Radial spiky steady states of a flux‐limited Keller–Segel model: Existence, asymptotics, and stability

2021 ◽  
Author(s):  
Zhi‐An Wang ◽  
Xin Xu
Keyword(s):  
Steady States ◽  
Model Existence

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.

Stochastic pumping of non-equilibrium steady-states: how molecules adapt to a fluctuating environment

2018 ◽  
Vol 54 (5) ◽  
pp. 427-444 ◽  
Author(s):  
R. D. Astumian
Keyword(s):  
Steady States ◽  
Absolute Amount ◽  
Fluctuating Environment ◽  
The Absolute ◽  
Non Equilibrium

Fluctuations favour state B = (B,B′) based on kinetic asymmetry combined with moderate dissipation rather than state A = (A,A′) in which the absolute amount of dissipation is greater but where there is no kinetic asymmetry.

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