States In One-dimensional Systems Research Articles

Proof of universality in one-dimensional few-body systems including anisotropic interactions

We provide an analytical proof of universality for bound states in one-dimensional systems of two and three particles, valid for short-range interactions with negative or vanishing integral over space. The proof is performed in the limit of weak pair-interactions and covers both binding energies and wave functions. Moreover, in this limit the results are formally shown to converge to the respective ones found in the case of the zero-range contact interaction.

Bosonization for fermions and parafermions

Parafermions are fractional excitations which can be regarded as generalizations of Majorana bound states, but in contrast to the latter they require electron-electron interactions. Compared to Majorana bound states, they offer richer non-Abelian braiding statistics, and have thus been proposed as building blocks for topologically protected universal quantum computation. In this review, we provide a pedagogical introduction to the field of parafermion bound states in one-dimensional systems. We present the necessary theoretical tools for their study, in particular bosonization and the renormalization-group technique, and show how those can be applied to study parafermions.

Interaction of Dot Clasters

Models of the pointed interactions approximately describing real interactions of nuclear particles in quantum mechanics are considered. The concept of “a dot cluster”—a complex of charges which at the zero size create possibility of localization of a trial particle in the field of the final size is entered. States in one-dimensional systems, and also in three-dimensional systems with “a local isotropy” are studied. The conditions of dot systems characterized by the nonzero, including fractional, orbital moment were studied.

Delocalization to localization transition in one-dimensional systems with long-range correlated off-diagonal disorder

The combined effects of long-range correlations and disorder strength on critical properties of electronic states in one-dimensional systems with long-range correlated off-diagonal disorder are investigated for the whole energy band. Numerical studies on the localization length demonstrate the existence of disorder-induced delocalization-to-localization transition (DLT) and energy-induced DLT in such systems when the correlations of hopping terms are strong enough to generate extended states. Further calculations confirm that the critical disorder strength and critical energy related to these DLTs are Wc=2t0−|E| and ±Ec=±|2t0−W|, respectively. Based on these critical points, the detailed phase diagrams in different parameter spaces are obtained.

Dynamics of bound soliton states in regularized dispersive equations

The nonstationary dynamics of topological solitons (dislocations, domain walls, fluxons) and their bound states in one-dimensional systems with high dispersion are investigated. Dynamical features of a moving kink emitting radiation and breathers are studied analytically. Conditions of the breather excitation and its dynamical properties are specified. Processes of soliton complex formation are studied analytically and numerically in relation to the strength of the dispersion, soliton velocity, and distance between solitons. It is shown that moving bound soliton complexes with internal structure can be stabilized by an external force in a dissipative medium then their velocities depend in a step-like manner on a driving strength.

Localization length enhancement in two-dimensional self-assembled systems

Disorder correlations lead to important effects on the localization of states inone-dimensional systems, as shown for a large number of correlation models in the contextof polymers and macromolecules. The extension of the problem to two-dimensional systemshas been less frequently discussed due to the lack, until recently, of realistic systems withproperties that could be addressed to the effects of correlations in disorder. The advent ofself-assembled quantum dots, which may show short-range ordering, has changed thisscenario. In the present work we investigate the properties of a two-dimensional disorderedlattice with short-range correlations in the disorder that reveals itself as a minimal modelfor self-assembled quantum dots. The short-range correlations in disorder may leadto significant enhancement of the localization length for wide energy windows.

Determinant of Wave Operator as a Measure for Resonance and Bound States in One-Dimensional Potential Scattering System

The determinant of the wave operator or its transposed operator (source operator) works as a measure for resonance and bound states in one-dimensional potential scattering system. This fact is based on an identity proved here: the determinant of the wave or source operator equals to the transmission coefficient, which represents the field amplitude in the forward side of the scatterer. Utilizing this measure, resonance and bound states in one-dimensional system are properly assigned without solving wave equation. In future, local enhancement of optical near-field in three-dimensional system, i.e., local plasmon resonance will be treated, generalizing the present method.

A novel approach to probe the presence of correlation in energetic disorder: A theoretical study

Fluorescence spectra are used to study exciton spectral dynamics, resulting from hopping of excitons over localized states in one-dimensional systems of chromophores with correlated disorder. The complexity of exciton relaxation which is a direct consequence of the interplay of localization, intra-band or intra-segment relaxation and radiative relaxation of excitons is theoretically studied using a master equation. We show that in the case of resonant excitation the exciton spectral dynamics strongly depends on the presence of intermolecular correlation in the static disorder. We predict that the fluorescence with narrow band excitation could be used as an alternative tool to reveal the presence of the intermolecular correlation.

