Real-time methods for spectral functions

Abstract

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.

35 pages, 8 figures, revised version accepted for publication in PRD

References in corpus (18)

• Exact evolution equation for the effective potential
• Renormalization Group Approach towards the QCD Phase Diagram
• Non-perturbative Approach to Critical Dynamics
• Portable implementation of a quantum thermal bath for molecular dynamics simulations
• Landau gauge Yang-Mills propagators in the complex momentum plane
• Ghost spectral function from the spectral Dyson-Schwinger equation
• Flow equations for spectral functions at finite external momenta
• Spectral functions in the ${\varphi }^4$-theory from the spectral DSE
• Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
• Heisenberg-Langevin vs. quantum master equation
• Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
• Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories
• Vector and Axial-Vector Mesons in Nuclear Matter
• Spectral functions from the real-time functional renormalization group
• Real-time dynamics of the $O(4)$ scalar theory within the fRG approach
• Self-consistent $O(4)$ model spectral functions from analytically continued FRG flows
• Thermal contribution of unstable states
• QFT treatment of a bound state in a thermal gas

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