31 research outputs found
Analytic Lyapunov exponents in a classical nonlinear field equation
It is shown that the nonlinear wave equation , which is the continuum limit of
the Fermi-Pasta-Ulam (FPU) beta model, has a positive Lyapunov exponent
lambda_1, whose analytic energy dependence is given. The result (a first
example for field equations) is achieved by evaluating the lattice-spacing
dependence of lambda_1 for the FPU model within the framework of a Riemannian
description of Hamiltonian chaos. We also discuss a difficulty of the
statistical mechanical treatment of this classical field system, which is
absent in the dynamical description.Comment: 4 pages, 1 figur
On the origin of Phase Transitions in the absence of Symmetry-Breaking
In this paper we investigate the Hamiltonian dynamics of a lattice gauge
model in three spatial dimension. Our model Hamiltonian is defined on the basis
of a continuum version of a duality transformation of a three dimensional Ising
model. The system so obtained undergoes a thermodynamic phase transition in the
absence of symmetry-breaking. Besides the well known use of quantities like the
Wilson loop we show how else the phase transition in such a kind of models can
be detected. It is found that the first order phase transition undergone by
this model is characterised according to an Ehrenfest-like classification of
phase transitions applied to the configurational entropy. On the basis of the
topological theory of phase transitions, it is discussed why the seemingly
divergent behaviour of the third derivative of configurational entropy can be
considered as the "shadow" of some suitable topological transition of certain
submanifolds of configuration space.Comment: 31 pages, 9 figure
One-dimensional s-p superlattice
The physics of one dimensional optical superlattices with resonant -
orbitals is reexamined in the language of appropriate Wannier functions. It is
shown that details of the tight binding model realized in different optical
potentials crucially depend on the proper determination of Wannier functions.
We discuss the properties of a superlattice model which quasi resonantly
couples and orbitals and show its relation with different tight binding
models used in other works.Comment: 9pp, 10 figures, updated references, comments to [email protected]
Self-consistent tight-binding description of Dirac points moving and merging in two dimensional optical lattices
We present an accurate ab initio tight-binding model, capable of describing
the dynamics of Dirac points in tunable honeycomb optical lattices following a
recent experimental realization [L. Tarruell et al., Nature 483, 302 (2012)].
Our scheme is based on first-principle maximally localized Wannier functions
for composite bands. The tunneling coefficients are calculated for different
lattice configurations, and the spectrum properties are well reproduced with
high accuracy. In particular, we show which tight binding description is needed
in order to accurately reproduce the position of Dirac points and the
dispersion law close to their merging, for different laser intensities.Comment: 11 pages, 16 figure
Ab initio analysis of the topological phase diagram of the Haldane model
We present an ab initio analysis of a continuous Hamiltonian that maps into
the celebrated Haldane model. The tunnelling coefficients of the tight-binding
model are computed by means of two independent methods - one based on the
maximally localized Wannier functions, the other through analytic expressions
in terms of gauge-invariant properties of the spectrum - that provide a
remarkable agreement and allow to accurately reproduce the exact spectrum of
the continuous Hamiltonian. By combining these results with the numerical
calculation of the Chern number, we are able to draw the phase diagram in terms
of the physical parameters of the microscopic model. Remarkably, we find that
only a small fraction of the original phase diagram of the Haldane model can be
accessed, and that the topological insulator phase is suppressed in the deep
tight-binding regime.Comment: 11 pages, 9 figure