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Soluble Model of Interacting Bosons Trapped in Harmonic Potential: Quality of Bogoliubov Approximation

100%
Załuska-Kotur M., Gajda M., Mostowski J.
Acta Physica Polonica A
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2001
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vol. 100
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issue 4
485-504
EN
We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for a detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactly soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives a quite accurate description of the system in the limit of weak interactions.
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New Results on Gain-Loss Asymmetry for Stock Markets Time Series

88%
Grudziecki M., Gnatowska E., Karpio K., Orłowski A., Załuska-Kotur M.
Acta Physica Polonica A
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2008
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vol. 114
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issue 3
569-574
EN
A method called investment horizon approach was successfully used to analyze stock markets of many different countries. Here we apply a version of this method to study characteristics of the Polish Pioneer mutual funds. We decided to analyze Pioneer because of its longest involvement in investing on the Polish market. Moreover, it apparently manages the biggest amount of money among all similar institutions in Poland. We compare various types of Pioneer mutual funds, characterized by different financial instruments they invest in. Previously, investment horizon approach produced different characteristics of emerging markets as opposed to mature ones, providing a possible way to quantify stock market maturity. Here we generalize the above mentioned results for mutual funds of various types.
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