Stationary localized states in one-dimensional systems due to modified nonlinear impurities

Discrete nonlinear Schr\"odinger equation (DNLS) of the form ${i(dC}_{n}{/dt)=C}_{n+1}{+C}_{n\ensuremath{-}1}\ensuremath{-}{\ensuremath{\chi}}_{n}(|{C}_{n+1}{|}^{2}+|{C}_{n\ensuremath{-}1}{|}^{2}\ensuremath{-}2|{C}_{n}{|}^{2}{)C}_{n}$ is used to study the formation of stationary localized states in one dimensional system due to a single as well as a dimeric nonlinear impurity. The stability of the states and its connection with the nonlinear strength is presented. Results are compared with those obtained from other DNLS's. It is found that the DNLS used in this paper has more impact on the formation of stationary localized states.

Stationary self-localized states due to quadratic nonlinearity in one-dimensional systems

We investigate the effect of a nondegenerate quadratic nonlinear dimeric impurity on the formation of stationary localized states in one-dimensional systems. We also consider the formation of stationary self-localized states in a translationally invariant fully nonlinear system where alternative sites have the same nonlinear strengths. Appropriate ansatze have been chosen for all of the cases which reproduce the known results for special cases. The connection of the stability of a state to its energy is presented graphically.

Equation-of-Motion Calculations on an Isolated Chain of Polyacetylene

Abstract An equation-of-motion (EOM) method for calculating the excited states of one-dimensional systems is discussed. This method is similar to configuration-interaction theory except the ground state is constrained to remain the Hartree-Fock ground state. Issues relating to the size-consistency of the method are briefly discussed. EOM calculations are performed using the semi-empirical Hamiltonian appropriate for gas-phase polyenes. In these calculations, electrons and holes are created on the Hartree-Fock ground state. In the low energy states, the electrons and holes get bound together by Coulomb forces into many-body excitations, or effective particles. These effective particles are delocalized over the entire polymer, but there is limited separation between the electrons and holes within the particle. The effective particles may have significant contributions from both single and double electron-hole pair configurations. It is speculated that dielectric screening may be much weaker for states with ...

The parity anomaly in condensed matter physics

I discuss in detail the recently proposed physical realization of the Parity Anomaly in a PbTe-type crystal with a stacking fault. A close analogy with charged soliton states in one-dimensional systems is presented. A possible way to introduce chiral fermions in a Lattice Gauge Theory is discussed.

On the equivalence of boundary conditions

We show that ifb andb′ are two boundary conditions (b.c.) for general spin systems on ℤ d such that the difference in the energies of a spin configuration σΛ in Λ ⊂ ℤ d is uniformly bounded, |H Λ,b (σΛ)−H Λ,b′(σΛ)|⩽C < ∞, then any infinite-volume Gibbs statesρ and ρ′ obtained with these b.c. have the same measure-zero sets. This implies that the decompositions ofρ and ρ′ into extremal Gibbs states are equivalent (mutually absolutely continuous). In particular, ifρ is extremal,ρ=ρ′. Application of this observation yields in an easy way (among other things) (a) the uniqueness of the Gibbs states for one-dimensional systems with forces that are not too long-range; (b) the fact that various b.c. that are natural candidates for producing non-translation-invariant Gibbs states cannot lead to such an extremal Gibbs state in two dimensions.

Electrical conductivity in a one-dimensional aperiodic solid

Although there has been much interest in the energy bands and the localization of electronic states in one-dimensional systems, and although there has been some discussion of the relation between characteristic momentum and conductivity, there has as yet appeared no direct calculation of the electrical conductivity. We present here the first direct numerical computation of the (frequency dependent) electrical conductivity of one electron in an aperiodic one-dimensional chain of delta-function potentials. Results are obtained for chains of various lengths and various degrees of disorder. They show that although the ground state binding energy and the density of states converge rapidly to an ensemble average for long chains, the conductivity spectrum varies with the particular chain chosen and does not converge to the ensemble average. This disagrees with the popular view of low frequency conductivity in amorphous solids, but is generally in accord with the recent theoretical work of Landauer.

Symmetry properties of exciton states in one-dimensional systems

We discuss a cyclic chain of N identical sites, each with two possible quantum states, whose Hamiltonian may be written in terms of the spin operators for N spins S = 1/2, and transformed into the Fermi site excitation representation. We show that in the Fermion wave representation the requirement that the states transform according to irreducible representations of the translational symmetry group demands that the quasiparticle momenta are drawn from the representations of the double group. They must be all integral or all half-integral when the number of quasiparticles is odd or even respectively. The requirement that a quantum-mechanical operator has a definite symmetry type leads to very complicated conditions unless the operator conserves the odd or even particle number. If it does the symmetry operator can be defined in terms of Fermi wave operators and projection operators. The time reversal transformation is developed in detail and applied to problems of degeneracy in McConnell's model of singlet excitons and in the anisotropic transverse Heisenberg antiferromagnet. In the Bogoliubov-Valatin transformation time reversal shifts the quasiparticle momenta by ± π, converting integral into half-integral momenta when N is odd. The energies of the excited states are doubly-periodic functions of the momentum.