Clustering of linearly interacting diffusions and universality of their long-time limit distribution

2000 ◽  
Vol 118 (4) ◽  
pp. 574-594 ◽  
Author(s):  
J. M. Swart
Keyword(s):  
Limit Distribution ◽  
Time Limit ◽  
Interacting Diffusions ◽  
Long Time

scholarly journals A limit distribution for a quantum walk driven by a five-diagonal unitary matrix

2021 ◽  
Vol 21 (1&2) ◽  
pp. 0019-0036
Author(s):  
Takuya Machida
Keyword(s):  
Time Evolution ◽  
Limit Distribution ◽  
Quantum Walk ◽  
Time Limit ◽  
Unitary Matrix ◽  
Exact Form ◽  
Special Values ◽  
The Matrix ◽  
Long Time ◽  
Phase Term

In this paper, we work on a quantum walk whose system is manipulated by a five-diagonal unitary matrix, and present long-time limit distributions. The quantum walk launches off a location and delocalizes in distribution as its system is getting updated. The five-diagonal matrix contains a phase term and the quantum walk becomes a standard coined walk when the phase term is fixed at special values. Or, the phase term gives an effect on the quantum walk. As a result, we will see an explicit form of a long-time limit distribution for a quantum walk driven by the matrix, and thanks to the exact form, we understand how the quantum walker approximately distributes in space after the long-time evolution has been executed on the walk.

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.

LONG‐TIME RESPONSE PREDICTED BY EXACT ELASTIC RAY THEORY

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 363-368 ◽  
Author(s):  
T. W. Spencer
Keyword(s):  
Formal Solution ◽  
Intermediate Stage ◽  
Time Limit ◽  
Time Interval ◽  
Individual Response ◽  
Axially Symmetric ◽  
Long Time ◽  
The Difference ◽  
The Individual ◽  
Significant Figures

The formal solution for an axially symmetric radiation field in a multilayered, elastic system can be expanded in an infinite series. Each term in the series is associated with a particular raypath. It is shown that in the long‐time limit the individual response functions produced by a step input in particle velocity are given by polynomials in odd powers of the time. For rays which suffer m reflections, the degree of the polynomials is 2m+1. The total response is obtained by summing all rays which contribute in a specified time interval. When the rays are selected indiscriminately, the difference between the magnitude of the partial sum at an intermediate stage of computation and the magnitude of the correct total sum may be greater than the number of significant figures carried by the computer. A prescription is stated for arranging the rays into groups. Each group response function varies linearly in the long‐time limit and goes to zero when convolved with a physically realizable source function.

scholarly journals A limit theorem for a splitting distribution of a quantum walk

2018 ◽  
Vol 16 (03) ◽  
pp. 1850023
Author(s):  
Takuya Machida
Keyword(s):  
Limit Theorem ◽  
Probability Distribution ◽  
Random Walks ◽  
Discrete Time ◽  
Limit Distribution ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Unitary Evolution ◽  
Time Quantum ◽  
Long Time

Discrete-time quantum walks are considered a counterpart of random walks and their study has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to two parts. The quantum walker with two coin states spreads at points, represented by integers, and we analyze the chance of finding the walker at each position after it carries out a unitary evolution a lot of times. The result is reported as a long-time limit distribution from which one can see an approximation to the finding probability.

scholarly journals Cancellation of vacuum diagrams and the long-time limit in out-of-equilibrium diagrammatic quantum Monte Carlo

2019 ◽  
Vol 100 (8) ◽  
Author(s):  
Alice Moutenet ◽  
Priyanka Seth ◽  
Michel Ferrero ◽  
Olivier Parcollet
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Time Limit ◽  
Long Time
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