Interval Evaluation of Stationary State Probabilities for Markov Set-Chain Models

2020 ◽  
Author(s):  
Leonid Lyubchyk ◽  
Galyna Grinberg ◽  
Maria Lubchick ◽  
Alexey Galuza ◽  
Olena Akhiiezer
Keyword(s):  
Stationary State ◽  
Interval Evaluation

scholarly journals A Discontinuity of the Energy of Quantum Walk in Impurities

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1134
Author(s):  
Kenta Higuchi ◽  
Takashi Komatsu ◽  
Norio Konno ◽  
Hisashi Morioka ◽  
Etsuo Segawa
Keyword(s):  
Unit Circle ◽  
Stationary State ◽  
Discrete Time ◽  
Quantum Walk ◽  
Time Limit ◽  
The Other ◽  
Unitary Matrix ◽  
Initial State ◽  
Time Quantum ◽  
Long Time

We consider the discrete-time quantum walk whose local dynamics is denoted by a common unitary matrix C at the perturbed region {0,1,⋯,M−1} and free at the other positions. We obtain the stationary state with a bounded initial state. The initial state is set so that the perturbed region receives the inflow ωn at time n(|ω|=1). From this expression, we compute the scattering on the surface of −1 and M and also compute the quantity how quantum walker accumulates in the perturbed region; namely, the energy of the quantum walk, in the long time limit. The frequency of the initial state of the influence to the energy is symmetric on the unit circle in the complex plain. We find a discontinuity of the energy with respect to the frequency of the inflow.

The stationary state and the heat equation for a variant of Davies' model of heat conduction

1985 ◽  
Vol 38 (5-6) ◽  
pp. 1051-1070 ◽  
Author(s):  
R. Artuso ◽  
V. Benza ◽  
A. Frigerio ◽  
V. Gorini ◽  
E. Montaldi
Keyword(s):  
Heat Conduction ◽  
Heat Equation ◽  
Stationary State

Adjustment of vorticity fields with specified values of Casimir invariants as initial condition for simulated annealing of an incompressible, ideal neutral fluid and its MHD in two dimensions

2015 ◽  
Vol 774 ◽  
pp. 443-459 ◽  
Author(s):  
Y. Chikasue ◽  
M. Furukawa
Keyword(s):  
Simulated Annealing ◽  
Finite Number ◽  
Stationary State ◽  
Two Dimensions ◽  
Annealing Process ◽  
Initial Condition ◽  
Vorticity Field ◽  
Casimir Invariants

A method is developed to adjust a vorticity field to satisfy specified values for a finite number of Casimir invariants. The developed method is tested numerically for a neutral fluid in two dimensions. The adjusted vorticity field is adopted as an initial condition for simulated annealing (SA) of an incompressible, ideal neutral fluid and its magnetohydrodynamics (MHD), where SA enables us to obtain a stationary state of the fluid. Since the Casimir invariants are kept unchanged during the annealing process, the obtained stationary state has the required values of the Casimir invariants specified by our method.

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