A. Ossipov

University of Nottingham, Nottingham, ENG, United Kingdom

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Publications (27)84.09 Total impact

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    A. Ossipov
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    ABSTRACT: We derive a field-theoretical 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 non-random 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
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    A Ossipov, I Rushkin, E Cuevas
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    ABSTRACT: We study level-number variance in a two-dimensional random matrix model characterized by a power-law 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
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    A Ossipov
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    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 two-level 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
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    A Ossipov, I Rushkin, E Cuevas
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    ABSTRACT: We consider a simple model of quantum disorder in two dimensions, characterized by a long-range site-to-site hopping. The system undergoes a metal–insulator transition--its 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 one-dimensional 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
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    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
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    I. Rushkin, A. Ossipov, Y. V. Fyodorov
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    ABSTRACT: We calculate perturbatively the multifractality spectrum of wave-functions 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 model-specific. Explicit results for the anomalous dimensions are derived in the power-law and ultrametric random matrix ensembles.
    Journal of Statistical Mechanics Theory and Experiment 01/2011; 3(03). · 1.87 Impact Factor
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    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 power-law 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
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    ABSTRACT: We demonstrate that by considering disordered single-particle Hamiltonians (or their random matrix versions) on ultrametric spaces one can generate an interesting class of models exhibiting Anderson metal-insulator 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
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    ABSTRACT: Photonic crystals with a two-dimensional triangular lattice have a conical singularity in the spectrum. Close to this so-called Dirac point, Maxwell's equations reduce to the Dirac equation for an ultrarelativistic spin-1/2 particle. Here we show that the half-integer spin and the associated Berry phase remain observable in the presence of disorder in the crystal. While constructive interference of a scalar (spin-zero) wave produces a coherent backscattering peak, consisting of a doubling of the disorder-averaged 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 time-reversal 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
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    Oleg Yevtushenko, Alexander Ossipov
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    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 off-diagonal 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 m-th virial coefficient governed by the ``interaction'' of m supermatrices is presented and calculated explicitly in the cases of 2- and 3-matrix ``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
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    ABSTRACT: We study the interplay of Klein tunneling (=interband tunneling) between n-doped and p-doped regions in graphene and Andreev reflection (=electron-hole conversion) at a superconducting electrode. The tunneling conductance of an n-p-n junction initially increases upon lowering the temperature, while the coherence time of the electron-hole 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 electron-hole pairs.
    Physical review. B, Condensed matter 01/2007; · 3.77 Impact Factor
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    ABSTRACT: We calculate the density of states of electron-hole excitations in a superconductor–normal-metal–superconductor (SNS) junction in graphene, in the long-junction 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 boundaries—transporting 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
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    M. Hiller, T. Kottos, A. Ossipov
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    ABSTRACT: We investigate the structure of resonance widths of a Bose-Hubbard Dimer with intersite hopping amplitude $k$, which is coupled to continuum at one of the sites with strength $\gamma$. Using an effective non-Hermitian Hamiltonian formalism, we show that by varying the on-site interaction term $\chi$ the resonances undergo consequent bifurcations. For $\Lambda=k/\gamma\geq 0.5$, the bifurcation points follow a scaling law ${\tilde \chi}_n \equiv \chi_n N/k = f_{\Lambda}(n-0.5/\Lambda)$, 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 figures
    Physical Review A 02/2006; · 3.04 Impact Factor
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    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 spin-orbit 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 two-dimensional 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
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    A. Ossipov, V. E. Kravtsov
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    ABSTRACT: A new super-symmetric representation for quantum disordered systems is derived. This representation is exact and is dual to that of the nonlinear sigma-model. 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 pages
    Physical review. B, Condensed matter 08/2005; · 3.77 Impact Factor
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    A. Ossipov, Y. V. Fyodorov
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    ABSTRACT: We reveal a general explicit relation between the statistics of delay times in one-channel 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 quasi-one 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 references
    Physical Review B 11/2004; · 3.66 Impact Factor
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    T. Sedrakyan, A. Ossipov
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    ABSTRACT: The generalization of the dimer model on a two-leg 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 localization-delocalization transition manifest itself in the behavior of the distribution.
    Physical Review B 06/2004; · 3.66 Impact Factor
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    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 anti-localization in disordered systems with spin-orbit interaction. Our analytical result is also confirmed by numerical calculations for the symplectic quantum kicked rotor. Comment: 4 pages, 2 figures
    Physics of Condensed Matter 06/2004; · 1.28 Impact Factor
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    Yan V Fyodorov, Alexander Ossipov
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    ABSTRACT: Employing the chiral Gaussian unitary ensemble of random matrices, we calculate the probability distribution of the local density of states for zero-dimensional ("quantum chaotic") two-sublattice 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
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    Alexander Ossipov, Tsampikos Kottos
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    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

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
    • Georg-August-Universität Göttingen
      • Institute for Nonlinear Dynamics
      Göttingen, Lower Saxony, Germany