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.

arXiv comment35 pages, 8 figures, revised version accepted for publication in PRD

References in corpus (49)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Signatures of the Tricritical Point in QCD
• Aspects of the Functional Renormalisation Group
• Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
• Slowing Out of Equilibrium Near the QCD Critical Point
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Lectures on the functional renormalization group method
• Analytic structure of the Landau gauge gluon propagator
• Renormalization Group Approach towards the QCD Phase Diagram
• Nonequilibrium time evolution of the spectral function in quantum field theory
• Spectral Functions for the Quark-Meson Model Phase Diagram from the Functional Renormalization Group
• Classical approximation for time dependent quantum field theory: diagrammatic analysis for hot scalar fields
• Thermodynamic Equilibrium as a Symmetry of the Schwinger-Keldysh Action
• The Schrödinger-Langevin equation with and without thermal fluctuations
• Non perturbative renormalisation group and momentum dependence of $n$-point functions (I)
• Path integral methods for the dynamics of stochastic and disordered systems
• Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group
• Non-perturbative Approach to Critical Dynamics
• Portable implementation of a quantum thermal bath for molecular dynamics simulations
• Introduction to the nonequilibrium functional renormalization group
• Hydro+ in Action: Understanding the Out-of-Equilibrium Dynamics Near a Critical Point in the QCD Phase Diagram
• 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
• Chiral Mirror-Baryon-Meson Model and Nuclear Matter beyond Mean-Field
• Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
• Dynamic critical phenomena from spectral functions on the lattice
• Heisenberg-Langevin vs. quantum master equation
• Spectral function at high temperature in the classical approximation
• Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
• Spectral functions and critical dynamics of the $O(4)$ model from classical-statistical lattice simulations
• Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories
• Vector and Axial-Vector Mesons in Nuclear Matter
• From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group
• Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model
• Spectral functions from the real-time functional renormalization group
• Coherence and entanglement of mechanical oscillators mediated by coupling to different baths
• A Lindblad Model of Quantum Brownian Motion
• Real-time dynamics of the $O(4)$ scalar theory within the fRG approach
• Entanglement and dephasing of quantum dissipative systems
• Self-consistent $O(4)$ model spectral functions from analytically continued FRG flows
• von Neumann entropy and the entropy production of a damped harmonic oscillator
• Thermal contribution of unstable states
• Real-time dynamics of matrix quantum mechanics beyond the classical approximation
• Application of a time-convolutionless stochastic Schrödinger equation to energy transport and thermal relaxation
• QFT treatment of a bound state in a thermal gas

Cited by in corpus (6)

• QCD at finite temperature and density within the fRG approach: An overview
• On the quark spectral function in QCD
• The QCD moat regime and its real-time properties
• Dissipation dynamics of a scalar field
• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• Universality of pseudo-Goldstone damping near critical points