Publications (27)84.09 Total impact

Article: Anderson localization on a simplex
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ABSTRACT: We derive a fieldtheoretical representation for the moments of the eigenstates in the generalized Anderson model. The representation is exact and can be used for the Anderson model with generic nonrandom hopping elements in any dimensions. We apply this method to the simplex model, for which the hopping amplitude between any two lattice sites is the same, and find that the eigenstates are localized at any strength of disorder. Our analytical predictions are in excellent agreement with the results of numerical simulations.Journal of Physics A Mathematical and Theoretical 11/2012; 46(10). · 1.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study levelnumber variance in a twodimensional random matrix model characterized by a powerlaw decay of the matrix elements. The amplitude of the decay is controlled by the parameter b. We find analytically that at small values of b the level number variance behaves linearly, with the compressibility χ between 0 and 1, which is typical for critical systems. For large values of b, we derive that χ=0, as one would normally expect in the metallic phase. Using numerical simulations we determine the critical value of b at which the transition between these two phases occurs.Physical Review E 02/2012; 85(2 Pt 1):021127. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We develop a perturbative approach to study the supersymmetric nonlinear sigma model characterized by a generic coupling matrix in the strong coupling limit. The method allows us to calculate explicitly the moments of the eigenfunctions and the twolevel correlation function in the lowest order of the perturbative expansion. We find that the obtained expressions are equivalent to the results derived before for the corresponding random matrix ensembles. Such an equivalence is elucidated and generalized to all orders of the perturbative expansion by mapping the sigma model onto the field theory describing the almost diagonal random matrices.Journal of Physics A Mathematical and Theoretical 01/2012; 45(33). · 1.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider a simple model of quantum disorder in two dimensions, characterized by a longrange sitetosite hopping. The system undergoes a metal–insulator transitionits eigenfunctions change from being extended to being localized. We demonstrate that at the point of the transition the nature of the eigenfunctions depends crucially on the magnitude of the hopping amplitude. At small amplitudes they are strongly multifractal. In the opposite limit of large amplitudes, the eigenfunctions do not become fractal. Their density moments do not scale as a power of the system size; instead our result suggests a power of the logarithm of the system size. In this regard, the transition differs from a similar one in the onedimensional version of the same system, as well as from the conventional Anderson transition in more than two dimensions.Journal of Physics Condensed Matter 09/2011; 23(41):415601. · 2.22 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large system size. Using the supersymmetric virial expansion we confirm the scaling law and find analytical expressions for the fractal dimension of the wave functions $d_2$ and the dynamical scaling exponent $\mu$. By comparing them we verify the validity of the Chalker's ansatz for dynamical scaling.Journal of Physics A Mathematical and Theoretical 04/2011; 44(30). · 1.77 Impact Factor 
Article: Universal and nonuniversal features of the multifractality exponents of critical wavefunctions
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ABSTRACT: We calculate perturbatively the multifractality spectrum of wavefunctions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order corrections are modelspecific. Explicit results for the anomalous dimensions are derived in the powerlaw and ultrametric random matrix ensembles.Journal of Statistical Mechanics Theory and Experiment 01/2011; 3(03). · 1.87 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The dynamical scaling for statistics of critical multifractal eigenstates proposed by Chalker is analytically verified for the critical random matrix ensemble in the limit of strong multifractality controlled by the small parameter b⪡1. The powerlaw behavior of the quantum return probability PN(τ) as a function of the matrix size N or time τ is confirmed in the limits τ/N→∞ and N/τ→∞, respectively, and it is shown that the exponents characterizing these power laws are equal to each other up to the order b2. The corresponding analytical expression for the fractal dimension d2 is found.Physical review. B, Condensed matter 08/2010; 82(16). · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We demonstrate that by considering disordered singleparticle Hamiltonians (or their random matrix versions) on ultrametric spaces one can generate an interesting class of models exhibiting Anderson metalinsulator transition. We use the weak disorder virial expansion to determine the critical value of the parameters and to calculate the values of the multifractal exponents for inverse participation ratios. Direct numerical simulations agree favourably with the analytical predictions.Journal of Statistical Mechanics Theory and Experiment 09/2009; 12(12). · 1.87 Impact Factor 
