40,031 research outputs found
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
Structured backward errors for eigenvalues of linear port-Hamiltonian descriptor systems
When computing the eigenstructure of matrix pencils associated with the
passivity analysis of perturbed port-Hamiltonian descriptor system using a
structured generalized eigenvalue method, one should make sure that the
computed spectrum satisfies the symmetries that corresponds to this structure
and the underlying physical system. We perform a backward error analysis and
show that for matrix pencils associated with port-Hamiltonian descriptor
systems and a given computed eigenstructure with the correct symmetry structure
there always exists a nearby port-Hamiltonian descriptor system with exactly
that eigenstructure. We also derive bounds for how near this system is and show
that the stability radius of the system plays a role in that bound
Study of diatomic molecules. 2: Intensities
The theory of perturbations, giving the diatomic effective Hamiltonian, is used for calculating actual molecular wave functions and intensity factors involved in transitions between states arising from Hund's coupling cases a,b, intermediate a-b, and c tendency. The Herman and Wallis corrections are derived, without any knowledge of the analytical expressions of the wave functions, and generalized to transitions between electronic states with whatever symmetry and multiplicity. A general method for studying perturbed intensities is presented using primarily modern spectroscopic numerical approaches. The method is used in the study of the ScO optical emission spectrum
Lax-Phillips scattering theory for PT-symmetric \rho-perturbed operators
The S-matrices corresponding to PT-symmetric \rho-perturbed operators are
defined and calculated by means of an approach based on an operator-theoretical
interpretation of the Lax-Phillips scattering theory
Crystalline Confinement
We show that exotic phases arise in generalized lattice gauge theories known
as quantum link models in which classical gauge fields are replaced by quantum
operators. While these quantum models with discrete variables have a
finite-dimensional Hilbert space per link, the continuous gauge symmetry is
still exact. An efficient cluster algorithm is used to study these exotic
phases. The -d system is confining at zero temperature with a
spontaneously broken translation symmetry. A crystalline phase exhibits
confinement via multi-stranded strings between charge-anti-charge pairs. A
phase transition between two distinct confined phases is weakly first order and
has an emergent spontaneously broken approximate global symmetry. The
low-energy physics is described by a -d effective field
theory, perturbed by a dangerously irrelevant breaking operator, which
prevents the interpretation of the emergent pseudo-Goldstone boson as a dual
photon. This model is an ideal candidate to be implemented in quantum
simulators to study phenomena that are not accessible using Monte Carlo
simulations such as the real-time evolution of the confining string and the
real-time dynamics of the pseudo-Goldstone boson.Comment: Proceedings of the 31st International Symposium on Lattice Field
Theory - LATTICE 201
Continued fractions and transcendental numbers
It is widely believed that the continued fraction expansion of every
irrational algebraic number either is eventually periodic (and we know
that this is the case if and only if is a quadratic irrational), or it
contains arbitrarily large partial quotients. Apparently, this question was
first considered by Khintchine. A preliminary step towards its resolution
consists in providing explicit examples of transcendental continued fractions.
The main purpose of the present work is to present new families of
transcendental continued fractions with bounded partial quotients. Our results
are derived thanks to new combinatorial transcendence criteria recently
obtained by Adamczewski and Bugeaud
Hidden symmetry breaking in quantum spin systems with applications to measurement-based quantum computation
We extend the hidden symmetry breaking picture, first proposed by Kennedy and Tasaki in the context of the Haldane phase, to a wider class of symmetry-protected topological (SPT) phases. We construct a generalization of the Kennedy-Tasaki transformation that transforms SPT phases into symmetry-breaking phases and relates long-range order in the latter to the more subtle “string order” in the former. In doing so we directly connect the form of the Kennedy-Tasaki transformation to the modern formulation of SPT order. We apply our generalized Kennedy-Tasaki transformation to solve the following problem in quantum information theory. We consider the 2-D cluster state, a simple “toy model” of a locally interacting system whose ground state is a universal resource for MBQC. We prove that, in the presence of a perturbation to the interaction Hamiltonian, the perturbed ground state remains a universal resource. We do this by using the generalized Kennedy-Tasaki transformation to prove that, if we employ the techniques of fault-tolerant quantum computation, the ground states of models in an appropriate SPT phases can serve as universal resources for MBQC provided that the symmetry-breaking is sufficiently strong in the symmetry-breaking phase obtained through the generalized Kennedy-Tasaki transformation
- …