arXiv subjects

J. C. Eilbeck

Publications and source records attributed to J. C. Eilbeck.

29 records · Page 2Linked to original sources

arXiv2005

Aharonov-Bohm effect for an exciton in a finite width nano-ring

We study the Aharonov-Bohm effect for an exciton on a nano-ring using a 2D attractive fermionic Hubbard model. We extend previous results obtained for a 1D ring in which only azimuthal motion is considered, to a more general case of 2D annular lattices. In general, we show that the existence of the localization effect, increased by the nonlinearity, makes the phenomenon in the 2D system similar to the 1D case. However, the introduction of radial motion introduces extra frequencies, different from the original isolated frequency corresponding to the excitonic Aharonov-Bohm oscillations. If the circumference of the system becomes large enough, the Aharonov-Bohm effect is suppressed.

cond-mat.str-el↗

arXiv2004

Dynamical two electron states in a Hubbard-Davydov model

We study a model in which a Hubbard Hamiltonian is coupled to the dispersive phonons in a classical nonlinear lattice. Our calculations are restricted to the case where we have only two quasi-particles of opposite spins, and we investigate the dynamics when the second quasi-particle is added to a state corresponding to a minimal energy single quasi-particle state. Depending on the parameter values, we find a number of interesting regimes. In many of these, discrete breathers (DBs) play a prominent role with a localized lattice mode coupled to the quasiparticles. Simulations with a purely harmonic lattice show much weaker localization effects. Our results support the possibility that DBs are important in HTSC.

cond-mat.supr-con↗

arXiv2003

Quantum signatures of breather-breather interactions

The spectrum of the Quantum Discrete Nonlinear Schrödinger equation on a periodic 1D lattice shows some interesting detailed band structure which may be interpreted as the quantum signature of a two-breather interaction in the classical case. We show that this fine structure can be interpreted using degenerate perturbation theory.

quant-ph↗

arXiv2003

Quantum breathers in an attractive fermionic Hubbard model

In one-dimensional translationally invariant anharmonic lattices, an extended Bloch state with two or more strongly correlated particles is usually called a quantum breather. Here we study an attractive fermionic Hubbard model with two kind of particles of opposite spin. We discuss the existence of breathers, and several effects that break the translational symmetry of the system and localize the breather in the lattice.

nlin.PS↗

arXiv2003

Trapping in quantum chains

A quantum breather on a translationally invariant one-dimensional anharmonic lattice is an extended Bloch state with two or more particles in a strongly correlated state. We discuss several effects that break the lattice symmetry and lead to spatial localization of the breather.

nlin.PS↗

arXiv2003

Influence of moving breathers on vacancies migration

A vacancy defect is described by a Frenkel--Kontorova model with a discommensuration. This vacancy can migrate when interacts with a moving breather. We establish that the width of the interaction potential must be larger than a threshold value in order that the vacancy can move forward. This value is related to the existence of a breather centred at the particles adjacent to the vacancy.

nlin.PS↗

arXiv1999

Quasi-Periodic and Periodic Solutions for Systems of Coupled Nonlinear SCHRÖdinger Equations

We consider travelling periodic and quasiperiodic wave solutions of a set of coupled nonlinear Schrödimger equations. In fibre optics these equations can be used to model single mode fibers with strong birefringence and two-mode optical fibres. Recently these equations appear as modes, which describe pulse-pulse interaction in wavelength-division-multiplexed channels of optical fiber transmission systems. Two phase quasi-periodic solutions for integrable Manakov system are given in tems of two-dimensional Kleinian functions. The reduction of quasi-periodic solutions to elliptic functions is dicussed. New solutions in terms of generalized Hermite polynomilas, which are associated with two-gap Treibich-Verdier potentials are found.

solv-int↗

arXiv1997

Localized moving breathers in a 2-D hexagonal lattice

We show for the first time that highly localized in-plane breathers can propagate in specific directions with minimal lateral spreading in a model 2-D hexagonal non-linear lattice. The lattice is subject to an on-site potential in addition to longitudinal nonlinear inter-particle interactions. This study investigates the prediction that stable breather-like solitons could be formed as a result of energetic scattering events in a given layered crystal and would propagate in atomic-chain directions in certain atomic planes. This prediction arose from a long-term study of previously unexplained dark lines in natural crystals of muscovite mica.

patt-sol↗

arXiv1994

Quantum Lattice Solitons

The number state method is used to study soliton bands for three anharmonic quantum lattices: i) The discrete nonlinear Schrödinger equation, ii) The Ablowitz-Ladik system, and iii) A fermionic polaron model. Each of these systems is assumed to have $f$-fold translational symmetry in one spatial dimension, where $f$ is the number of freedoms (lattice points). At the second quantum level $(n=2)$ we calculate exact eigenfunctions and energies of pure quantum states, from which we determine binding energy $(E_{\rm b})$, effective mass $(m^{*})$ and maximum group velocity $(V_{\rm m})$ of the soliton bands as functions of the anharmonicity in the limit $f \to \infty$. For arbitrary values of $n$ we have asymptotic expressions for $E_{\rm b}$, $m^{*}$, and $V_{\rm m}$ as functions of the anharmonicity in the limits of large and small anharmonicity. Using these expressions we discuss and describe wave packets of pure eigenstates that correspond to classical solitons.

hep-th↗

arXiv1993

Linear $r$-Matrix Algebra for Systems Separable\\ in Parabolic Coordinates

We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of $2\times 2$ matrices for the whole hierarchy, we construct the associated linear $r$-matrix algebra with the $r$-matrix dependent on the dynamical variables. A dynamical Yang-Baxter equation is discussed.

hep-th↗

arXiv1993

Linear $r$-matrix algebra for classical separable systems

We consider a hierarchy of the natural type Hamiltonian systems of $n$ degrees of freedom with polynomial potentials separable in general ellipsoidal and general paraboloidal coordinates. We give a Lax representation in terms of $2\times 2$ matrices for the whole hierarchy and construct the associated linear $r$-matrix algebra with the $r$-matrix dependent on the dynamical variables. A Yang-Baxter equation of dynamical type is proposed. Using the method of variable separation we provide the integration of the systems in classical mechanics conctructing the separation equations and, hence, the explicit form of action variables. The quantisation problem is discussed with the help of the separation variables.

hep-th↗