scholarly journals Numerical evaluation of two-time correlation functions in open quantum systems with matrix product state methods: a comparison

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Stefan Wolff ◽  
Ameneh Sheikhan ◽  
Corinna Kollath
Keyword(s):  
Correlation Functions ◽  
Open Quantum Systems ◽  
Time Correlation ◽  
Quantum Systems ◽  
Quantum Trajectories ◽  
Time Correlation Functions ◽  
Matrix Product ◽  
Product State ◽  
Open Quantum ◽  
Matrix Product State

We compare the efficiency of different matrix product state (MPS) based methods for the calculation of two-time correlation functions in open quantum systems. The methods are the purification approach[1] and two approaches[2,3] based on the Monte-Carlo wave function (MCWF) sampling of stochastic quantum trajectories using MPS techniques. We consider a XXZ spin chain either exposed to dephasing noise or to a dissipative local spin flip. We find that the preference for one of the approaches in terms of numerical efficiency depends strongly on the specific form of dissipation.

scholarly journals Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 77
Author(s):  
Angus J. Dunnett ◽  
Alex W. Chin
Keyword(s):  
Finite Temperature ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Steady States ◽  
Matrix Product ◽  
Open Quantum ◽  
Matrix Product State ◽  
Wide Range ◽  
Boson Model ◽  
Non Equilibrium

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

scholarly journals Matrix Product State Simulations of Non-equilibirum Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

2020 ◽  
Author(s):  
Angus Dunnett ◽  
Alex W. Chin
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Steady States ◽  
Matrix Product ◽  
Data Set ◽  
Open Quantum ◽  
Matrix Product State ◽  
Markovian Dynamics ◽  
Wide Range ◽  
Boson Model

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to expore the striking theory of Tamescelli et al. that shows how finite temperture open dyanmics can be obtained from zero temperature, i.e. pure wave function, simulations. Using this approach, we produce a benchmark data set for the dynamics of the Ohmic spin-boson model across a wide range of coupling and temperatures, and also present detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

scholarly journals Non-Markovian correlation functions for open quantum systems

2016 ◽  
Vol 18 (8) ◽  
pp. 083038 ◽  
Author(s):  
Jinshuang Jin ◽  
Christian Karlewski ◽  
Michael Marthaler
Keyword(s):  
Correlation Functions ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Equivalence of matrix product ensembles of trajectories in open quantum systems

2015 ◽  
Vol 92 (1) ◽  
Author(s):  
Jukka Kiukas ◽  
Mădălin Guţă ◽  
Igor Lesanovsky ◽  
Juan P. Garrahan
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Matrix Product ◽  
Open Quantum

scholarly journals Gaussian Quantum Trajectories for the Variational Simulation of Open Quantum-Optical Systems

2018 ◽  
Vol 8 (9) ◽  
pp. 1427 ◽  
Author(s):  
Wouter Verstraelen ◽  
Michiel Wouters
Keyword(s):  
Open Quantum Systems ◽  
Computational Cost ◽  
System Size ◽  
Quantum Systems ◽  
Optical Systems ◽  
Quantum Trajectory ◽  
Quantum Trajectories ◽  
Open Quantum ◽  
Quantum Optical ◽  
Bistability Regime

We construct a class of variational methods for the study of open quantum systems based on Gaussian ansatzes for the quantum trajectory formalism. Gaussianity in the conjugate position and momentum quadratures is distinguished from Gaussianity in density and phase. We apply these methods to a driven-dissipative Kerr cavity where we study dephasing and the stationary states throughout the bistability regime. Computational cost proves to be similar to the Truncated Wigner Approximation (TWA) method, with at most quadratic scaling in system size. Meanwhile, strong correspondence with the numerically-exact trajectory description is maintained so that these methods contain more information on the ensemble constitution than TWA and can be more robust.

FEEDBACK IN OPEN QUANTUM SYSTEMS

1995 ◽  
Vol 09 (11n12) ◽  
pp. 629-654 ◽  
Author(s):  
H. M. WISEMAN
Keyword(s):  
System Dynamics ◽  
Feedback Loop ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Feedback Mechanism ◽  
The Other ◽  
Langevin Equations ◽  
Quantum Trajectories ◽  
Classical Counterpart ◽  
Open Quantum

Open quantum systems continually lose information to their surroundings. In some cases this information can be readily retrieved from the environment and put to good use by engineering a feedback loop to control the system dynamics. Two cases are distinguished: one where the feedback mechanism involves a measurement of the environment, and the other where no measurement is made. It is shown that the latter case can always replicate the former, but not vice versa. This emphasizes the quantum nature of the information being fed back. Two approaches are used to describe the feedback: quantum trajectories (which apply only for feedback based on measurement) and quantum Langevin equations (which can be used in either case), and the results are shown to be equivalent. The obvious applications for the theory are in quantum optics, where the information is lost by radiation damping and can be retrieved by photodetection. A few examples are discussed, one of which is particularly interesting as it has no classical counterpart.

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