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Register a new userBoundary State in an Integrable Quantum Field Theory Out of Equilibrium
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We study a quantum quench of the mass and the interaction in the Sinh-Gordon model starting from a large initial mass and zero initial coupling. Our focus is on the determination of the expansion of the initial state in terms of post-quench excitations. We argue that the large energy profile of the involved excitations can be relevant for the late time behaviour of the system and common regularization schemes are unreliable. We therefore proceed in determining the initial state by first principles expanding it in a systematic and controllable fashion on the basis of the asymptotic states. Our results show that, for the special limit of pre-quench parameters we consider, it assumes a squeezed state form that has been shown to evolve so as to exhibit the equilibrium behaviour predicted by the Generalized Gibbs Ensemble.
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We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions deter- mining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provide a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.
We consider the out-of-equilibrium transport in $Tbar{T}$-deformed (1+1)-dimension conformal field theories (CFTs). The theories admit two disparate approaches, integrability and holography, which we make full use of in order to compute the transport quantities, such as the the exact non-equilibrium steady state currents. We find perfect agreements between the results obtained from these two methods, which serve as the first checks of the $Tbar{T}$-deformed holographic correspondence from the dynamical standpoint. It turns out that integrability also allows us to compute the momentum diffusion, which is given by a universal formula. We also remark on an intriguing connection between the $Tbar{T}$-deformed CFTs and reversible cellular automata.
Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of classical integrable field theory. Classical field GHD is based on a known formalism for Gibbs ensembles of classical fields, that resembles the thermodynamic Bethe ansatz of quantum models, which we extend to generalized Gibbs ensembles (GGEs). In general, GHD must take into account both solitonic and radiative modes of classical fields. We observe that the quasi-particle formulation of GHD remains valid for radiative modes, even though these do not display particle-like properties in their precise dynamics. We point out that because of a UV catastrophe similar to that of black body radiation, radiative modes suffer from divergences that restrict the set of finite-average observables; this set is larger for GGEs with higher conserved charges. We concentrate on the sinh-Gordon model, which only has radiative modes, and study transport in the domain-wall initial problem as well as Euler-scale correlations in GGEs. We confirm a variety of exact GHD predictions, including those coming from hydrodynamic projection theory, by comparing with Metropolis numerical evaluations.
We consider a quantum Brownian particle interacting with two harmonic baths, which is then perturbed by a cubic coupling linking the particle and the baths. This cubic coupling induces non-linear dissipation and noise terms in the influence functional/master equation of the particle. Its effect on the Out-of-Time-Ordered Correlators (OTOCs) of the particle cannot be captured by the conventional Feynman-Vernon formalism.We derive the generalised influence functional which correctly encodes the physics of OTO fluctuations, response, dissipation and decoherence. We examine an example where Markovian approximation is valid for the OTO dynamics. If the original cubic coupling has a definite time-reversal parity, the leading order OTO influence functional is completely determined by the couplings in the usual master equation via OTO generalisation of Onsager-Casimir relations. New OTO fluctuation-dissipation relations connect the non-Gaussianity of the thermal noise to the thermal jitter in the damping constant of the Brownian particle.
We consider a quantum quench in a finite system of length $L$ described by a 1+1-dimensional CFT, of central charge $c$, from a state with finite energy density corresponding to an inverse temperature $betall L$. For times $t$ such that $ell/2<t<(L-ell)/2$ the reduced density matrix of a subsystem of length $ell$ is exponentially close to a thermal density matrix. We compute exactly the overlap $cal F$ of the state at time $t$ with the initial state and show that in general it is exponentially suppressed at large $L/beta$. However, for minimal models with $c<1$ (more generally, rational CFTs), at times which are integer multiples of $L/2$ (for periodic boundary conditions, $L$ for open boundary conditions) there are (in general, partial) revivals at which $cal F$ is $O(1)$, leading to an eventual complete revival with ${cal F}=1$. There is also interesting structure at all rational values of $t/L$, related to properties of the CFT under modular transformations. At early times $t!ll!(Lbeta)^{1/2}$ there is a universal decay ${cal F}simexpbig(!-!(pi c/3)Lt^2/beta(beta^2+4t^2)big)$. The effect of an irrelevant non-integrable perturbation of the CFT is to progressively broaden each revival at $t=nL/2$ by an amount $O(n^{1/2})$.
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