P. A. Kalozoumis

Entropic sampling via Wang-Landau random walks in dominant energy subspaces.

Dominant energy subspaces of statistical systems are defined with the help of restrictive conditions on various characteristics of the energy distribution, such as the probability density and the fourth order Binders cumulant. Our analysis generalizes the ideas of the critical minimum energy subspace (CRMES) technique, applied previously to study the specific heats finite-size scaling. Here, we illustrate alternatives that are useful for the analysis of further finite-size anomalies and the behavior of the corresponding dominant subspaces is presented for the two-dimensional (2D) Baxter-Wu and the 2D and 3D Ising models. In order to show that a CRMES technique is adequate for the study of magnetic anomalies, we study and test simple methods which provide the means for an accurate determination of the energy-order-parameter (E,M) histograms via Wang-Landau random walks. The 2D Ising model is used as a test case and it is shown that high-level Wang-Landau sampling schemes yield excellent estimates for all magnetic properties. Our estimates compare very well with those of the traditional Metropolis method. The relevant dominant energy subspaces and dominant magnetization subspaces scale as expected with exponents alpha/nu and gamma/nu, respectively. Using the Metropolis method we examine the time evolution of the corresponding dominant magnetization subspaces and we uncover the reasons behind the inadequacy of the Metropolis method to produce a reliable estimation scheme for the tail regime of the order-parameter distribution.

Monte Carlo studies of the square Ising model with next-nearest-neighbor interactions

Abstract.We apply a new entropic scheme to study the critical behavior of the square-lattice Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions. Estimates of the present scheme are compared with those of the Metropolis algorithm. We consider interactions in the range where superantiferromagnetic (SAF) order appears at low temperatures. A recent prediction of a first-order transition along a certain range (0.5–1.2) of the interaction ratio (R=Jnnn/Jnn) is examined by generating accurate data for large lattices at a particular value of the ratio (R=1). Our study does not support a first-order transition and a convincing finite-size scaling analysis of the model is presented, yielding accurate estimates for all critical exponents for R=1. The magnetic exponents are found to obey “weak universality” in accordance with a previous conjecture.

Local symmetries and perfect transmission in aperiodic photonic multilayers

We develop a classification of perfectly transmitting resonances occuring in effectively onedimensional optical media which are decomposable into locally reflection symmetric parts. The local symmetries of the medium are shown to yield piecewise translation-invariant quantities, which are used to distinguish resonances with arbitrary field profile from resonances following the medium symmetries. Focusing on light scattering in aperiodic multilayer structures, we demonstrate this classification for representative setups, providing insight into the origin of perfect transmission. We further show how local symmetries can be utilized for the design of optical devices with perfect transmission at prescribed energies. Providing a link between resonant scattering and local symmetries of the underlying medium, the proposed approach may contribute to the understanding of optical response in complex systems.

Invariants of broken discrete symmetries.

The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions

We implement a new and accurate numerical entropic scheme to investigate the first-order transition features of the triangular Ising model with nearest-neighbor (Jnn) and next-nearest-neighbor (Jnnn) antiferromagnetic interactions in ratio R=Jnn/Jnnn=1. Important aspects of the existing theories of first-order transitions are briefly reviewed, tested on this model, and compared with previous work on the Potts model. Using lattices with linear sizes L=30,40,…,100,120,140,160,200,240,360 and 480 we estimate the thermal characteristics of the present weak first-order transition. Our results improve the original estimates of Rastelli et al. and verify all the generally accepted predictions of the finite-size scaling theory of first-order transitions, including transition point shifts, thermal, and magnetic anomalies. However, two of our findings are not compatible with current phenomenological expectations. The behavior of transition points, derived from the number-of-phases parameter, is not in accordance with the theoretically conjectured exponentially small shift behavior and the well-known double Gaussian approximation does not correctly describe higher correction terms of the energy cumulants. It is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections.

Local symmetries in one-dimensional quantum scattering

Submitted by ΑΝΝΑ ΠΟΡΤΙΝΟΥ (annaportinou@ekt.gr) on 2016-04-26T07:50:49Z No. of bitstreams: 1 1.91_ΔΗΜ_21_3_13.pdf: 1122571 bytes, checksum: 48967897cf9f5f603bff546034242108 (MD5)

Local symmetry dynamics in one-dimensional aperiodic lattices: a numerical study

A unifying description of lattice potentials generated by aperiodic one-dimensional sequences is proposed in terms of their local reflection or parity symmetry properties. We demonstrate that the ranges and axes of local reflection symmetry possess characteristic distributional and dynamical properties, determined here numerically for certain lattice types. A striking aspect of such a property is given by the return maps of sequential spacings of local symmetry axes, which typically traverse few-point symmetry orbits. This local symmetry dynamics allows for a description of inherently different aperiodic lattices according to fundamental symmetry principles. Illustrating the local symmetry distributional and dynamical properties for several representative binary lattices, we further show that the renormalized axis-spacing sequences follow precisely the particular type of underlying aperiodic order, revealing the presence of dynamical self-similarity. Our analysis thus provides evidence that the long-range order of aperiodic lattices can be characterized in a compellingly simple way by its local symmetry dynamics.

PT-symmetry breaking in waveguides with competing loss-gain pairs

We consider a periodic waveguide array whose unit cell consists of a

Invariant currents in lossy acoustic waveguides with complete local symmetry

\mathcal{PT}

Emitter and absorber assembly for multiple self-dual operation and directional transparency

-symmetric quadrimer with two competing loss/gain parameter pairs which lead to qualitatively different symmetry-broken phases. It is shown that the transitions between the phases are described by a symmetry-adapted nonlocal current which maps the spectral properties to the spatially resolved field, for the lattice as well as for the isolated quadrimer. Its site-average acts like a natural order parameter for the general class of one-dimensional