Article: Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum
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ABSTRACT: Photonic crystals with a twodimensional triangular lattice have a conical singularity in the spectrum. Close to this socalled Dirac point, Maxwell's equations reduce to the Dirac equation for an ultrarelativistic spin1/2 particle. Here we show that the halfinteger spin and the associated Berry phase remain observable in the presence of disorder in the crystal. While constructive interference of a scalar (spinzero) wave produces a coherent backscattering peak, consisting of a doubling of the disorderaveraged reflected photon flux, the destructive interference caused by the Berry phase suppresses the reflected intensity at an angle which is related to the angle of incidence by timereversal symmetry. We demonstrate this extinction of coherent backscattering by a numerical solution of Maxwell's equations and compare with analytical predictions from the Dirac equation.EPL (Europhysics Letters) 11/2008; · 2.26 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We develop a supersymmetric field theoretical description of the Gaussian ensemble of the almost diagonal Hermitian Random Matrices. The matrices have independent random entries H_{ij} with parametrically small offdiagonal elements H_{ij}/H_{ii} ~ B << 1. We derive a regular virial expansion of correlation functions in the number of ``interacting'' supermatrices associated with different sites in the real space and demonstrate that the perturbation theory constructed in this way is controlled by a small parameter B. General form of the integral expression for the mth virial coefficient governed by the ``interaction'' of m supermatrices is presented and calculated explicitly in the cases of 2 and 3matrix ``interaction''. The suggested technique allows us to calculate both the spectral correlations and the correlations of the eigenfunctions taken at different energies and in different space points.Journal of Physics A Mathematical and Theoretical 02/2007; · 1.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the interplay of Klein tunneling (=interband tunneling) between ndoped and pdoped regions in graphene and Andreev reflection (=electronhole conversion) at a superconducting electrode. The tunneling conductance of an npn junction initially increases upon lowering the temperature, while the coherence time of the electronhole pairs is still less than their lifetime, but then drops back again when the coherence time exceeds the lifetime. This reentrance effect, known from diffusive conductors and ballistic quantum dots, provides a method to detect phase coherent Klein tunneling of electronhole pairs.Physical review. B, Condensed matter 01/2007; · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We calculate the density of states of electronhole excitations in a superconductornormalmetalsuperconductor (SNS) junction in graphene, in the longjunction regime that the superconducting gap is much larger than the Thouless energy ET=hv/d (with v the carrier velocity in graphene and d the separation of the NS boundaries). If the normal region is undoped, the excitation spectrum consists of neutral modes that propagate along the boundariestransporting energy but no charge. These Andreev modes are a coherent superposition of electron states from the conduction band and hole states from the valence band, coupled by specular Andreev reflection at the superconductor.Physical review. B, Condensed matter 01/2007; · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the structure of resonance widths of a BoseHubbard Dimer with intersite hopping amplitude $k$, which is coupled to continuum at one of the sites with strength $\gamma$. Using an effective nonHermitian Hamiltonian formalism, we show that by varying the onsite interaction term $\chi$ the resonances undergo consequent bifurcations. For $\Lambda=k/\gamma\geq 0.5$, the bifurcation points follow a scaling law ${\tilde \chi}_n \equiv \chi_n N/k = f_{\Lambda}(n0.5/\Lambda)$, where $N$ is the number of bosons. For the function $f_{\Lambda}$ two different $\Lambda$ dependences are found around the minimum and the maximum bifurcation point. Comment: 4 pages, 3 figuresPhysical Review A 02/2006; · 3.04 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The shot noise in the electrical current through a ballistic chaotic quantum dot with $N$channel point contacts is suppressed for $N\rightarrow\infty$, because of the transition from stochastic scattering of quantum wave packets to deterministic dynamics of classical trajectories. The dynamics of the electron spin remains quantum mechanical in this transition, and can affect