Unitary perturbation theory approach to real-time evolution problems

Abstract

We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations of motion for an operator. It is our purpose to illustrate the accuracy of this approach by studying dissipative quantum systems on all time scales. In particular, we obtain results for non-equilibrium correlation functions for general initial conditions. We illustrate our ideas for the exactly solvable dissipative oscillator, and, as a non-trivial model, for the dissipative two-state system.

23 pages, 6 figures several misprints corrected, added one reference final version as accepted by Journal of Physics C

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Cited by in corpus (24)

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• Real-time evolution for weak interaction quenches in quantum systems
• Time Evolution of Many-Body Localized Systems with the Flow Equation Approach
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Non-perturbative stochastic method for driven spin-boson model
• A renormalization group approach to time dependent transport through correlated quantum dots
• Green's function methods for single molecule junctions
• Hybrid NRG-DMRG approach to real-time dynamics of quantum impurity systems
• Nonequilibrium Spin Dynamics in the Ferromagnetic Kondo Model
• Non-Equilibrium Kondo Model with Voltage Bias in a Magnetic Field
• Flow Equation Calculation of Transient and Steady State Currents in the Anderson Impurity Model
• Photo-induced nonequilibrium states in Mott insulators
• Quasi-Many-Body Localization of Interacting Fermions with Long-Range Couplings
• Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems
• Relaxation dynamics of an exactly solvable electron-phonon model
• Non-equilibrium magnetization dynamics of ferromagnetically coupled Kondo spins
• Non-equilibrium time evolution of bosons from the functional renormalization group
• Imaginary-time quantum many-body theory out of equilibrium I: Formal equivalence to Keldysh real-time theory and calculation of static properties
• Flow Equations for Disordered Floquet Systems
• Non-equilibrium dynamics of a system with Quantum Frustration
• The excitation operator approach to non-Markovian dynamics of quantum impurity models in the Kondo regime
• Master equation based steady-state cluster perturbation theory
• The excitation operator method in the spin dynamics of the one-dimensional XXZ model
• Solving real time evolution problems by constructing excitation operators