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1
Content available remote

Edge Switching Transformations of Quantum Graphs

100%
Aizenman M., Schanz H., Smilansky U., Warzel S.
Acta Physica Polonica A
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2017
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vol. 132
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issue 6
1699-1703
EN
Discussed here are the effects of basics graph transformations on the spectra of associated quantum graphs. In particular it is shown that under an edge switch the spectrum of the transformed Schrödinger operator is interlaced with that of the original one. By implication, under edge swap the spectra before and after the transformation, denoted by {Eₙ}^{∞}ₙ₌₁ and {Ẽₙ}^{∞}ₙ₌₁ correspondingly, are level-2 interlaced, so that Eₙ-₂ ≤ Ẽₙ ≤ Eₙ₊₂. The proofs are guided by considerations of the quantum graphs' discrete analogs.
2
Content available remote

Application of the Four Colour Theorem to Identify Spatial Regional Poles and Turnpikes of Economic Growth

100%
Jakimowicz A., Rzeczkowski D.
Acta Physica Polonica A
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2018
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vol. 133
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issue 6
1362-1370
EN
This paper presents a method for identifying regional poles and the turnpikes of growth based on the following foundations: four colour theorem, Wikinomics business model in the form of platforms for participation, evaluation of the functionality of websites run by public administration municipal offices, and dual graph reduction. The province of Warmia and Mazury, which is the subject of the study, is one of the poorest provinces in Poland in terms of economic development. It is therefore natural that the growth of this region requires external enterprise sources. This role can be best performed primarily by websites run by municipal offices, which initiate business activity in their corresponding areas, and consequently, can be regarded as Wikinomics platforms of participation. Using the k-means clustering method, these websites were divided into four separate quality classes. These classes were assigned four various colours, which were subsequently used for preparing the map of the province. Each municipality was marked with a colour corresponding to the quality class of the website run by the state administration unit operating in a given area. The system of colours resulting from the four colour theorem and a corresponding dual graph serve as a frame of reference with regard to each empirical colour distribution and to another, related, dual graph. Thus, the four colour theorem describes the largest diversity of regional growth poles. The measure of the economic growth of the region is a degree of reduction of the dual graph corresponding to the empirical colour distribution, which identifies actual growth poles and determines the turnpikes of growth. The ultimate development objective, although not always achievable, is a reduction of the dual graph to a single vertex, when all municipal offices in the province have websites of the highest quality.
3
Content available remote

Quantum Hall State ν = 1/3 and Antilexicographic Order of Partitions

80%
Kuśmierz B., Wójs A.
Acta Physica Polonica A
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2016
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vol. 130
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issue 5
1183-1186
EN
We focus on a certain aspect of trial wave function approach in the fractional quantum Hall effect. We analyze the role of partition orderings and discuss the possible numerical search for the partition determining the subspace of the Hilbert space containing a particular quantum Hall wave function. This research is inspired by analogical properties of certain polynomials which are the object of interest of the symmetric function theory, especially the Jack polynomials (related to the so-called "Jack states"). Presented method may be used in the search of candidate trial wave functions. We also justify (in certain cases) diagonalization of the Coulomb repulsion Hamiltonian restricted to certain subspaces. We focus on the states at filling factor ν=1/3 in the lowest and second Landau level.
4
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Asymptotics of Resonances Induced by Point Interactions

80%
Lipovský J., Lotoreichik V.
Acta Physica Polonica A
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2017
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vol. 132
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issue 6
1677-1682
EN
We consider the resonances of the self-adjoint three-dimensional Schrödinger operator with point interactions of constant strength supported on the set X={xₙ}_{n=1}^{N}. The size of X is defined by V_{X} = max_{π ∈ Π_{N}} ∑_{n=1}^{N} |xₙ - x_{π(n)}|, where Π_{N} is the family of all the permutations of the set {1,2,...,N}. We prove that the number of resonances counted with multiplicities and lying inside the disc of radius R behaves asymptotically linear W_{X}/πR + O(1) as R → ∞, where the constant W_{X} ∈ [0,V_{X}] can be seen as the effective size of X. Moreover, we show that there exist a configuration of any number of points such that W_{X}=V_{X}. Finally, we construct an example for N=4 with W_{X} < V_{X}, which can be viewed as an analogue of a quantum graph with non-Weyl asymptotics of resonances.
5
Content available remote

Commutators of Jastrow Factors and Angular Momentum Operators

80%
Kuśmierz B., Wójs A.
Acta Physica Polonica A
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2017
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vol. 132
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issue 2
405-407
EN
We present detailed calculations of commutators of the Jastrow factor and certain differential operators useful in the fractional quantum Hall effect. In particular, we analyze action of the angular momentum operators projected from the Haldane sphere on an arbitrary composite fermions state. Examined L⁺ and L¯ momentum operators and following uniformity condition had proven to be useful in the search for candidates for quantum Hall ground states among many families of polynomials including the Jack polynomials.
6
Content available remote

Pseudo-Orbit Expansion for the Resonance Condition on Quantum Graphs and the Resonance Asymptotics

80%
Lipovský J.
Acta Physica Polonica A
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2015
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vol. 128
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issue 6
968-973
EN
In this note we explain the method how to find the resonance condition on quantum graphs, which is called pseudo-orbit expansion. In three examples with standard coupling we show in detail how to obtain the resonance condition. We focus on non-Weyl graphs, i.e. the graphs which have fewer resonances than expected. For these graphs we explain benefits of the method of "deleting edges" for simplifying the graph.
7
Content available remote

