376 research outputs found
Non linear integral equation and excited--states scaling functions in the sine-Gordon model
The NLIE (the non-linear integral equation equivalent to the Bethe Ansatz
equations for finite size) is generalized to excited states, that is states
with holes and complex roots over the antiferromagnetic ground state. We
consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of
length using the light-cone approach, in which the sG/mT model is obtained
as the continuum limit of an inhomogeneous six vertex model. This NLIE is an
useful starting point to compute the spectrum of excited states both
analytically in the large (perturbative) and small (conformal) regimes
as well as numerically.Comment: LaTeX file, 40 pages, 4 figures in a tar.Z file (3 figures added and
few misprints corrected w.r.t. previous version
Yang--Baxter symmetry in integrable models: new light from the Bethe Ansatz solution
We show how any integrable 2D QFT enjoys the existence of infinitely many
non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry
algebra. These charges are generated by quantum monodromy operators and provide
a representation of deformed affine Lie algebras. We review and generalize
the work of de Vega, Eichenherr and Maillet on the bootstrap construction of
the quantum monodromy operators to the sine--Gordon (or massive Thirring)
model, where such operators do not possess a classical analogue. Within the
light--cone approach to the mT model, we explicitly compute the eigenvalues of
the six--vertex alternating transfer matrix \tau(\l) on a generic physical
state, through algebraic Bethe ansatz. In the thermodynamic limit \tau(\l)
turns out to be a two--valued periodic function. One determination generates
the local abelian charges, including energy and momentum, while the other
yields the abelian subalgebra of the (non--local) YB algebra. In particular,
the bootstrap results coincide with the ratio between the two determinations of
the lattice transfer matrix.Comment: 30 page
Ultraviolet cascade in the thermalization of the classical phi^4 theory in 3+1 dimensions
We investigate the dynamics of thermalization and the approach to equilibrium
in the classical phi^4 theory in 3+1 spacetime dimensions. The non-equilibrium
dynamics is studied by numerically solving the equations of motion in a light-
cone-like discretization of the model for a broad range of initial conditions
and energy densities.A smooth cascade of energy towards the ultraviolet is
found to be the basic mechanism of thermalization.After an initial transient
stage,at a time scale of several hundreds inverse masses,the squared of the
field gradient becomes larger than the nonlinear term and a stage of universal
cascade emerges. As the cascade progresses, the modes with higher wavenumbers
exhibit weaker and weaker nonlinearities well described by the Hartree
approximation while the infrared modes retain strong selfinteractions. Two
timescales for equilibration appears.For k^2>(t) we observe an effective
thermalization with a time scale in the thousands of inverse masses and the
Hartree approximation holds. By effective thermalization we mean that the
observable acquires the equilibrium functional form with an effective time
dependent temperature Teff, which slowly decreases with time. Infrared modes
with k^2 (t) equilibrate only by time scales in the millions of
inverse masses. Infrared modes with k^2 (t) equilibrate only by time
scales in the millions.Virialization and the equation of state start to set
much earlier than effective thermalization.The applicability of these results
in quantum field theory for large occupation numbers and small coupling is
analyzed.Comment: 47 pages, 31 figures. Presentation improved, 4 new figure
A local and integrable lattice regularization of the massive Thirring model
The light--cone lattice approach to the massive Thirring model is
reformulated using a local and integrable lattice Hamiltonian written in terms
of discrete fermi fields. Several subtle points concerning boundary conditions,
normal--ordering, continuum limit, finite renormalizations and decoupling of
fermion doublers are elucidated. The relations connecting the six--vertex
anisotropy and the various coupling constants of the continuum are analyzed in
detail.Comment: Latex, 24 pages, some corrected misprints and minor changes, 2
Postscript figures unchange
Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories
We present a unified approach to the Thermodynamic Bethe Ansatz (TBA) for
magnetic chains and field theories that includes the finite size (and zero
temperature) calculations for lattice BA models. In all cases, the free energy
follows by quadratures from the solution of a {\bf single} non-linear integral
equation (NLIE). [A system of NLIE appears for nested BA]. We derive the NLIE
for: a) the six-vertex model with twisted boundary conditions; b) the XXZ chain
in an external magnetic field and c) the sine-Gordon-massive Thirring
model (sG-mT) in a periodic box of size \b \equiv 1/T using the light-cone
approach. This NLIE is solved by iteration in one regime (high in the XXZ
chain and low in the sG-mT model). In the opposite (conformal) regime, the
leading behaviors are obtained in closed form. Higher corrections can be
derived from the Riemann-Hilbert form of the NLIE that we present.Comment: Expanded Introduction. Version to appear in Nucl. Phys. B. 60 pages,
TeX, Uses phyzz
The pre-inflationary and inflationary fast-roll eras and their signatures in the low CMB multipoles
We study the entire coupled evolution of the inflaton and the scale factor
for general initial conditions at a given initial time. The generic early
universe evolution has three stages: decelerated fast-roll followed by
inflationary fast roll and then inflationary slow-roll. This evolution is valid
