Ondrej Turek

J-GLOBAL         Last updated: Nov 3, 2018 at 10:10
Ondrej Turek
Kochi University of Technology
Laboratory for Unified Quantum Devices
Job title
Visiting Researcher
PhD(2009, Czech Technical University in Prague; Université de Toulon)

Research Areas


Published Papers

Pavel Exner, Ondrej Turek, Milos Tater
J. Phys. A: Math. Theor.   51(28) 285301   Jul 2018   [Refereed]
The paper discusses quantum graphs with a vertex coupling which interpolates between the common one of the δ type and a coupling introduced recently by two of the authors which exhibits a preferred orientation. Describing the interpolation family ...
Pavel Exner, Ondrej Turek
J. Phys. A: Math. Theor.   50(45) 455201   Nov 2017   [Refereed]
The paper is concerned with the number of open gaps in spectra of periodic quantum graphs. The well-known conjecture by Bethe and Sommerfeld (1933) says that the number of open spectral gaps for a system periodic in more than one direction is fini...
Pavel Exner, Ondrej Turek
8(3) 305-309   Jun 2017   [Refereed]
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of graph Hamil...
Dardo Goyeneche, Ondrej Turek
J. Phys. A: Math. Theor.   50(24) 245304   Jun 2017   [Refereed]
We demonstrate that a complex equiangular tight frame composed of N vectors in dimension d, denoted ETF (d, N), exists if and only if a certain bistochastic matrix, univocally determined by N and d, belongs to a special class of unistochastic matr...
Ondrej Turek
Functional Analysis and Operator Theory for Quantum Physics (EMS Proceedings, Pavel Exner Anniversary Volume; eds.: J. Dittrich, H. Kovarik, A. Laptev)   543-563   May 2017   [Refereed][Invited]
We examine transmission through a quantum graph vertex to which auxiliary edges with constant potentials are attached. We find a characterization of vertex couplings for which the transmission probability from a given ``input'' line to a given ``o...
Pavel Exner, Ondrej Turek
Integr. Equat. Oper. Th.   81(4) 535-557   Apr 2015   [Refereed]
We analyze spectrum of Laplacian supported by a periodic honeycomb lattice with generally unequal edge lengths and a δ type coupling in the vertices. Such a quantum graph has nonempty point spectrum with compactly supported eigenfunctions provided...
Ondrej Turek, Taksu Cheon
Linear Algebra Appl.   469 569-593   Mar 2015   [Refereed]
We study Hermitian unitary matrices Tex with the following property: There exist Tex and Tex such that the entries of Tex satisfy Tex and Tex for all $j,k=1,\ldots...
Ondrej Turek
J. Integer Seq.   18(3) Article 15.3.4-(29 pp.)   Feb 2015   [Refereed]
According to a result of Richomme, Saari and Zamboni, the abelian complexity of the Tribonacci word satisfies Tex for each Tex. In this paper we derive an automaton that evaluates the function $\rho...
Ondrej Turek
Theor. Comput. Sci.   566 26-38   Feb 2015   [Refereed]
Abelian complexity of a word u is a function that counts the number of pairwise non-abelian-equivalent factors of u of length n. We prove that for any c-balanced Parry word u, the values of the abelian complexity function can be computed by a fini...
Karel Brinda, Edita Pelantova, Ondrej Turek
Fund. Inform.   132(1) 33-61   Mar 2014   [Refereed]
The Tex-bonacci word is a generalization of the Fibonacci word to the Tex-letter alphabet Tex. It is the unique fixed point of the Pisot--type substitution $\varphi_m: 0\to 01,\ 1\to 02,\ \ldots,\ (m-2)\to0(m-1),\text...
Taksu Cheon, Atushi Tanaka, Ondrej Turek
Acta Polytechnica   53(5) 410-415   Nov 2013   [Refereed]
We study a family of closed quantum graphs described by one singular vertex of order n=4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed path in the parameter space that physically corresponds to th...
Ondrej Turek, Taksu Cheon
J. Math. Phys.   54(3) 032104-(17 pp.)   Mar 2013   [Refereed]
We study the transmission of a quantum particle along a straight input–output line to which a graph Γ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant coupling with a ...
Ondrej Turek, Taksu Cheon
Ann. Phys. (NY)   330 104-141   Mar 2013   [Refereed]
We study the scattering in a quantum star graph with a Fülöp--Tsutsui coupling in its vertex and with external potentials on the lines. We find certain special couplings for which the probability of the transmission between two given lines of ...
Ondrej Turek
Theor. Comput. Sci.   469 77-91   Jan 2013   [Refereed]
We propose a technique for exploring the abelian complexity of recurrent
infinite words, focusing particularly on infinite words associated with Parry
numbers. Using that technique, we give the affirmative answer to the open
question posed by Rich...
Ondrej Turek, Taksu Cheon
EPL - Europhys. Lett.   98 50005 (5 pp.)   Jun 2012   [Refereed]
We design two simple quantum devices applicable as an adjustable quantum spectral filter and as a flux controller. Their function is based upon the threshold resonance in a Fülöp-Tsutsui type star graph with an external potential added on one ...
Ondrej Turek, Taksu Cheon
Phys. Lett. A   375(43) 3775-3780   Oct 2011   [Refereed]
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix Tex. Observing that if Tex has at most two eigenvalues, then the scattering matrix Tex of the vertex is a linear combination of the identit...
Lubomira Balkova, Karel Brinda, Ondrej Turek
Theor. Comput. Sci.   412(45) 6252-6260   Oct 2011   [Refereed]
We derive an explicit formula for the Abelian complexity of infinite words associated with quadratic Parry numbers.
Taksu Cheon, Pavel Exner, Ondrej Turek
Phys. Rev. A 83 (2011) 062715      Jun 2011   [Refereed]
We demonstrate how the inverse scattering problem of a quantum star graph can
be solved by means of diagonalization of Hermitian unitary matrix when the
vertex coupling is of the scale invariant (or Fül\H{o}p-Tsutsui) form. This
enables the cons...
Taksu Cheon, Pavel Exner, Ondrej Turek
Phys. Lett. A   375(2) 113-118   Nov 2010   [Refereed]
We discuss formulations of boundary conditions in a quantum graph vertex and demonstrate that the so-called Tex-form can be further reduced up to a form more effective in certain applications: In particular, in identifying the number of independe...
Pavel Exner, Ondrej Turek
J. Phys. A: Math. Theor.   43 474024   Nov 2010   [Refereed]
We investigate a periodic quantum graph in form of a square lattice with a
general self-adjoint coupling at the vertices. We analyze the spectrum, in
particular, its high-energy behaviour. Depending on the coupling type, bands
and gaps have differ...