Finite representations of continuum environments

Abstract

Understanding dissipative and decohering processes is fundamental to the study of quantum systems. An accurate and generic method for investigating these processes is to simulate both the system and environment, which, however, is computationally very demanding. We develop a novel approach to constructing finite representations of the environment based on the influence of different frequency scales on the system's dynamics. As an illustration, we analyze a solvable model of an optical mode decaying into a reservoir. The influence of the environment modes is constant for small frequencies, but drops off rapidly for large frequencies, allowing for a very sparse representation at high frequencies that gives a significant computational speedup in simulating the environment. This approach provides a general framework for simulating open quantum systems.

4 pages, 3 figures, updated to fix fonts

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Cited by in corpus (13)

• Quantum Darwinism in a hazy environment
• How to discretize a quantum bath for real-time evolution
• Quantum Darwinism in non-ideal environments
• Breaking the entanglement barrier: Tensor network simulation of quantum transport
• Adaptive logarithmic discretization for numerical renormalization group methods
• Open System Tensor Networks and Kramers' Crossover for Quantum Transport
• Density matrix renormalization group study of a quantum impurity model with Landau-Zener time-dependent Hamiltonian
• Performance of Reservoir Discretizations in Quantum Transport Simulations
• Analytic expressions for the steady-state current with finite extended reservoirs
• Accumulative reservoir construction: Bridging continuously relaxed and periodically refreshed extended reservoirs
• Gibbs phenomenon and the emergence of the steady-state in quantum transport
• Transport in a periodically driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit
• Approaching the scaling limit of transport through lattices with dephasing