On Pseudo Random Bit Generators via Two-Dimensional Hybrid Cellular Automata

80%
Temiz F., Siap I., Akin H.
Acta Physica Polonica A
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2014
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vol. 125
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issue 2
534-537
EN
In this work, we study the structure of two-dimensional linear hybrid cellular automata with respect to adiabatic boundary condition. Further, we check the performance of hybrid cellular automata constructed through the members of this family in generating pseudo random bits.
8
Content available remote

One-Dimensional Cellular Automata with Reflective Boundary Conditions and Radius Three

80%
Akin H., Siap I., Uguz S.
Acta Physica Polonica A
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2014
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vol. 125
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issue 2
405-407
EN
A family of one-dimensional finite linear cellular automata with reflective boundary condition over the field Z_p is defined. The generalizations are the radius and the field that states take values. Here, we establish a connection between reversibility of cellular automata and the rule matrix of the cellular automata with radius three. Also, we prove that the reverse CA of this family again falls into this family.
9
Content available remote

Paths vs. Winding Numbers for the Two-Magnon Sector of the XXX Heisenberg Magnet

80%
Labuz M.
Acta Physica Polonica A
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2015
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vol. 128
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issue 2
190-192
EN
Bethe Ansatz is the famous method of determination of eigenstates and eigenenergies for a wide range of quantum problems, e.g. for the Heisenberg XXX s=1/2 model. The Bethe equations applied to solve the problem of N nodes and r overturned spins on a magnetic chain are labeled by sets of winding numbers {n_i}, however the condition for admissible sets give an overcomplete number of results. On the other hand, combinatorial objects, so called "paths", give the exact number of eigenvectors for the problem described by (N,r) values. The paper presents the method of determining the set of winding numbers from the appropriate path for the sector of r=2 spin deviations.
10
Content available remote

2-Dimensional Reversible Hexagonal Cellular Automata with Periodic Boundary

80%
Uguz S., Siap I., Akin H.
Acta Physica Polonica A
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2013
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vol. 123
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issue 2
480-483
EN
In this paper, we study 2-dimensional finite cellular automata defined by hexagonal local rule with periodic boundary over the field Z_3. We construct the rule matrix corresponding to the hexagonal cellular automata. For some given coefficients and the number of columns of hexagonal information matrix, we prove that the hexagonal cellular automata are reversible.
11
Content available remote

Characterization of 2D Hybrid Cellular Automata with Periodic Boundary

80%
Acar E., Uguz S., Akin H.
Acta Physica Polonica A
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2017
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vol. 131
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issue 3
432-436
EN
We investigate main theoretical aspects of two-dimensional linear-hybrid cellular automata with periodic boundary condition over the Galois field GF(2). We focus on the characterization of two-dimensional hybrid linear cellular automata by way of a special algorithm. Here we set up a relation between reversibility of cellular automata and characterization of two-dimensional hybrid linear cellular automata with a special boundary conditions, i.e. periodic case. The determination of the characterization problem of special type of cellular automaton is studied by means of the matrix algebra theory. It is believed that this type of cellular automata could find many different applications in special case situations, e.g. image processing area, textile design, video processing, DNA research, etc., in the near future.
12
Content available remote

2D Cellular Automata with an Image Processing Application

80%
Uguz S., Sahin U., Siap I., Akin H.
Acta Physica Polonica A
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2014
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vol. 125
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issue 2
435-438
EN
This paper investigates the theoretical aspects of two-dimensional linear cellular automata with image applications. We consider geometrical and visual aspects of patterns generated by cellular automata evolution. The present work focuses on the theory of two-dimensional linear cellular automata with respect to uniform periodic and adiabatic boundary cellular automata conditions. Multiple copies of any arbitrary image corresponding to cellular automata find so many applications in real life situation e.g. textile design, DNA genetics research, etc.
13
Content available remote

Scattering from a Ring Graph - A~Simple Model for the Study of Resonances

80%
Waltner D., Smilansky U.
Acta Physica Polonica A
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2013
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vol. 124
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issue 6
1087-1090
EN
Scattering from the very simple ring graph is shown to display several basic features which underlie the complex (chaotic) phenomena observed in scattering from more complex graphs. In particular we demonstrate the appearance of arbitrarily narrow resonances - the "topological resonances" which are directly linked to the existence of cycles. We use the ring graph to study the response of such resonances to perturbations induced by a time-dependent random noise.
14
Content available remote

Bethe Ansatz and Geometry of the Classical Configuration Space

70%
Lulek B., Lulek T., Milewski J.
Acta Physica Polonica A
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2009
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vol. 115
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issue 1
159-161
EN
We demonstrate that the seminal one-dimensional model of the Heisenberg magnet, consisting of N spins 1/2 with the nearest-neighbour isotropic interaction, solved exactly by Bethe ansatz, admits an interpretation of a system of r=N/2-M pseudoparticles (spin deviations) which are indistinguishable, have hard cores and move on the chain by local hoppings. Such an approach allows us to construct a manifold with some boundaries, which is genericly r-dimensional, and whose F-dimensional regions, 0
15
Content available remote

Covering group and graph of discretized volumes

51%
Makai M., Orechwa Y.
Open Physics
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2004
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vol. 2
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issue 4
660-686
EN
We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γv associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.
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