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Luttinger Liquid as a New Metallic State of Correlated Fermions

100%
Byczuk K., Spałek J.
Acta Physica Polonica A
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1996
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vol. 90
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issue 4
595-602
EN
This article provides an elementary introduction to the physics of the Luttinger liquid and summarizes its basic properties, as well as discusses examples, where such quantum liquid would be or has been observed experimentally. A comparison with the Fermi-liquid state is made
2
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Soluble Model of Interacting Bosons Trapped in Harmonic Potential: Quality of Bogoliubov Approximation

63%
Załuska-Kotur M., Gajda M., Mostowski J.
Acta Physica Polonica A
|
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.
3
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Numerical Stability of Solution of Recursion Relation for Ideal Quantum Gases Containing Finite Number of Harmonically Trapped Particles

63%
Paszkiewicz T., Wolski S.
Acta Physica Polonica A
|
2015
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vol. 128
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issue 2
204-207
EN
The numerical stability of the solution of recursion relation for mean occupation numbers derived by Schönhammer for ideal Fermi gas trapped in 1D harmonic potential is studied. In low temperature region there exists a solution of this recursion relation. In high temperature region the iteration becomes unstable. In low and high temperature regions with growing number of particles the region of numerical instability diminishes.
4
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A New Microscopic Calculation for the Uniform Electron Fluid

51%
Bouchebak A., Al-Sugheir M., Ghassib H.
Acta Physica Polonica A
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2011
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vol. 119
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issue 3
312-322
EN
The static fluctuation approximation is applied for the first time to an electronic system. A simple model (a uniform electron fluid) is chosen to explore the applicability of static fluctuation approximation to electrons in metals. The thermodynamic properties - the internal energy per particle, the pressure, the entropy per unit volume, the heat capacity per unit volume, and the chemical potential - are calculated over a wide range of densities within the metallic-density region. Finally, the pair-correlation function for the electron fluid is evaluated. Values of this function are then tabulated for zero-interparticle separation at several densities of interest. The results of this work are found to be in good agreement with several other many-body calculations.
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