128 research outputs found
Semiclassical Energy Levels of Sine-Gordon Model on a Strip with Dirichlet Boundary Conditions
We derive analytic expressions of the semiclassical energy levels of
Sine-Gordon model in a strip geometry with Dirichlet boundary condition at both
edges. They are obtained by initially selecting the classical backgrounds
relative to the vacuum or to the kink sectors, and then solving the Schodinger
equations (of Lame' type) associated to the stability condition. Explicit
formulas are presented for the classical solutions of both the vacuum and kink
states and for the energy levels at arbitrary values of the size of the system.
Their ultraviolet and infrared limits are also discussed.Comment: 14 pages, 7 figure
Local Correlations in the Super Tonks-Girardeau Gas
We study the local correlations in the super Tonks-Girardeau gas, a highly
excited, strongly correlated state obtained in quasi one-dimensional Bose gases
by tuning the scattering length to large negative values using a
confinement-induced resonance. Exploiting a connection with a relativistic
field theory, we obtain results for the two-body and three-body local
correlators at zero and finite temperature. At zero temperature our result for
the three-body correlator agrees with the extension of the results of Cheianov
et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground-state of
the repulsive Lieb-Liniger gas, to the super Tonks-Girardeau state. At finite
temperature we obtain that the three-body correlator has a weak dependence on
the temperature up to the degeneracy temperature. We also find that for
temperatures larger than the degeneracy temperature the values of the
three-body correlator for the super Tonks-Girardeau gas and the corresponding
repulsive Lieb-Liniger gas are rather similar even for relatively small
couplings
Kink scaling functions in 2D non--integrable quantum field theories
We determine the semiclassical energy levels for the \phi^4 field theory in
the broken symmetry phase on a 2D cylindrical geometry with antiperiodic
boundary conditions by quantizing the appropriate finite--volume kink
solutions. The analytic form of the kink scaling functions for arbitrary size
of the system allows us to describe the flow between the twisted sector of c=1
CFT in the UV region and the massive particles in the IR limit. Kink-creating
operators are shown to correspond in the UV limit to disorder fields of the c=1
CFT. The problem of the finite--volume spectrum for generic 2D Landau--Ginzburg
models is also discussed.Comment: 30 pages, 10 figure
Expectation Values in the Lieb-Liniger Bose Gas
Taking advantage of an exact mapping between a relativistic integrable model
and the Lieb-Liniger model we present a novel method to compute expectation
values in the Lieb-Liniger Bose gas both at zero and finite temperature. These
quantities, relevant in the physics of one-dimensional ultracold Bose gases,
are expressed by a series that has a remarkable behavior of convergence. Among
other results, we show the computation of the three-body expectation value at
finite temperature, a quantity that rules the recombination rate of the Bose
gas.Comment: Published version. Selected for the December 2009 issue of Virtual
Journal of Atomic Quantum Fluid
Boundary Quantum Field Theories with Infinite Resonance States
We extend a recent work by Mussardo and Penati on integrable quantum field
theories with a single stable particle and an infinite number of unstable
resonance states, including the presence of a boundary. The corresponding
scattering and reflection amplitudes are expressed in terms of Jacobian
elliptic functions, and generalize the ones of the massive thermal Ising model
and of the Sinh-Gordon model. In the case of the generalized Ising model we
explicitly study the ground state energy and the one-point function of the
thermal operator in the short-distance limit, finding an oscillating behaviour
related to the fact that the infinite series of boundary resonances does not
decouple from the theory even at very short-distance scales. The analysis of
the generalized Sinh-Gordon model with boundary reveals an interesting
constraint on the analytic structure of the reflection amplitude. The roaming
limit procedure which leads to the Ising model, in fact, can be consistently
performed only if we admit that the nature of the bulk spectrum uniquely fixes
the one of resonance states on the boundary.Comment: 18 pages, 11 figures, LATEX fil
On the Form Factors of Relevant Operators and their Cluster Property
We compute the Form Factors of the relevant scaling operators in a class of
integrable models without internal symmetries by exploiting their cluster
properties. Their identification is established by computing the corresponding
anomalous dimensions by means of Delfino--Simonetti--Cardy sum--rule and
further confirmed by comparing some universal ratios of the nearby
non--integrable quantum field theories with their independent numerical
determination.Comment: Latex file, 35 pages with 5 Postscript figure
On the mass spectrum of the two-dimensional O(3) sigma model with theta term
Form Factor Perturbation Theory is applied to study the spectrum of the O(3)
non--linear sigma model with the topological term in the vicinity of . Its effective action near this value is given by the non--integrable
double Sine--Gordon model. Using previous results by Affleck and the explicit
expressions of the Form Factors of the exponential operators , we show that the spectrum consists of a stable triplet
of massive particles for all values of and a singlet state of higher
mass. The singlet is a stable particle only in an interval of values of
close to whereas it becomes a resonance below a critical value
.Comment: 4 pages REVTEX4, 2 figures reference added,corrected typo
Integrable Quantum Field Theories in Finite Volume: Excited State Energies
We develop a method of computing the excited state energies in Integrable
Quantum Field Theories (IQFT) in finite geometry, with spatial coordinate
compactified on a circle of circumference R. The IQFT ``commuting
transfer-matrices'' introduced by us (BLZ) for Conformal Field Theories (CFT)
are generalized to non-conformal IQFT obtained by perturbing CFT with the
operator . We study the models in which the fusion relations for
these ``transfer-matrices'' truncate and provide closed integral equations
which generalize the equations of Thermodynamic Bethe Ansatz to excited states.
The explicit calculations are done for the first excited state in the ``Scaling
Lee-Yang Model''.Comment: 54 pages, harvmac, epsf, TeX file and postscript figures packed in a
single selfextracting uufile. Compiles only in the `Big' mode with harvma
Correlation functions of disorder operators in massive ghost theories
The two-dimensional ghost systems with negative integral central charge
received much attention in the last years for their role in a number of
applications and in connection with logarithmic conformal field theory. We
consider the free massive bosonic and fermionic ghost systems and concentrate
on the non-trivial sectors containing the disorder operators. A unified
analysis of the correlation functions of such operators can be performed for
ghosts and ordinary complex bosons and fermions. It turns out that these
correlators depend only on the statistics although the scaling dimensions of
the disorder operators change when going from the ordinary to the ghost case.
As known from the study of the ordinary case, the bosonic and fermionic
correlation functions are the inverse of each other and are exactly expressible
through the solution of a non-linear differential equation.Comment: 8 pages, late
Semiclassical Particle Spectrum of Double Sine-Gordon Model
We present new theoretical results on the spectrum of the quantum field
theory of the Double Sine Gordon model. This non-integrable model displays
different varieties of kink excitations and bound states thereof. Their mass
can be obtained by using a semiclassical expression of the matrix elements of
the local fields. In certain regions of the coupling-constants space the
semiclassical method provides a picture which is complementary to the one of
the Form Factor Perturbation Theory, since the two techniques give information
about the mass of different types of excitations. In other regions the two
methods are comparable, since they describe the same kind of particles.
Furthermore, the semiclassical picture is particularly suited to describe the
phenomenon of false vacuum decay, and it also accounts in a natural way the
presence of resonance states and the occurrence of a phase transition.Comment: 32 pages, latex, 8 figure
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