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P. Markos

Publications and source records attributed to P. Markos.

30 records · Page 2Linked to original sources
arXiv2004

Conductance distribution in 3D Anderson insulators: deviation from log-normal form

We show how a recent proposal to obtain the distribution of conductances in three dimensions (3D) from a generalized Fokker-Planck equation for the joint probability distribution of the transmission eigenvalues can be implemented for all strengths of disorder by numerically evaluating certain correlations of transfer matrices. We then use this method to obtain analytically, for the first time, the 3D conductance distribution in the insulating regime and provide a simple understanding of why it differs qualitatively from the log-normal distribution of a quasi one-dimensional wire.

cond-mat.mes-hall↗
arXiv2003

Resonant and anti-resonant frequency dependence of the effective parameters of metamaterials

We present a numerical study of the electromagnetic response of the metamaterial elements that are usedto construct materials with negative refractive index. For an array of split ring resonators (SRR) we find that the resonant behavior of the effective magnetic permeability is accompanied by an anti-resonant behavior of the effective permittivity. In addition, the imaginary parts of the effective permittivity and permeability are opposite in sign. We also observe an identical resonant versus anti-resonant frequency dependence of the effective materials parameters for a periodic array of thin metallic wires with cuts placed periodically along the length of the wire, with roles of the permittivity and permeability reversed from the SRR case. We show in a simple manner that the finite unit cell size is responsible for the anti-resonant behavior.

cond-mat.mtrl-sci↗
arXiv2003

Absorption losses in periodic arrays of thin metallic wires

We analyze the transmission and reflection of the electromagnetic wave calculated from transfer matrix simulations of periodic arrangements of thin metallic wires. The effective permittivity and the absorption is determined. Their dependence on the wire thickness and the conductance of the metallic wires is studied. The cutoff frequency or effective plasma frequency is obtained and is compared with analytical predictions. It is shown that the periodic arrangement of wires exhibits a frequency region in which the real part of the permittivity is negative while its imaginary part is very small. This behavior is seen for wires with thickness as small as 17 $μ$m with a lattice constant of 3.33 mm.

cond-mat.mtrl-sci↗
arXiv2002

Coherent resistance of a disordered 1D wire: Expressions for all moments and evidence for non-Gaussian distribution

We study coherent electron transport in a one-dimensional wire with disorder modeled as a chain of randomly positioned scatterers. We derive analytical expressions for all statistical moments of the wire resistance $ρ$. By means of these expressions we show analytically that the distribution $P(f)$ of the variable $f=\ln(1+ρ)$ is not exactly Gaussian even in the limit of weak disorder. In a strict mathematical sense, this conclusion is found to hold not only for the distribution tails but also for the bulk of the distribution $P(f)$.

cond-mat.mes-hall↗
arXiv2002

Conductance statistics near the Anderson transition

Paper reviews recent numerical data for the conductance distribution of disordered systems in the critical regime and in the localized regime. Of particular interest is the non-analytical form of the critical conductance distribution in the 3D and 4D systems, non-Gaussian form of the distribution of P(ln g) in localized 3D systems.

cond-mat.mes-hall↗
arXiv2002

Determination of Effective Permittivity and Permeability of Metamaterials from Reflection and Transmission Coefficients

We analyze the reflection and transmission coefficients calculated from transfer matrix simulations on finite lenghts of electromagnetic metamaterials, to determine the effective permittivity and permeability. We perform this analysis on structures composed of periodic arrangements of wires, split ring resonators (SRRs) and both wires and SRRs. We find the recovered frequency-dependent permittivity and permeability are entirely consistent with analytic expressions predicted by effective medium arguments. Of particular relevance are that a wire medium exhibits a frequency region in which the real part of permittivity is negative, and SRRs produce a frequency region in which the real part of permeability is negative. In the combination structure, at frequencies where both the recovered real part of permittivity and permeability are simultaneously negative, the real part of the index-of-refraction is found also to be unambigously negative.

physics.class-ph↗
arXiv2001

Transmission Studies of Left-handed Materials

Left-handed materials are studied numerically using an improved version of the transfer-matrix method. The transmission, reflection, the phase of the reflection and the absorption are calculated and compared with experiments for both single split-ring resonators (SRR) with negative permeability and left-handed materials (LHMs) which have both the permittivity and permeability negative. Our results suggest ways of positively identifying materials that have both permittivity and permeability negative, from materials that have either permeability or permittivity negative.

cond-mat.mtrl-sci↗
arXiv1999

Metal-insulator transition in system with topological disorder

Metal-insulator transition in anisotropic disordered Anderson model with both topological and diagonal disorder is investigated numerically. For four sets of the model parameters we found the critical disorder and the critical exponent and prove that they do not depend on the transport direction. The system size independent critical conductance distribution P_c(g) is found for each critical point. The form of P_c(g) depends on the model parameters and on the direction of the treansport. Arguments in favor of the one-parameter scaling are presented. This paper has been withdrawn

cond-mat.dis-nn↗
arXiv1999

Metal-insulator transition in three dimensional Anderson model: universal scaling of higher Lyapunov exponents

Numerical studies of the Anderson transition are based on the finite-size scaling analysis of the smallest positive Lyapunov exponent. We prove numerically that the same scaling holds also for higher Lyapunov exponents. This scaling supports the hypothesis of the one-parameter scaling of the conductance distribution. From the collected numerical data for quasi one dimensional systems up to the system size 24 x 24 x infinity we found the critical disorder 16.50 < Wc < 16.53 and the critical exponent 1.50 < ν< 1.54. Finite-size effects and the role of irrelevant scaling parameters are discussed.

cond-mat.mes-hall↗
arXiv1999

Numerical studies of Anderson transition

We present numerical results for the statistics of $z$'s ($z$'s are defined as logarithm of eigenvalues of the transfermatrix $T^†T$) at the critical points of Anderson transition in 3D and 4D. The change of the density of $z$ due to the crossover from the metallic to the localized regime is described. Linear behavior $ρ(z)= z$ at the critical point in 3D is proven and discussed. In the insulating regime, the universal form of $ρ$ has been found.

cond-mat.dis-nn↗
arXiv1999

The Sixth-Moment Sum Rule For the Pair Correlations of the Two-Dimensional One-Component Plasma: Exact Result

The system under consideration is a two-dimensional one-component plasma in fluid regime, at density n and at arbitrary coupling Gamma=beta e^2 (e=unit charge, beta = inverse temperature). The Helmholtz free energy of the model, as the generating functional for the direct pair correlation c, is treated in terms of a convergent renormalized Mayer diagrammatic expansion in density. Using specific topological transformations within the bond-renormalized Mayer expansion we prove that the nonzero contributions to the regular part of the Fourier component of c up to the k^2-term originate exclusively from the ring diagrams (unable to undertake the bond-renormalization procedure) of the Helmholtz free energy. In particular, c(k)=-Gamma/k^2 + Gamma/(8 pi n) - k^2/[96(pi n)^2] + O(k^4). This result fixes via the Ornstein-Zernike relation, besides the well-known zeroth-, second- and fourth- moment sum rules, the new six-momnt condition for the truncated pair correlation h, n(pi Gamma n/2)^3 Integral r^6 h(r) d^2 r = 3(Gamma-6)(8-3 Gamma)/4.

cond-mat.stat-mech↗