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We discuss the quench dynamics near a quantum critical point focusing on the sine-Gordon model as a primary example. We suggest a unified approach to sudden and slow quenches, where the tuning parameter $lambda(t)$ changes in time as $lambda(t)sim upsilon t^r$, based on the adiabatic expansion of the excitation probability in powers of $upsilon$. We show that the universal scaling of the excitation probability can be understood through the singularity of the generalized adiabatic susceptibility $chi_{2r+2}(lambda)$, which for sudden quenches ($r=0$) reduces to the fidelity susceptibility. In turn this class of susceptibilities is expressed through the moments of the connected correlation function of the quench operator. We analyze the excitations created after a sudden quench of the cosine potential using a combined approach of form-factors expansion and conformal perturbation theory for the low-energy and high-energy sector respectively. We find the general scaling laws for the probability of exciting the system, the density of excited quasiparticles, the entropy and the heat generated after the quench. In the two limits where the sine-Gordon model maps to hard core bosons and free massive fermions we provide the exact solutions for the quench dynamics and discuss the finite temperature generalizations.
We study the dynamical response of a system to a sudden change of the tuning parameter $lambda$ starting (or ending) at the quantum critical point. In particular we analyze the scaling of the excitation probability, number of excited quasiparticles,
We present a numerical computation of overlaps in mass quenches in sine-Gordon quantum field theory using truncated conformal space approach (TCSA). To improve the cut-off dependence of the method, we use a novel running coupling definition which has
In this note, we study the hyperbolic stochastic damped sine-Gordon equation (SdSG), with a parameter $beta^2 > 0$, and its associated Gibbs dynamics on the two-dimensional torus. After introducing a suitable renormalization, we first construct the G
We consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the one-dimensional case we classify all bounded steady states and exhibit
The standard phase-ordering process is obtained by quenching a system, like the Ising model, to below the critical point. This is usually done with periodic boundary conditions to insure ergodicity breaking in the low temperature phase. With this arr