arXiv subjects

Leon J. Sieke

Publications and source records attributed to Leon J. Sieke.

3 recordsLinked to original sources

arXiv2026

Non-equilibrium scaling across first-order transitions with relativistic scalar fields

We investigate the out-of-equilibrium dynamics of a relativistic $Z_2$-symmetric scalar field theory with Langevin dynamics in two and three spatial dimensions under linear driving across magnetic first-order phase transitions, close to and far below the critical temperature $T_c$. Using classical-statistical lattice simulations, we find that if the driving timescale is sufficiently fast, the system exhibits finite-time scaling behavior independent of temperature and dimensionality, identical to that observed in mean-field simulations. In slow quenches near $T_c$ this mean-field behavior crosses over to critical Kibble-Zurek scaling behavior, while for temperatures $T \ll T_c$ nucleation and growth dominate the transition dynamics, resulting in corrections to scaling. Near the transition point where the order parameter changes sign, the crossover between mean-field and critical out-of-equilibrium dynamics is found to be well described by the leading algebraic correction to Kibble-Zurek scaling. We find that universal non-equilibrium scaling behavior can be observed for $T \lesssim T_c$, provided the driving is fast enough to avoid nucleation but slow enough for correlations to form, and compute the associated universal scaling functions for the order parameter.

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arXiv2024

Universal non-equilibrium scaling of cumulants across a critical point

We study the critical dynamics of a scalar field theory with $Z_2$ symmetry in the dynamic universality class of Model A in two and three spatial dimensions with classical-statistical lattice simulations. In particular, we measure the non-equilibrium behavior of the system under a quench protocol in which the symmetry-breaking external field is changed at a constant rate through the critical point. Using the well-established Kibble-Zurek scaling theory we compute non-equilibrium scaling functions of cumulants of the order parameter up to fourth order. Together with the static critical exponents and the dynamic critical exponent, these fully describe the universal non-equilibrium evolution of the system near the critical point. We further extend the analysis to include finite-size effects and observe good collapse of our data onto two-dimensional universal non-equilibrium and finite-size scaling functions.

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arXiv2022

Real-time methods for spectral functions

In this paper we develop and compare different real-time methods to calculate spectral functions. These are classical-statistical simulations, the Gaussian state approximation (GSA), and the functional renormalization group (FRG) formulated on the Keldysh closed-time path. Our test-bed system is the quartic anharmonic oscillator, a single self-interacting bosonic degree of freedom, coupled to an external heat bath providing dissipation analogous to the Caldeira-Leggett model. As our benchmark we use the spectral function from exact diagonalization with constant Ohmic damping. To extend the GSA for the open system, we solve the corresponding Heisenberg-Langevin equations in the Gaussian approximation. For the real-time FRG, we introduce a novel general prescription to construct causal regulators based on introducing scale-dependent fictitious heat baths. Our results explicitly demonstrate how the discrete transition lines of the quantum system gradually build up the broad continuous structures in the classical spectral function as temperature increases. At sufficiently high temperatures, classical, GSA and exact-diagonalization results all coincide. The real-time FRG is able to reproduce the effective thermal mass, but overestimates broadening and only qualitatively describes higher excitations, at the present order of our combined vertex and loop expansion. As temperature is lowered, the GSA follows the ensemble average of the exact solution better than the classical spectral function. In the low-temperature strong-coupling regime, the qualitative features of the exact result are best captured by our real-time FRG calculation, with quantitative improvements to be expected at higher truncation orders.

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