the electrical current via spinorbit interaction. We explain how the role of the channel number $N$ in determining the shot noise is taken over by the ratio $l_\textrm{so}/\lambda_{F}$ of spin precession length $l_\textrm{so}$ and Fermi wavelength $\lambda_{F}$, and present computer simulations in a twodimensional billiard geometry (Lyapunov exponent $\alpha$, mean dwell time $\tau_\textrm{dwell}$, point contact width $W$) to demonstrate the scaling $\ensuremath{\propto(\lambda_{F}/l_\textrm{so})^{1/\alpha\tau_\textrm{dwell}}}$ of the shot noise in the regime $\lambda_{F}\ll l_\textrm{so}\ll W$.EPL (Europhysics Letters) 01/2006; · 2.26 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A new supersymmetric representation for quantum disordered systems is derived. This representation is exact and is dual to that of the nonlinear sigmamodel. The new formalism is tested by calculating the distribution of wave function amplitudes in the 1d Anderson model. The deviation from the distribution found for a thick wire is detected near the band center E=0. Comment: 4 pagesPhysical review. B, Condensed matter 08/2005; · 3.77 Impact Factor 
Article: Statistics of delay times in mesoscopic systems as a manifestation of eigenfunction fluctuations
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ABSTRACT: We reveal a general explicit relation between the statistics of delay times in onechannel reflection from a mesoscopic sample of any spatial dimension and the statistics of the eigenfunction intensities in its closed counterpart. This opens a possibility to use experimentally measurable delay times as a sensitive probe of eigenfunction fluctuations. For the particular case of quasione dimensional geometry of the sample we use an alternative technique to derive the probability density of partial delay times for any number of open channels. Comment: 12 pages; published version with updated referencesPhysical Review B 11/2004; · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The generalization of the dimer model on a twoleg ladder is defined and investigated both, analytically and numerically. For the closed system we calculate the Landauer resistance analytically and found the presence of the point of delocalization at the band center which is confirmed by the numerical calculations of the Lyapunov exponent. We calculate also analytically the localization length index and present the numerical investigations of the density of states (DOS). For the open counterpart of this model the distribution of the Wigner delay times is calculated numerically. It is shown how the localizationdelocalization transition manifest itself in the behavior of the distribution.Physical Review B 06/2004; · 3.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider energy absorption by driven chaotic systems of the symplectic symmetry class. According to our analytical perturbative calculation, at the initial stage of evolution the energy growth with time can be faster than linear. This appears to be an analog of weak antilocalization in disordered systems with spinorbit interaction. Our analytical result is also confirmed by numerical calculations for the symplectic quantum kicked rotor. Comment: 4 pages, 2 figuresPhysics of Condensed Matter 06/2004; · 1.28 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Employing the chiral Gaussian unitary ensemble of random matrices, we calculate the probability distribution of the local density of states for zerodimensional ("quantum chaotic") twosublattice systems at the point of chiral symmetry E=0 and in the presence of uniform absorption. The obtained result can be used to find the distributions of the reflection coefficient and of the Wigner time delay for such systems.Physical Review Letters 03/2004; 92(8):084103. · 7.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the proximity effect of a superconductor to a normal system with a fractal spectrum. We find that there is no gap in the excitation spectrum, even in the case where the underlying classical dynamics of the normal system is chaotic. An analytical expression for the distribution of the smallest excitation eigenvalue E1 of the hybrid structure is obtained. On small scales it decays algebraically as P(E1) approximately E1(D0), where D0 is the fractal dimension of the spectrum of the normal system. Our theoretical predictions are verified by numerical calculations performed for various models.Physical Review Letters 02/2004; 92(1):017004. · 7.73 Impact Factor
Publication Stats
316  Citations  
84.09  Total Impact Points  
Top Journals
Institutions

2008–2012

University of Nottingham
 School of Mathematical Sciences
Nottingham, ENG, United Kingdom


2006–2007

Leiden University
Leyden, South Holland, Netherlands


2004

Abdus Salam International Centre for Theoretical Physics
Trst, Friuli Venezia Giulia, Italy 
Brunel University
 Department of Mathematical Sciences
London, ENG, United Kingdom


1999–2002

GeorgAugustUniversität Göttingen
 Institute for Nonlinear Dynamics
Göttingen, Lower Saxony, Germany
