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arXiv:1404.6143 · Theoretical Chemistry Accounts

Computer simulation of quantum dynamics in a classical spin environment

Alessandro Sergi

Published May 19, 2014• 8 citations
arXivHTMLPDF
DOI
10.1007/s00214-014-1495-4

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When modelling real physical systems, one should always consider the influence of the environment.The study of open quantum systems aims precisely at the assessment of the role of the environment in the evolution of these systems.The computational study of these systems is in general a formidable task.However, in many instances one can approximate the environment by means of classical dynamics.For such cases, when the environment is in a thermal state, one can generalize non-Hamiltonian equations of motion to quantum-classical dynamics in order to control the thermodynamic temperature.Such a generalization is achieved within the partial Wigner representation of quantum mechanics, and leads to a quantum-classical evolution of the system.We have studied how to simulate a thermal bath, by means of the least possible number of additional extended variables [1].This has been achieved upon reformulating the Nosé-Hoover Power (NHP) thermostat in quantum-classical theory.When applied to the dissipative evolution of a quantum spin the NHP thermostat, obtained numerical results in agreement with those obtained using Nosè-Hoover chains.However, since a fewer number of variables are needed to achieve the correct sampling of the canonical distribution at equilibrium, the NHP thermostat promises to be better suited for the simulation of low dimensional open quantum system on discrete grids.Following this the quantum dynamics of a XXZ two-spin chain interacting with multiple bosonic baths have been studied, within the mixed Wigner-Heisenberg representation of quantum mechanics.In particular, we have simulated the dynamics of the reduced density matrix ρ s (t), along with the time evolution of the quantum entanglement of the two spins via the concurrence C (ρ).

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A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the evolution of the density matrix. The weak coupling limit of the equation can be integrated by standard algorithms and provides a non-Markovian approach to the computer simulation of quantum systems in classical spin environments. It is expected that the theory and numerical schemes presented here have a wide applicability.
When modelling real physical systems, one should always consider the influence of the environment.The study of open quantum systems aims precisely at the assessment of the role of the environment in the evolution of these systems.The computational study of these systems is in general a formidable task.However, in many instances one can approximate the environment by means of classical dynamics.For such cases, when the environment is in a thermal state, one can generalize non-Hamiltonian equations of motion to quantum-classical dynamics in order to control the thermodynamic temperature.Such a generalization is achieved within the partial Wigner representation of quantum mechanics, and leads to a quantum-classical evolution of the system.We have studied how to simulate a thermal bath, by means of the least possible number of additional extended variables [1].This has been achieved upon reformulating the Nosé-Hoover Power (NHP) thermostat in quantum-classical theory.When applied to the dissipative evolution of a quantum spin the NHP thermostat, obtained numerical results in agreement with those obtained using Nosè-Hoover chains.However, since a fewer number of variables are needed to achieve the correct sampling of the canonical distribution at equilibrium, the NHP thermostat promises to be better suited for the simulation of low dimensional open quantum system on discrete grids.Following this the quantum dynamics of a XXZ two-spin chain interacting with multiple bosonic baths have been studied, within the mixed Wigner-Heisenberg representation of quantum mechanics.In particular, we have simulated the dynamics of the reduced density matrix ρ s (t), along with the time evolution of the quantum entanglement of the two spins via the concurrence C (ρ).