839 research outputs found
Geometry of mixed states for a q-bit and the quantum Fisher information tensor
After a review of the pure state case, we discuss from a geometrical point of
view the meaning of the quantum Fisher metric in the case of mixed states for a
two-level system, i.e. for a q-bit, by examining the structure of the fiber
bundle of states, whose base space can be identified with a co-adjoint orbit of
the unitary group. We show that the Fisher Information metric coincides with
the one induced by the metric of the manifold of SU(2), i.e. the 3-dimensional
sphere , when the mixing coefficients are varied. We define the notion of
Fisher Tensor and show that its anti-symmetric part is intrinsically related to
the Kostant Kirillov Souriau symplectic form that is naturally defined on
co-adjoint orbits, while the symmetric part is nontrivially again represented
by the Fubini Study metric on the space of mixed states, weighted by the mixing
coefficients.Comment: 20 pages; Abstract and Introduction modified, references added. Final
published versio
Continuum in the Excitation Spectrum of the S=1 Compound CsNiCl_3
Recent neutron scattering experiments on CsNiCl_3 reveal some features which
are not well described by the nonlinear sigma model nor by numerical
simulations on isolated S=1 spin chains. In particular, in real systems the
intensity of the continuum of multiparticle excitations, at T=6K, is about 5
times greater than predicted. Also the gap is slightly higher and the
correlation length is smaller. We propose a theoretical scenario where the
interchain interaction is approximated by a staggered magnetic field, yielding
to a correct prediction of the observed quantities.Comment: 4 pages, 2 figures (.eps), RevTe
Edge States in Gauge Theories: Theory, Interpretations and Predictions
Gauge theories on manifolds with spatial boundaries are studied. It is shown
that observables localized at the boundaries (edge observables) can occur in
such models irrespective of the dimensionality of spacetime. The intimate
connection of these observables to charge fractionation, vertex operators and
topological field theories is described. The edge observables, however, may or
may not exist as well-defined operators in a fully quantized theory depending
on the boundary conditions imposed on the fields and their momenta. The latter
are obtained by requiring the Hamiltonian of the theory to be self-adjoint and
positive definite. We show that these boundary conditions can also have nice
physical interpretations in terms of certain experimental parameters such as
the penetration depth of the electromagnetic field in a surrounding
superconducting medium. The dependence of the spectrum on one such parameter is
explicitly exhibited for the Higgs model on a spatial disc in its London limit.
It should be possible to test such dependences experimentally, the above Higgs
model for example being a model for a superconductor. Boundary conditions for
the 3+1 dimensional system confined to a spatial ball are studied. Their
physical meaning is clarified and their influence on the edge states of this
system (known to exist under certain conditions) is discussed. It is pointed
out that edge states occur for topological solitons of gauge theories such as
the 't Hooft-Polyakov monopoles.Comment: 36 pages, LATEX File (revised because figures had problems
Discretized Laplacians on an Interval and their Renormalization Group
The Laplace operator admits infinite self-adjoint extensions when considered
on a segment of the real line. They have different domains of essential
self-adjointness characterized by a suitable set of boundary conditions on the
wave functions. In this paper we show how to recover these extensions by
studying the continuum limit of certain discretized versions of the Laplace
operator on a lattice. Associated to this limiting procedure, there is a
renormalization flow in the finite dimensional parameter space describing the
dicretized operators. This flow is shown to have infinite fixed points,
corresponding to the self-adjoint extensions characterized by scale invariant
boundary conditions. The other extensions are recovered by looking at the other
trajectories of the flow.Comment: 23 pages, 2 figures, DSF-T-28/93,INFN-NA-IV-28/93, SU-4240-54
Bent surface free energy differences from simulation
We present a calculation of the change of free energy of a solid surface upon
bending of the solid. It is based on extracting the surface stress through a
molecular dynamics simulation of a bent slab by using a generalized stress
theorem formula, and subsequent integration of the stress with respect to
strain as a function of bending curvature. The method is exemplified by
obtaining and comparing free energy changes with curvature of various
reconstructed Au(001) surfaces.Comment: 14 pages, 2 figures, accepted for publication in Surface Science
(ECOSS-19
Realistic simulations of Au(100): Grand Canonical Monte Carlo and Molecular Dynamics
The large surface density changes associated with the (100) noble metals
surface hex-reconstruction suggest the use of non-particle conserving
simulation methods. We present an example of a surface Grand Canonical Monte
Carlo applied to the transformation of a square non reconstructed surface to
the hexagonally covered low temperature stable Au(100). On the other hand,
classical Molecular Dynamics allows to investigate microscopic details of the
reconstruction dynamics, and we show, as an example, retraction of a step and
its interplay with the surface reconstruction/deconstruction mechanism.Comment: 9 pages, 5 figures, accepted for publication in Surf. Rev. and
Letters (ICSOS-6
Low-Dimensional Spin Systems: Hidden Symmetries, Conformal Field Theories and Numerical Checks
We review here some general properties of antiferromagnetic Heisenberg spin
chains, emphasizing and discussing the role of hidden symmetries in the
classification of the various phases of the models. We present also some recent
results that have been obtained with a combined use of Conformal Field Theory
and of numerical Density Matrix Renormalization Group techniques.Comment: To be published in the proceedings of the XIII Conference on
"Symmetries in Physics", held in Bregenz (Voralberg, Austria), 21-24/7/2003.
Plain LaTeX2e, 4 EPS figure
Melting and nonmelting of solid surfaces and nanosystems
We present an extensive but concise review of our present understanding,
largely based on theory and simulation work from our group, on the equilibrium
behavior of solid surfaces and nanosystems close to the bulk melting point. In
the first part we define phenomena, in particular surface melting and
nonmelting, and review some related theoretical approaches, from heuristic
theories to computer simulation. In the second part we describe the surface
melting/nonmelting behavior of several different classes of solids, ranging
from van der Waals crystals, to valence semiconductors, to ionic crystals and
metals. In the third part, we address special cases such as strained solids,
the defreezing of glass surfaces, and rotational surface melting. Next, we
digress briefly to surface layering of a liquid metal, possibly leading to
solid-like or hexatic two dimensional phases floating on the liquid. In the
final part, the relationship of surface melting to the premelting of
nanoclusters and nanowires is reviewed.Comment: 54 pages, 26 figure
Alternative Hamiltonian Desciptions and Statistical Mechanics
We argue here that, as it happens in Classical and Quantum Mechanics, where
it has been proven that alternative Hamiltonian descriptions can be compatible
with a given set of equations of motion, the same holds true in the realm of
Statistical Mechanics, i.e. that alternative Hamiltonian descriptions do lead
to the same thermodynamical description of any physical system.Comment: 11 page
On critical phases in anisotropic spin-1 chains
Quantum spin-1 chains may develop massless phases in presence of Ising-like
and single-ion anisotropies. We have studied c=1 critical phases by means of
both analytical techniques, including a mapping of the lattice Hamiltonian onto
an O(2) nonlinear sigma model, and a multi-target DMRG algorithm which allows
for accurate calculation of excited states. We find excellent quantitative
agreement with the theoretical predictions and conclude that a pure Gaussian
model, without any orbifold construction, describes correctly the low-energy
physics of these critical phases. This combined analysis indicates that the
multicritical point at large single-ion anisotropy does not belong to the same
universality class as the Takhtajan-Babujian Hamiltonian as claimed in the
past. A link between string-order correlation functions and twisting vertex
operators, along the c=1 line that ends at this point, is also suggested.Comment: 9 pages, 3 figures, svjour format, submitted to Eur. Phys. J.
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