We address the out-of-equilibrium critical dynamics of the three-dimensional lattice Z_{2} gauge model, and in particular the critical relaxational flows arising from instantaneous quenches to the critical point, driven by purely relaxational (single-spin-flip Metropolis) upgradings of the link Z_{2} gauge variables. We monitor the critical relaxational dynamics by computing the energy density, which is the simplest local gauge-invariant quantity that can be measured in a lattice gauge theory. The critical relaxational flow of the three-dimensional lattice Z_{2} gauge model is analyzed within an out-of-equilibrium finite-size scaling framework, which allows us to compute the dynamic critical exponent z associated with the purely relaxational dynamics of the three-dimensional Z_{2} gauge universality class. We obtain z=2.610(15), which significantly improves earlier results obtained by other methods, in particular those obtained by analyzing the equilibrium critical dynamics.We address the out-of-equilibrium critical dynamics of the three-dimensional lattice Z_{2} gauge model, and in particular the critical relaxational flows arising from instantaneous quenches to the critical point, driven by purely relaxational (single-spin-flip Metropolis) upgradings of the link Z_{2} gauge variables. We monitor the critical relaxational dynamics by computing the energy density, which is the simplest local gauge-invariant quantity that can be measured in a lattice gauge theory. The critical relaxational flow of the three-dimensional lattice Z_{2} gauge model is analyzed within an out-of-equilibrium finite-size scaling framework, which allows us to compute the dynamic critical exponent z associated with the purely relaxational dynamics of the three-dimensional Z_{2} gauge universality class. We obtain z=2.610(15), which significantly improves earlier results obtained by other methods, in particular those obtained by analyzing the equilibrium critical dynamics.

Physical review. EMay 2, 20256 citations

Resonance and Relaxation

Frederic R. Morgenthaler

Jan 1, 19670 citations

Probing local relaxation of cold atoms in optical superlattices

Andreas Flesch, M. Cramer, Ian P. McCulloch +2 more

In the study of relaxation processes in coherent nonequilibrium dynamics of quenched quantum systems, ultracold atoms in optical superlattices with periodicity 2 provide a very fruitful test ground. We consider the dynamics of a particular, experimentally accessible initial state prepared in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the entire range of interaction strengths, further investigating the issues raised by Cramer et al. [Phys. Rev. Lett. 101, 063001 (2008)]. We investigate the relaxation dynamics analytically in the noninteracting and hard-core bosonic limits, deriving explicit expressions for the dynamics of certain correlation functions, and numerically for finite interaction strengths using the time-dependent density-matrix renormalization (t-DMRG) approach. We can identify signatures of local relaxation that can be accessed experimentally with present technology. While the global system preserves the information about the initial condition, locally the system relaxes to the state having maximum entropy respecting the constraints of the initial condition. For finite interaction strengths and finite times, the relaxation dynamics contains signatures of the relaxation dynamics of both the noninteracting and hard-core bosonic limits.In the study of relaxation processes in coherent nonequilibrium dynamics of quenched quantum systems, ultracold atoms in optical superlattices with periodicity 2 provide a very fruitful test ground. We consider the dynamics of a particular, experimentally accessible initial state prepared in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the entire range of interaction strengths, further investigating the issues raised by Cramer et al. [Phys. Rev. Lett. 101, 063001 (2008)]. We investigate the relaxation dynamics analytically in the noninteracting and hard-core bosonic limits, deriving explicit expressions for the dynamics of certain correlation functions, and numerically for finite interaction strengths using the time-dependent density-matrix renormalization (t-DMRG) approach. We can identify signatures of local relaxation that can be accessed experimentally with present technology. While the global system preserves the information about the initial condition, locally the system relaxes to the state having maximum entropy respecting the constraints of the initial condition. For finite interaction strengths and finite times, the relaxation dynamics contains signatures of the relaxation dynamics of both the noninteracting and hard-core bosonic limits.

arXiv:0808.3779Physical Review ASep 12, 2008104 citations

Relaxation Effects

WORLD SCIENTIFIC eBooksOct 1, 20080 citations

Out-of-equilibrium critical dynamics of the three-dimensional ${\mathbb Z}_2$ gauge model along critical relaxational flowsOut-of-equilibrium critical dynamics of the three-dimensional ${\mathbb Z}_2$ gauge model along critical relaxational flows

Claudio Bonati, H. Panagopoulos, Ettore Vicari

We address the out-of-equilibrium critical dynamics of the three-dimensional lattice ${\mathbb Z}_2$ gauge model, and in particular the critical relaxational flows arising from instantaneous quenches to the critical point, driven by purely relaxational (single-spin-flip Metropolis) upgradings of the link ${\mathbb Z}_2$ gauge variables. We monitor the critical relaxational dynamics by computing the energy density, which is the simplest local gauge-invariant quantity that can be measured in a lattice gauge theory. The critical relaxational flow of the three-dimensional lattice ${\mathbb Z}_2$ gauge model is analyzed within an out-of-equilibrium finite-size scaling framework, which allows us to compute the dynamic critical exponent $z$ associated with the purely relaxational dynamics of the three-dimensional ${\mathbb Z}_2$ gauge universality class. We obtain $z=2.610(15)$ , which significantly improves earlier results obtained by other methods, in particular those obtained by analyzing the equilibrium critical dynamics.We address the out-of-equilibrium critical dynamics of the three-dimensional lattice ${\mathbb Z}_2$ gauge model, and in particular the critical relaxational flows arising from instantaneous quenches to the critical point, driven by purely relaxational (single-spin-flip Metropolis) upgradings of the link ${\mathbb Z}_2$ gauge variables. We monitor the critical relaxational dynamics by computing the energy density, which is the simplest local gauge-invariant quantity that can be measured in a lattice gauge theory. The critical relaxational flow of the three-dimensional lattice ${\mathbb Z}_2$ gauge model is analyzed within an out-of-equilibrium finite-size scaling framework, which allows us to compute the dynamic critical exponent $z$ associated with the purely relaxational dynamics of the three-dimensional ${\mathbb Z}_2$ gauge universality class. We obtain $z=2.610(15)$, which significantly improves earlier results obtained by other methods, in particular those obtained by analyzing the equilibrium critical dynamics.

arXiv:2501.09975Jan 17, 20250 citations

Out-of-equilibrium critical dynamics of the three-dimensional

{\mathbb Z}_2

gauge model along critical relaxational flows

We address the out-of-equilibrium critical dynamics of the three-dimensional lattice

{\mathbb Z}_2

gauge model, and in particular the critical relaxational flows arising from instantaneous quenches to the critical point, driven by purely relaxational (single-spin-flip Metropolis) upgradings of the link

{\mathbb Z}_2

gauge variables. We monitor the critical relaxational dynamics by computing the energy density, which is the simplest local gauge-invariant quantity that can be measured in a lattice gauge theory. The critical relaxational flow of the three-dimensional lattice

{\mathbb Z}_2

gauge model is analyzed within an out-of-equilibrium finite-size scaling framework, which allows us to compute the dynamic critical exponent

z

associated with the purely relaxational dynamics of the three-dimensional

{\mathbb Z}_2

gauge universality class. We obtain

z=2.610(15)

, which significantly improves earlier results obtained by other methods, in particular those obtained by analyzing the equilibrium critical dynamics.