11 research outputs found
Cluster Percolation in O(n) Spin Models
The spontaneous symmetry breaking in the Ising model can be equivalently
described in terms of percolation of Wolff clusters. In O(n) spin models
similar clusters can be built in a general way, and they are currently used to
update these systems in Monte Carlo simulations. We show that for 3-dimensional
O(2), O(3) and O(4) such clusters are indeed the physical `islands' of the
systems, i.e., they percolate at the physical threshold and the percolation
exponents are in the universality class of the corresponding model. For O(2)
and O(3) the result is proven analytically, for O(4) we derived it by numerical
simulations.Comment: 11 pages, 8 figures, 2 tables, minor modification
Robustness of optimal working points for non-adiabatic holonomic quantum computation
Geometric phases are an interesting resource for quantum computation, also in
view of their robustness against decoherence effects. We study here the effects
of the environment on a class of one-qubit holonomic gates that have been
recently shown to be characterized by "optimal" working times. We numerically
analyze the behavior of these optimal points and focus on their robustness
against noise.Comment: 14 pages, 8 figure
q-Quaternions and q-deformed su(2) instantons
We construct (anti)instanton solutions of a would-be q-deformed su(2)
Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant
noncommutative space] by reinterpreting the function algebra on the latter as a
q-quaternion bialgebra. Since the (anti)selfduality equations are covariant
under the quantum group of deformed rotations, translations and scale change,
by applying the latter we can generate new solutions from the one centered at
the origin and with unit size. We also construct multi-instanton solutions. As
they depend on noncommuting parameters playing the roles of `sizes' and
`coordinates of the centers' of the instantons, this indicates that the moduli
space of a complete theory will be a noncommutative manifold. Similarly, gauge
transformations should be allowed to depend on additional noncommutative
parameters.Comment: Latex file, 39 pages. Final version appeared in JM
q-Deformed quaternions and su(2) instantons
We have recently introduced the notion of a q-quaternion bialgebra and shown
its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4.
Adopting the available differential geometric tools on the latter and the
quaternion language we have formulated and found solutions of the
(anti)selfduality equation [instantons and multi-instantons] of a would-be
deformed su(2) Yang-Mills theory on this quantum space. The solutions depend on
some noncommuting parameters, indicating that the moduli space of a complete
theory should be a noncommutative manifold. We summarize these results and add
an explicit comparison between the two SO_q(4)-covariant differential calculi
on R_q^4 and the two 4-dimensional bicovariant differential calculi on the bi-
(resp. Hopf) algebras M_q(2),GL_q(2),SU_q(2), showing that they essentially
coincide.Comment: Latex file, 18 page
Spontaneous Magnetization of Axion Domain Wall and Primordial Magnetic Field
We show that axion domain walls gain spontaneous magnetization in early
universe by trapping either electrons or positrons with their spins polarized.
The reason is that the walls produces an attractive potential for these
particles. We argue that the wall bounded by an axionic superconducting string
leaves a magnetic field after its decay. We obtain a field
Gauss on the scale of horizon at the recombination.Comment: 10 Pages, Revte
Mutual Exclusion Statistics in Exactly Solvable Models in One and Higher Dimensions at Low Temperatures
We study statistical characterization of the many-body states in exactly
solvable models with internal degrees of freedom. The models under
consideration include the isotropic and anisotropic Heisenberg spin chain, the
Hubbard chain, and a model in higher dimensions which exhibits the Mott
metal-insulator transition. It is shown that the ground state of these systems
is all described by that of a generalized ideal gas of particles (called
exclusons) which have mutual exclusion statistics, either between different
rapidities or between different species. For the Bethe ansatz solvable models,
the low temperature properties are well described by the excluson description
if the degeneracies due to string solutions with complex rapidities are taken
into account correctly. {For} the Hubbard chain with strong but finite
coupling, charge-spin separation is shown for thermodynamics at low
temperatures. Moreover, we present an exactly solvable model in arbitrary
dimensions which, in addition to giving a perspective view of spin-charge
separation, constitutes an explicit example of mutual exclusion statistics in
more than two dimensions
Spin - or, actually: Spin and Quantum Statistics
The history of the discovery of electron spin and the Pauli principle and the
mathematics of spin and quantum statistics are reviewed. Pauli's theory of the
spinning electron and some of its many applications in mathematics and physics
are considered in more detail. The role of the fact that the tree-level
gyromagnetic factor of the electron has the value g = 2 in an analysis of
stability (and instability) of matter in arbitrary external magnetic fields is
highlighted. Radiative corrections and precision measurements of g are
reviewed. The general connection between spin and statistics, the CPT theorem
and the theory of braid statistics are described.Comment: 50 pages, no figures, seminar on "spin
Constraints on pre-big bang models for seeding large-scale anisotropy by massive Kalb-Ramond axions
We discuss the conditions under which pre-big bang models can fit the
observed large-scale anisotropy with a primordial spectrum of massive
(Kalb--Ramond) axion fluctuations.
The primordial spectrum must be sufficiently flat at low frequency and
sufficiently steeper at high frequency. For a steep and/or long enough
high-frequency branch of the spectrum the bounds imposed by COBE's
normalization allow axion masses of the typical order for a
Peccei--Quinn--Weinberg--Wilczek axion. We provide a particular example in
which an appropriate axion spectrum is obtained from a class of backgrounds
satisfying the low-energy string cosmology equations.Comment: 11 pages, revtex, two figures included using epsfig. An updated
collection of papers on the pre-big bang scenario is available at
http://www.to.infn.it/~gasperi