for all regular inflaton potentials. In addition, we find a special (extreme)
slow-roll solution starting at t = -infty in which the fast-roll stages are
absent. At some time t = t_*, the generic evolution backwards in time reaches a
mathematical singu- larity where a(t) vanishes and Hubble becomes singular. We
find the general behaviour near the singularity. The classical inflaton
description is valid for t-t_* > 10 t_{Planck} well before the beginning of
inflation, quantum loop effects are negligible there. The singularity is never
reached in the validity region of the classical treatment and therefore it is
not a real physical phenomenon here. The whole evolution of the fluctuations is
computed. The Bunch-Davies initial conditions (BDic) are generalized for the
present case. The power spectrum gets dynamically modified by the effect of the
fast-roll eras and the BDic choice at a finite time through the transfer
function D(k) of initial conditions. D(0) = 0. D(k) presents a first peak for k
~ 2/eta_0 (eta_0 being the conformal initial time), then oscillates with
decreasing amplitude and vanishes asymptotically for k -> infty. The transfer
function D(k) affects the low CMB multipoles C_l: the change Delta C_l/C_l for
l=1-5 is computed as a function of the starting instant of the fluctuations
t_0. CMB quadrupole observations give large suppressions which are well
reproduced here(Abridged)Comment: 31 pages, 10 figures. Version to appear in PR
Quantum WDM fermions and gravitation determine the observed galaxy structures
Quantum mechanics is necessary to compute galaxy structures at kpc scales and
below. This is so because near the galaxy center, at scales below 10 - 100 pc,
warm dark matter (WDM) quantum effects are important: observations show that
the interparticle distance is of the order of, or smaller than the de Broglie
wavelength for WDM. This explains why all classical (non-quantum) WDM N-body
simulations fail to explain galactic cores and their sizes. We describe
fermionic WDM galaxies in an analytic semiclassical framework based on the
Thomas-Fermi approach, we resolve it numerically and find the main physical
galaxy magnitudes: mass, halo radius, phase-space density, velocity dispersion,
fully consistent with observations, including compact dwarf galaxies. Namely,
fermionic WDM treated quantum mechanically, as it must be, reproduces the
observed galaxy DM cores and their sizes. [In addition, as is known, WDM
simulations produce the right DM structures in agreement with observations for
scales > kpc]. We show that compact dwarf galaxies are natural quantum
macroscopic objects supported against gravity by the fermionic WDM quantum
pressure (quantum degenerate fermions) with a minimal galaxy mass and minimal
velocity dispersion. Interestingly enough, the minimal galaxy mass implies a
minimal mass m_{min} for the WDM particle. The lightest known dwarf galaxy
(Willman I) implies m > m_{min} = 1.91 keV. These results and the observed halo
radius and mass of the compact galaxies provide further indication that the WDM
particle mass m is approximately around 2 keV.Comment: 15 pages, 2 figures, expanded version to appear in Astroparticle
Physics. admin note: substantial text overlap with arXiv:1204.309
Warm dark matter primordial spectra and the onset of structure formation at redshift z
Analytic formulas reproducing the warm dark matter (WDM) primordial spectra
are obtained for WDM particles decoupling in and out of thermal equilibrium
which provide the initial data for WDM non-linear structure formation. We
compute and analyze the corresponding WDM overdensities and compare them to the
CDM case. We consider the ratio of the WDM to CDM primordial spectrum and the
WDM to CDM overdensities: they turn to be self-similar functions of k/k_{1/2}
and R/R_{1/2} respectively, k_{1/2} and R_{1/2} being the wavenumber and length
where the WDM spectrum and overdensity are 1/2 of the respective CDM
magnitudes. Both k_{1/2} and R_{1/2} show scaling as powers of the WDM particle
mass m while the self-similar functions are independent of m. The WDM
primordial spectrum sharply decreases around k_{1/2} with respect to the CDM
spectrum, while the WDM overdensity slowly decreases around R_{1/2}. The
nonlinear regions where WDM structure formation takes place are shown and
compared to those in CDM: the WDM non-linear structures start to form later
than in CDM, and as a general trend, decreasing the DM particle mass delays the
onset of the non-linear regime. The non-linear regime starts earlier for
smaller objects than for larger ones; smaller objects can form earlier both in
WDM and CDM. We compute and analyze the differential mass function dN/dM for
WDM at redshift z in the Press-Schechter approach. The WDM suppression effect
of small scale structure increases with the redshift z. Our results for dN/dM
are useful to be contrasted with observations, in particular for 4 < z < 12. We
perfom all these studies for the most popular WDM particle physics models.
Contrasting them to observations should point out the precise value of the WDM
particle mass in the keV scale, and help to single out the best WDM particle
physics model (Abridged).Comment: 18 pages, 8 figures. To appear in Phys Rev
The spectral dimension of random trees
We present a simple yet rigorous approach to the determination of the
spectral dimension of random trees, based on the study of the massless limit of
the Gaussian model on such trees. As a byproduct, we obtain evidence in favor
of a new scaling hypothesis for the Gaussian model on generic bounded graphs
and in favor of a previously conjectured exact relation between spectral and
connectivity dimensions on more general tree-like structures.Comment: 14 pages, 2 eps figures, revtex4. Revised version: changes in section
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