17,747 research outputs found
On the Clebsch-Gordan coefficients for the two-parameter quantum algebra
We show that the Clebsch - Gordan coefficients for the -
algebra depend on a single parameter Q = ,contrary to the explicit
calculation of Smirnov and Wehrhahn [J.Phys.A 25 (1992),5563].Comment: 5 page
Form factors of descendant operators: Free field construction and reflection relations
The free field representation for form factors in the sinh-Gordon model and
the sine-Gordon model in the breather sector is modified to describe the form
factors of descendant operators, which are obtained from the exponential ones,
\e^{\i\alpha\phi}, by means of the action of the Heisenberg algebra
associated to the field . As a check of the validity of the
construction we count the numbers of operators defined by the form factors at
each level in each chiral sector. Another check is related to the so called
reflection relations, which identify in the breather sector the descendants of
the exponential fields \e^{\i\alpha\phi} and \e^{\i(2\alpha_0-\alpha)\phi}
for generic values of . We prove the operators defined by the obtained
families of form factors to satisfy such reflection relations. A generalization
of the construction for form factors to the kink sector is also proposed.Comment: 29 pages; v2: minor corrections, some references added; v3: minor
corrections; v4,v5: misprints corrected; v6: minor mistake correcte
SLE-type growth processes and the Yang-Lee singularity
The recently introduced SLE growth processes are based on conformal maps from
an open and simply-connected subset of the upper half-plane to the half-plane
itself. We generalize this by considering a hierarchy of stochastic evolutions
mapping open and simply-connected subsets of smaller and smaller fractions of
the upper half-plane to these fractions themselves. The evolutions are all
driven by one-dimensional Brownian motion. Ordinary SLE appears at grade one in
the hierarchy. At grade two we find a direct correspondence to conformal field
theory through the explicit construction of a level-four null vector in a
highest-weight module of the Virasoro algebra. This conformal field theory has
central charge c=-22/5 and is associated to the Yang-Lee singularity. Our
construction may thus offer a novel description of this statistical model.Comment: 12 pages, LaTeX, v2: thorough revision with corrections, v3: version
to be publishe
Raising and lowering operators, factorization and differential/difference operators of hypergeometric type
Starting from Rodrigues formula we present a general construction of raising
and lowering operators for orthogonal polynomials of continuous and discrete
variable on uniform lattice. In order to have these operators mutually adjoint
we introduce orthonormal functions with respect to the scalar product of unit
weight. Using the Infeld-Hull factorization method, we generate from the
raising and lowering operators the second order self-adjoint
differential/difference operator of hypergeometric type.Comment: LaTeX, 24 pages, iopart style (late submission
Scaling Limit and Critical Exponents for Two-Dimensional Bootstrap Percolation
Consider a cellular automaton with state space
where the initial configuration is chosen according to a Bernoulli
product measure, 1's are stable, and 0's become 1's if they are surrounded by
at least three neighboring 1's. In this paper we show that the configuration
at time n converges exponentially fast to a final configuration
, and that the limiting measure corresponding to is in
the universality class of Bernoulli (independent) percolation.
More precisely, assuming the existence of the critical exponents ,
, and , and of the continuum scaling limit of crossing
probabilities for independent site percolation on the close-packed version of
(i.e., for independent -percolation on ), we
prove that the bootstrapped percolation model has the same scaling limit and
critical exponents.
This type of bootstrap percolation can be seen as a paradigm for a class of
cellular automata whose evolution is given, at each time step, by a monotonic
and nonessential enhancement.Comment: 15 page
Asymptotic Bound-state Model for Feshbach Resonances
We present an Asymptotic Bound-state Model which can be used to accurately
describe all Feshbach resonance positions and widths in a two-body system. With
this model we determine the coupled bound states of a particular two-body
system. The model is based on analytic properties of the two-body Hamiltonian,
and on asymptotic properties of uncoupled bound states in the interaction
potentials. In its most simple version, the only necessary parameters are the
least bound state energies and actual potentials are not used. The complexity
of the model can be stepwise increased by introducing threshold effects,
multiple vibrational levels and additional potential parameters. The model is
extensively tested on the 6Li-40K system and additional calculations on the
40K-87Rb system are presented.Comment: 13 pages, 8 figure
Quantum Quench in the Transverse Field Ising Chain
We consider the time evolution of observables in the transverse field Ising
chain (TFIC) after a sudden quench of the magnetic field. We provide exact
analytical results for the asymptotic time and distance dependence of one- and
two-point correlation functions of the order parameter. We employ two
complementary approaches based on asymptotic evaluations of determinants and
form-factor sums. We prove that the stationary value of the two-point
correlation function is not thermal, but can be described by a generalized
Gibbs ensemble (GGE). The approach to the stationary state can also be
understood in terms of a GGE. We present a conjecture on how these results
generalize to particular quenches in other integrable models.Comment: 4 pages, 1 figur
Quantum eigenstate tomography with qubit tunneling spectroscopy
Measurement of the energy eigenvalues (spectrum) of a multi-qubit system has
recently become possible by qubit tunneling spectroscopy (QTS). In the standard
QTS experiments, an incoherent probe qubit is strongly coupled to one of the
qubits of the system in such a way that its incoherent tunneling rate provides
information about the energy eigenvalues of the original (source) system. In
this paper, we generalize QTS by coupling the probe qubit to many source
qubits. We show that by properly choosing the couplings, one can perform
projective measurements of the source system energy eigenstates in an arbitrary
basis, thus performing quantum eigenstate tomography. As a practical example of
a limited tomography, we apply our scheme to probe the eigenstates of a kink in
a frustrated transverse Ising chain.Comment: 8 pages, 4 figure
Ray stability in weakly range-dependent sound channels
Ray stability is investigated in environments consisting of a
range-independent background sound-speed profile on which a range-dependent
perturbation, such as that produced by internal waves in deep ocean
environments, is superimposed. Numerical results show that ray stability is
strongly influenced by the background sound speed profile. Ray instability is
shown to increase with increasing magnitude of alpha := I omega^{prime} /
omega, where 2 pi / omega(I) is the range of a ray double loop and I is the ray
action variable. The mechanism, shear-induced instability enhancement, by which
alpha controls ray instability is described.Comment: To appear in JAS
The Sub-leading Magnetic Deformation of the Tricritical Ising Model in 2D as RSOS Restriction of the Izergin-Korepin Model
We compute the -matrix of the Tricritical Ising Model perturbed by the
subleading magnetic operator using Smirnov's RSOS reduction of the
Izergin-Korepin model. We discuss some features of the scattering theory we
obtain, in particular a non trivial implementation of crossing-symmetry,
interesting connections between the asymptotic behaviour of the amplitudes, the
possibility of introducing generalized statistics, and the monodromy properties
of the OPE of the unperturbed Conformal Field Theory.Comment: (13 pages
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