scholarly journals Spectral analysis for a multi-dimensional split-step quantum walk with a defect

2021 ◽  
Author(s):  
Toru Fuda ◽  
Akihiro Narimatsu ◽  
Kei Saito ◽  
Akito Suzuki
Keyword(s):  
Spectral Analysis ◽  
Quantum Walk

Localization of quantum walks via the CGMV method

2011 ◽  
Vol 11 (5&6) ◽  
pp. 485-496
Author(s):  
Norio Konno ◽  
Etsuo Segawa
Keyword(s):  
Spectral Analysis ◽  
Discrete Time ◽  
Spectral Measure ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Laurent Polynomials ◽  
Cmv Matrix ◽  
Orthogonal Laurent Polynomials ◽  
Homogeneous Trees ◽  
Time Quantum

We study discrete-time quantum walks on a half line by means of spectral analysis. Cantero et al. showed that the CMV matrix, which gives a recurrence relation for the orthogonal Laurent polynomials on the unit circle, expresses the dynamics of the quantum walk. Using the CGMV method introduced by them, the name is taken from their initials, we obtain the spectral measure for the quantum walk. As a corollary, we give another proof for localization of the quantum walk on homogeneous trees shown by Chisaki et al.

scholarly journals INVESTIGATION OF CONTINUOUS-TIME QUANTUM WALKS VIA SPECTRAL ANALYSIS AND LAPLACE TRANSFORM

2007 ◽  
Vol 05 (04) ◽  
pp. 575-596 ◽  
Author(s):  
M. A. JAFARIZADEH ◽  
R. SUFIANI
Keyword(s):  
Spectral Analysis ◽  
Laplace Transform ◽  
Continuous Time ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Inverse Laplace Transform ◽  
Stieltjes Transform ◽  
Stieltjes Function ◽  
Inverse Laplace Transformation ◽  
Time Quantum

Continuous-time quantum walk (CTQW) on a given graph is investigated using the techniques of the spectral analysis and inverse Laplace transform of the Stieltjes function (Stieltjes transform of the spectral distribution) associated with the graph. It is shown that the probability amplitude of observing the CTQW at a given site at time t is related to the inverse Laplace transformation of the Stieltjes function, namely, one can calculate the probability amplitudes only by taking the inverse laplace transform of the function iGμ(is), where Gμ(x) is the Stieltjes function of the graph. The preference of this procedure is that there is no need to know the spectrum of the graph.

A NOTE ON KONNO'S PAPER ON QUANTUM WALK

2006 ◽  
Vol 09 (02) ◽  
pp. 299-304 ◽  
Author(s):  
NOBUAKI OBATA
Keyword(s):  
Spectral Analysis ◽  
Quantum Walk

Konno's idea of quantum walk on trees remains applicable to a wider family of graphs by means of quantum probabilistic machinery for asymptotic spectral analysis of graphs.

Spectral analysis of asymmetry training effect for depression

2008 ◽  
Author(s):  
Ji Ha Lee ◽  
Sung Won Choi ◽  
Ji Sun Min ◽  
Eun Ju Jaekal ◽  
Gyhye Sung
Keyword(s):  
Spectral Analysis ◽  
Training Effect

Some problems in the spectral analysis of human behavior records

1953 ◽  
Author(s):  
C. J. Burke ◽  
R. Narasimhan ◽  
O. J. Benepe
Keyword(s):  
Spectral Analysis ◽  
Human Behavior
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