arXiv subjects

A. Ossipov

Publications and source records attributed to A. Ossipov.

At least 19 recordsLinked to original sources

arXiv2018

Gelfand-Yaglom formula for functional determinants in higher dimensions

The Gelfand-Yaglom formula relates functional determinants of the one-dimensional second order differential operators to the solutions of the corresponding initial value problem. In this work we generalise the Gelfand-Yaglom method by considering discrete and continuum partial second order differential operators in higher dimensions. To illustrate our main result we apply the generalised formula to the two-dimensional massive and massless discrete Laplace operators and calculate asymptotic expressions for their determinants.

math-ph↗

arXiv2018

Scattering approach to Anderson localisation

We develop a novel approach to the Anderson localisation problem in a $d$-dimensional disordered sample of dimension $L\times M^{d-1}$. Attaching a perfect lead with the cross-section $M^{d-1}$ to one side of the sample, we derive evolution equations for the scattering matrix and the Wigner-Smith time delay matrix as a function of $L$. Using them one obtains the Fokker-Planck equation for the distribution of the proper delay times and the evolution equation for their density at weak disorder. The latter can be mapped onto a non-linear partial differential equation of the Burgers type, for which a complete analytical solution for arbitrary $L$ is constructed. Analysing the solution for a cubic sample with $M=L$ in the limit $L\to \infty$, we find that for $d<2$ the solution tends to the localised fixed point, while for $d>2$ to the metallic fixed point and provide explicit results for the density of the delay times in these two limits.

cond-mat.mes-hall↗

arXiv2018

Stochastic multi-step polarization switching in ferroelectrics

Consecutive stochastic 90° polarization switching events, clearly resolved in recent experiments, are described by a new nucleation and growth multi-step model. It extends the classical Kolmogorov-Avrami-Ishibashi approach and includes possible consecutive 90°- and parallel 180°-switching events. The model predicts the results of simultaneous time-resolved macroscopic measurements of polarization and strain, performed on a tetragonal Pb(Zr,Ti)O3 ceramic in a wide range of electric fields over a time domain of five orders of the magnitude. It allows the determination of the fractions of individual switching processes, their characteristic switching times, activation fields, and respective Avrami indices.

cond-mat.mtrl-sci↗

arXiv2014

Entanglement entropy in Fermi gases and Anderson's orthogonality catastrophe

We study the ground-state entanglement entropy of a subsystem of size $L$ of non-interacting fermions scattered by a potential of finite range $a$. We derive a general relation between the scattering matrix and the overlap matrix and use it to prove, that for a one-dimensional symmetric potential the von Neumann entropy, the Rényi entropies and the full counting statistics are robust against potential scattering, provided that $L/a\gg 1$. The results of numerical calculations support the validity of this conclusion for a generic potential.

cond-mat.stat-mech↗

arXiv2013

Anderson localization on a simplex

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.

math-ph↗

arXiv2012

Virial expansion of the non-linear sigma model in the strong coupling limit

We develop a perturbative approach to study the supersymmetric non-linear 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.

cond-mat.dis-nn↗

arXiv2011

Level number variance and spectral compressibility in a critical two-dimensional random matrix model

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 chi between 0 and 1, which is typical for critical systems. For large values of b, we derive that chi=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.

cond-mat.dis-nn↗

arXiv2011

Return probability and scaling exponents in the critical random matrix ensemble

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 $μ$. By comparing them we verify the validity of the Chalker's ansatz for dynamical scaling.

cond-mat.dis-nn↗

arXiv2011

Universal and non-universal features of the multifractality exponents of critical wave-functions

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.

cond-mat.dis-nn↗

arXiv2011

Criticality without self-similarity: a 2D system with random long-range hopping

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 eigenfunctions do not become fractal. Their density moments do not scale as a power of the system size. Instead, in one of the considered limits 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.

cond-mat.dis-nn↗

arXiv2010

Dynamical scaling for critical states: is Chalker's ansatz valid for strong fractality?

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 $b\ll 1$. The power law behavior of the quantum return probability $P_{N}(τ)$ as a function of the matrix size $N$ or time $τ$ is confirmed in the limits $τ/N\rightarrow\infty$ and $N/τ\rightarrow\infty$, respectively, and it is shown that the exponents characterizing these power laws are equal to each other up to the order $b^{2}$. The corresponding analytical expression for the fractal dimension $d_{2}$ is found.

cond-mat.dis-nn↗

arXiv2009

Anderson localization transition and eigenfunction multifractality in ensemble of ultrametric random matrices

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.

cond-mat.mes-hall↗

arXiv2009

Extinction of coherent backscattering by a disordered photonic crystal with a Dirac spectrum

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.

cond-mat.mes-hall↗

arXiv2007

Reentrance effect in a graphene n-p-n junction coupled to a superconductor

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.

cond-mat.mes-hall↗

arXiv2006

Excitation gap of a graphene channel with superconducting boundaries

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. 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. The lowest Andreev mode has an excitation gap, which depends on the superconducting phase difference across the SNS graphene channel. At high doping the excitation gap vanishes and the usual gapless density of states of Andreev levels is recovered. We use our results to calculate the superconducting phase dependence of the thermal conductance of the graphene channel.

cond-mat.mes-hall↗

arXiv2006

Bifurcations in Resonance Widths of an Open Bose-Hubbard Dimer

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 $γ$. Using an effective non-Hermitian Hamiltonian formalism, we show that by varying the on-site interaction term $χ$ the resonances undergo consequent bifurcations. For $Λ=k/γ\geq 0.5$, the bifurcation points follow a scaling law ${\tilde χ}_n \equiv χ_n N/k = f_Λ(n-0.5/Λ)$, where $N$ is the number of bosons. For the function $f_Λ$ two different $Λ$ dependences are found around the minimum and the maximum bifurcation point.

cond-mat.other↗

arXiv2006

How spin-orbit interaction can cause electronic shot noise

The shot noise in the electrical current through a ballistic chaotic quantum dot with N-channel point contacts is suppressed for N --> infinity, 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_{so}/lambda_F of spin precession length l_{so} and Fermi wave length lambda_F, and present computer simulations in a two-dimensional billiard geometry (Lyapunov exponent alpha, mean dwell time tau_{dwell}, point contact width W) to demonstrate the scaling (lambda_F/l_{so})^{1/alpha tau_{dwell}} of the shot noise in the regime lambda_F << l_{so} << W.

cond-mat.mes-hall↗

arXiv2005

T-duality in supersymmetric theory of disordered quantum systems

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.

cond-mat.mes-hall↗