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C. Destri

Publications and source records attributed to C. Destri.

28 records · Page 2Linked to original sources
arXiv1999

Out-of-equilibrium dynamics of ϕ^4 QFT in finite volume

The $λϕ^4$ model in a finite volume is studied in the infinite $N$ limit and within a non-gaussian Hartree-Fock approximation both at equilibrium and out of equilibrium, with particular attention to certain fundamental features of the broken symmetry phase. The numerical solution of the dynamical evolution equations show that the zero-mode quantum fluctuations cannot grow macroscopically large starting from microscopic initial conditions. Thus we conclude that there is no evidence for a dynamical Bose-Einstein condensation. On the other hand, out of equilibrium the long-wavelength fluctuations do scale with the linear size of the system, signalling dynamical infrared properties quite different from the equilibrium ones characteristic of the same approximation schemes. This result suggests the cause, and the possible remedy, of some unlikely features of the application to out--of--equilibrium dynamics of the standard HF factorization scheme, which coincides with the gaussian restriction of our Hartree--Fock approximation.

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arXiv1997

Asymptotic Dynamics in Scalar Field Theory: Anomalous Relaxation

We analyze the dynamics of dissipation and relaxation in the unbroken and broken symmetry phases of scalar theory in the nonlinear regime for large initial energy densities, and after linear unstabilities (parametric or spinodal) are shut-off by the quantum backreaction. A new time scale emerges that separates the linear from the non-linear regimes. This scale is non- perturbative in the coupling and initial amplitude. The non-perturbative evolution is studied in the large the N limit for the O(N) vector model. A combination of numerical analysis and the multitime scale analysis reveals the presence of unstable bands in the nonlinear regime. These are associated with power law growth of quantum fluctuations, that result in power law relaxation and dissipation with non-universal and non-perturbative dynamical anomalous exponents.We find substantial particle production during this non-linear evolu- tion which is of the same order as that in the linear regime. The expectation value of the scalar field vanishes asymptotically transferring all of the initial energy into produced particles via the non-linear resonances in the unbroken symmetry phase.The effective mass for the quantum modes tends asympto- tically to a constant plus oscillating O(1/t) terms. This slow decay causes the power behaviour in the modes which become free for t=infty. We derive a simple expression for the equation of state for the fluid of produced particles that interpolates between radiation-type and dust-type equations according to the initial value of the order parameter for unbroken symmetry. For broken symmetry the produced particles are massless Goldstone bosons with a radiation-type equation of state. We find the onset of a novel form of dynamical Bose condensation in the collisionless regime in the absence of thermalization.

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arXiv1997

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 $L$ 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 $L$ (perturbative) and small $L$ (conformal) regimes as well as numerically.

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arXiv1995

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.

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arXiv1995

A numerical study of the RG equation for the deformed $O(3)$ nonlinear sigma model

The Renormalization Group equation describing the evolution of the metric of the nonlinear sigma model poses some nice mathematical problems involving functional analysis, differential geometry and numerical analysis. In this article we briefly report some results obtained from the numerical study of the solutions in the case of a two dimensional target space (deformation of the $O(3)$ sigma model). In particular, our analysis shows that the so-called sausages define an attracting manifold in the $U(1)$-symmetric case, at one-loop level. Moreover, data from two-loop evolution are used to test the association put forward in Nucl. Phys., B406 (1993) 521 between the so-called $SSM_ν$ field theory and a certain $U(1)$-symmetric, factorized scattering theory (FST).

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arXiv1994

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 $h_z$ 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 $T$ in the XXZ chain and low $T$ 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.

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arXiv1993

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 $q-$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 $τ(ł)$ on a generic physical state, through algebraic Bethe ansatz. In the thermodynamic limit $τ(ł)$ 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.

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arXiv1992

New Approach to Thermal Bethe Ansatz

We present a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisemberg chain we derive, for arbitrary values of the anysotropy, a {\bf single} non--linear integral equation from which the free energy can be exactly calculated. The high--temperature expansion follows in a sistematic and relatively simple way. For low temperatures we obtain the correct central charge and predict the analytic structure of the full expansion around $T=0$. Furthermore, we derive a single non-linear integral equation describing the finite--size ground--state energy of the Sine--Gordon quantum field theory. PACS: 05.30, 03.70. 75.10.5

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arXiv1992

Bethe Ansatz and Quantum Groups: The Light--Cone Approach. II. From RSOS($p+1$) models to $p-$restricted Sine--Gordon Field Theories

We solve the RSOS($p$) models on the light--cone lattice with fixed boundary conditions by disentangling the type II representations of $SU(2)_q$, at $q=e^{iπ/p}$, from the full SOS spectrum obtained through Algebraic Bethe Ansatz. The rule which realizes the quantum group reduction to the RSOS states is that there must not be {\it singular} roots in the solutions of the Bethe Ansatz equations describing the states with quantum spin $J<(p-1)/2$. By studying how this rule is active on the particle states, we are able to give a microscopic derivation of the lattice $S-$matrix of the massive kinks. The correspondence between the light--cone Six--Vertex model and the Sine--Gordon field theory implies that the continuum limit of the RSOS($p+1$) model is to be identified with the $p-$restricted Sine--Gordon field theory.

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