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1
Content available remote Application of imaging visibility to measurement of correlation coefficient of scattering potential
100%
Liu H. , Wang W. , Liu J. , Liu W.
Optica Applicata
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2011
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tom Vol. 41, nr 3
557--565
EN
It is shown that the imaging visibility of intensity correlated scattered field may be utilized to determine the normalized correlation coefficient of the scattering potential (CCSP) of the quasi-homogeneous (QH) media illuminated by a scalar plane wave. The relationship between the imaging visibility and the CCSP is constructed by analytical forms. As long as the visibility of the intensity correlated scattered field is known, the scaled width of the CCSP can be expressed by solutions of the inverse scattering problem.
2
Content available remote Scattering monodromy and the A 1 singularity
100%
Bates L. , Cushman R.
Open Mathematics
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2007
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tom 5
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nr 3
429-451
EN
We present the notion of scattering monodromy for a two degree of freedom hyperbolic oscillator and apply this idea to determine the Picard-Lefschetz monodromy of the isolated singular point of a quadratic function of two complex variables.
3
Content available Geometric properties of quantum graphs and vertex scattering matrices
80%
Kurasov P. , Nowaczyk M.
Opuscula Mathematica
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2010
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tom Vol. 30, no. 3
295-309
EN
Differential operators on metric graphs are investigated. It is proven that vertex matching (boundary) conditions can be successfully parameterized by the vertex scattering matrix. Two new families of matching conditions are investigated: hyperplanar Neumann and hyperplanar Dirichlet conditions. Using trace formula it is shown that the spectrum of the Laplace operator determines certain geometric properties of the underlying graph.
4
Content available remote Proposal to improve the behaviour of self-energy contributions to the S-matrix
80%
Tóth G.
Open Physics
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2010
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tom 8
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nr 4
527-541
EN
A simple modification of the definition of the S-matrix is proposed. It is expected that the divergences related to nonzero self-energies are considerably milder with the modified definition than with the usual one. This conjecture is verified in a few examples using perturbation theory. The proposed formula is written in terms of the total Hamiltonian operator and a free Hamiltonian operator and is therefore applicable in any case when these Hamiltonian operators are known.
5
Content available remote The J-matrix method: numerical computations
80%
Syty P.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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1999
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tom Vol. 3, No 3
269-276
EN
Numerical calculations of scattering phase shifts have been done using J-matrix method (both non-relativistic and relativistic versions). Results of computations for some simple potentials are described and discussed in this paper. In particularly, it has been shown, that successive numerical approximations converge to results obtained using an analytical formula.
6
Content available remote Time-delay of classical and quantum scattering processes: a conceptual overview and a general definition
70%
Sassoli de Bianchi M.
Open Physics
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2012
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tom 10
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nr 2
282-319
EN
We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of “fuzzy” and “free-flight” sojourn times that we use to provide the most general possible definition for the quantum time-delay, valid for simple and multichannel scattering systems, with or without conditions on the observation of the scattering particle, and for incoming wave packets whose energy can be smeared out or sharply peaked (fixed energy). We conclude our conceptual analysis by presenting what we think is the right interpretation of the concepts of sojourn and delay times in quantum mechanics, explaining why, in ultimate analysis, they should not be called “times.”
7
Content available remote On a property of weak resolvents and its application to a spectral problem
60%
Uetake Y.
Annales Polonici Mathematici
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1997
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tom 66
|
nr 1
263-268
EN
We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.
8
Content available remote Resistance simulations for junctions of SW and MW carbon nanotubes with various metal substrates
60%
Shunin Y. , Zhukovskii Y. , Burlutskaya N. , Bellucci S.
Open Physics
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2011
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tom 9
|
nr 2
519-529
EN
This theoretical study focuses on junctions between the carbon nanotubes (CNTs) and contacting metallic elements of a nanocircuit. Numerical simulations on the conductance and resistance of these contacts have been performed using the multiple scattering theory and the effective media cluster approach. Two models for CNT-metal contacts have been considered in this paper: a) first principles “liquid metal” model and b) semi-empirical model of “effective bonds” based on Landauer notions on ballistic conductivity. Within the latter, which is a more adequate description of chirality effects, we have simulated both single-wall (SW) and multi-wall (MW) CNTs with different morphology. Results of calculations on resistance for different CNT-Me contacts look quantitatively realistic (from several to hundreds kOhm, depending on chirality, diameter and thickness of MW CNT). The inter-wall transparency coefficient for MW CNT has been also simulated, as an indicator of possible ‘radial current’ losses.
9
Content available remote Katedra Metod Matematycznych Fizyki (KMMF) Wydziału Fizyki UW: tematyka, ludzie, historia
51%
Wojtkiewicz J.
Postępy Fizyki
|
2022
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tom T. 73, z. 3
2--10
PL
Artykuł ten jest pomyślany jako uzupełnienie wspomnień zamieszczonych w [1], poświęconych genezie i rozwojowi Katedry Metod Matematycznych Fizyki WF UW. Zamierzam przede wszystkim przedstawić główne nurty badań, prowadzonych w Katedrze. Nie będę też jednak stronić od aspektów historycznych z naciskiem na lata bardziej współczesne niż w [1]. Zamierzam również poczynić kilka uwag na temat związków między fizyką a matematyką.
EN
The aim of this article is continuation of memoirs devoted to the emergence and development of the Department for Mathematical Methods in Physics [1]. The main subject of the present article is presentation of directions of research performed in the Department. I will also present some historic aspects of the Department, complementing the story told in [1]. I will also put few remarks concerning connections and interrelations between mathematics and physics.
10
Content available remote Well-posed linear systems - a survey with emphasis on conservative systems
51%
Weiss G. , Staffans O. J. , Tucsnak M.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 1
7-33
EN
We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space. We give results about the stability, controllability and observability of such conservative systems and illustrate these with a system modeling a controlled beam.
11
Content available remote Well-Posed Linear Systems - a Survey With Emphasis on Conservative Systems
41%
Weiss G. , Staffans O. J. , Tucsnak M.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom Vol. 11, no 1
7-33
EN
We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space. We give results about the stability, controllability and observability of such conservative systems and illustrate these with a system modeling a controlled beam.
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