Search results

1

Edge Switching Transformations of Quantum Graphs

100%

Aizenman M., Schanz H., Smilansky U., Warzel S.

Acta Physica Polonica A

|

2017

|

vol. 132

|

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

Asymptotics of Resonances Induced by Point Interactions

76%

Lipovský J., Lotoreichik V.

Acta Physica Polonica A

|

2017

|

vol. 132

|

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.

3

Commutators of Jastrow Factors and Angular Momentum Operators

76%

Kuśmierz B., Wójs A.

Acta Physica Polonica A

|

2017

|

vol. 132

|

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.

4

Continuous lateral gradients in film morphology for position sensitive detection and organic solar cell optimization

64%

Campoy-Quiles M., Randon V., Mróz M. M., Jarzaguet M., Garriga M., Cabanillas-González J.

Organic Photonics and Photovoltaics

|

2013

|

vol. 1

11-23

EN

We present a method to fabricate binary organic donor and acceptor blends exhibiting a controlled lateral gradient in morphology. Upon combining photometry, ellipsometry and Xray maps together with photoinduced absorption measurements, we show how the gradual exposure to solvent vapor results in a varying degree of polymer crystallinity for the polythiophene/soluble fullerene system along one direction. These morphologically graded samples are characterized by a spectral photoresponse that depends on the specific location in the area of the device where the light beam impinges, a property that stands as proof-of-concept for position sensitive detection. Moreover, we demonstrate that the development of graded morphologies is an effective one-step method which allows for fast performance optimization of organic solar cells. Finally, the appropriateness of eight different solvents for morphology control via vapor annealing is evaluated in a time-effective way using the advanced method, which helps to identify boiling point and solubility as the key processing parameters.

Refine search results

3 Acta Physica Polonica A

1 Organic Photonics and Photovoltaics

3 2017

1 2013

1 Aizenman M.

1 Cabanillas-González J.

1 Campoy-Quiles M.

1 Garriga M.

1 Jarzaguet M.

1 Kuśmierz B.

1 Lipovský J.

1 Lotoreichik V.

1 Mróz M. M.

1 Randon V.

1 Schanz H.

1 Smilansky U.

1 Warzel S.

1 Wójs A.

Edge Switching Transformations of Quantum Graphs

Asymptotics of Resonances Induced by Point Interactions

Commutators of Jastrow Factors and Angular Momentum Operators

Continuous lateral gradients in film morphology for position sensitive detection and organic solar cell optimization