro-ph.SR↗

arXiv2009

Microwave stabilization of edge transport and zero-resistance states

Edge channels play a crucial role for electron transport in two dimensional electron gas under magnetic field. It is usually thought that ballistic transport along edges occurs only in the quantum regime with low filling factors. We show that a microwave field can stabilize edge trajectories even in the semiclassical regime leading to a vanishing longitudinal resistance. This mechanism gives a clear physical interpretation for observed zero-resistance states.

cond-mat.mes-hall↗

arXiv2009

Quantum synchronization and entanglement of two qubits coupled to a driven dissipative resonator

Using method of quantum trajectories we study the behavior of two identical or different superconducting qubits coupled to a quantum dissipative driven resonator. Above a critical coupling strength the qubit rotations become synchronized with the driving field phase and their evolution becomes entangled even if two qubits may significantly differ from one another. Such entangled qubits can radiate entangled photons that opens new opportunities for entangled wireless communication in a microwave range.

cond-mat.supr-con↗

arXiv2009

Synchronization mechanism of sharp edges in rings of Saturn

We propose a new mechanism which explains the existence of enormously sharp edges in the rings of Saturn. This mechanism is based on the synchronization phenomenon due to which the epicycle rotational phases of particles in the ring, under certain conditions, become synchronized with the phase of external satellite, e.g. with the phase of Mimas in the case of the outer B ring edge. This synchronization eliminates collisions between particles and suppress the diffusion induced by collisions by orders of magnitude. The minimum of the diffusion is reached at the center of the synchronization regime corresponding to the ratio 2:1 between the orbital frequency at the edge of B ring and the orbital frequency of Mimas. The synchronization theory gives the sharpness of the edge in few tens of meters that is in agreement with available observations.

astro-ph↗

arXiv2008

Chaotic dynamics of a Bose-Einstein condensate coupled to a qubit

We study numerically the coupling between a qubit and a Bose-Einstein condensate (BEC) moving in a kicked optical lattice, using Gross-Pitaevskii equation. In the regime where the BEC size is smaller than the lattice period, the chaotic dynamics of the BEC is effectively controlled by the qubit state. The feedback effects of the nonlinear chaotic BEC dynamics preserve the coherence and purity of the qubit in the regime of strong BEC nonlinearity. This gives an example of an exponentially sensitive control over a macroscopic state by internal qubit states. At weak nonlinearity quantum chaos leads to rapid dynamical decoherence of the qubit. The realization of such coupled systems is within reach of current experimental techniques.

cond-mat.stat-mech↗

arXiv2008

Ratchet transport of interacting particles

We study analytically and numerically the ratchet transport of interacting particles induced by a monochromatic driving in asymmetric two-dimensional structures. The ratchet flow is preserved in the limit of strong interactions and can become even stronger compared to the non-interacting case. The developed kinetic theory gives a good description of these two limiting regimes. The numerical data show emergence of turbulence in the ratchet flow under certain conditions.

cond-mat.stat-mech↗

arXiv2008

Time reversal of Bose-Einstein condensates

Using Gross-Pitaevskii equation, we study the time reversibility of Bose-Einstein condensates (BEC) in kicked optical lattices, showing that inside the regime of quantum chaos the dynamics can be inverted from explosion to collapse. The accuracy of time reversal decreases with the increase of atom interactions inside BEC, until it is completely lost. Surprisingly, quantum chaos helps to restore time reversibility. These predictions can be tested with existing experimental setups.

cond-mat.stat-mech↗

arXiv2007

Loschmidt cooling by time reversal of atomic matter waves

We propose an experimental scheme which allows to realize approximate time reversal of matter waves for ultracold atoms in the regime of quantum chaos. We show that a significant fraction of the atoms return back to their original state, being at the same time cooled down by several orders of magnitude. We give a theoretical description of this effect supported by extensive numerical simulations. The proposed scheme can be implemented with existing experimental setups.

cond-mat.stat-mech↗

arXiv2007

Fractal Weyl law for quantum fractal eigenstates

The properties of the resonant Gamow states are studied numerically in the semiclassical limit for the quantum Chirikov standard map with absorption. It is shown that the number of such states is described by the fractal Weyl law and their Husimi distributions closely follow the strange repeller set formed by classical orbits nonescaping in future times. For large matrices the distribution of escape rates converges to a fixed shape profile characterized by a spectral gap related to the classical escape rate.

cond-mat.dis-nn↗

arXiv2007

Synchronization and bistability of qubit coupled to a driven dissipative oscillator

We study numerically the behavior of qubit coupled to a quantum dissipative driven oscillator (resonator). Above a critical coupling strength the qubit rotations become synchronized with the oscillator phase. In the synchronized regime, at certain parameters, the qubit exhibits tunneling between two orientations with a macroscopic change of number of photons in the resonator. The life times in these metastable states can be enormously large. The synchronization leads to a drastic change of qubit radiation spectrum with appearance of narrow lines corresponding to recently observed single artificial-atom lasing [O. Astafiev {\it et al.} Nature {\bf 449}, 588 (2007)].

cond-mat.supr-con↗

arXiv2007

Destruction of Anderson localization by a weak nonlinearity

We study numerically a spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schrödinger lattice with disorder. We demonstrate that above a certain critical strength of nonlinearity the Anderson localization is destroyed and an unlimited subdiffusive spreading of the field along the lattice occurs. The second moment grows with time $ \propto t^α$, with the exponent $α$ being in the range $0.3 - 0.4$. For small nonlinearities the distribution remains localized in a way similar to the linear case.

cond-mat.dis-nn↗

arXiv2007

Synchnonization, zero-resistance states and rotating Wigner crystal

We show that rotational angles of electrons moving in two dimensions (2D) in a perpendicular magnetic field can be synchronized by an external microwave field which frequency is close to the Larmor frequency. The synchronization eliminates collisions between electrons and thus creates a regime with zero diffusion corresponding to the zero-resistance states observed in experiments with high mobility 2D electron gas (2DEG). For long range Coulomb interactions electrons form a rotating hexagonal Wigner crystal. Possible relevance of this effect for planetary rings is discussed.

cond-mat.mes-hall↗

arXiv2007

Photogalvanic current in artificial asymmetric nanostructures

We develop a theoretic description of the photogalvanic current induced by a high frequency radiation in asymmetric nanostructures and show that it describes well the results of numerical simulations. Our studies allow to understand the origin of the electronic ratchet transport in such systems and show that they can be used for creation of new types of detectors operating at room temperature in a terahertz radiation range.

cond-mat.mes-hall↗

arXiv2006

Magnetization of ballistic quantum dots induced by a linear-polarized microwave field

On a basis of extensive analytical and numerical studies we show that a linear-polarized microwave field creates a stationary magnetization in mesoscopic ballistic quantum dots with two-dimensional electron gas being at a thermal equilibrium. The magnetization is proportional to a number of electrons in a dot and to a microwave power. Microwave fields of moderate strength create in a one dot of few micron size a magnetization which is by few orders of magnitude larger than a magnetization produced by persistent currents. The effect is weakly dependent on temperature and can be observed with existing experimental techniques. The parallels between this effect and ratchets in asymmetric nanostructures are also discussed.

cond-mat.mes-hall↗