L. Nivanen - Academia.edu (original) (raw)
Papers by L. Nivanen
We comment on the problem of energy translation invariance of probability distribution and presen... more We comment on the problem of energy translation invariance of probability distribution and present some observations. It is shown that a probability distribution can be invariant in the thermodynamic limit if there is no long term interaction or correlation and no relativistic effect. So this invariance should not be considered as a universal theoretical property. Some peculiarities within the invariant
Reports on Mathematical Physics, 2009
Physica A: Statistical Mechanics and its Applications, 2004
This is a study of the information evolution of complex systems by a geometrical consideration. W... more This is a study of the information evolution of complex systems by a geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale reÿnement. Due to the incompleteness of the state number counting at any scale on fractal support, the incomplete normalization i p q i =1 is applied throughout the paper, where q is the fractal dimension divided by the dimension of the smooth Euclidean space in which the fractal structure of the phase space is embedded. It is shown that the information growth is nonadditive and is proportional to the trace-form i pi − i p q i which can be connected to several nonadditive entropies. This information growth can be extremized to give power-law distributions for these nonequilibrium systems. It can also be used for the study of the thermodynamics derived from Tsallis entropy for nonadditive systems which contain subsystems each having its own q. It is argued that, within this thermodynamics, the Stefan-Boltzmann law of blackbody radiation can be preserved.
Physica A: Statistical Mechanics and its Applications, 2007
This work is an extension of the incomplete probability theory from the simple case of monofracta... more This work is an extension of the incomplete probability theory from the simple case of monofractals previously studied to the more general case of multifractals which can occur in the phase space without equiprobable partition. PACS numbers : 05.20.-y (Classical statistical mechanics) 05.45.Df (Fractals) 02.50.-r (Probability theory, stochastic processes, and statistics)
Journal of Low Temperature Physics, 2008
Heavy electrons in superconducting materials are widely studied with the Kondo lattice t-J model.... more Heavy electrons in superconducting materials are widely studied with the Kondo lattice t-J model. Numerical results have shown that the Fermi surface of these correlated particles undergoes a flattening effect according to the coupling degree J. This behaviour is not easy to understand from the theoretical point of view within standard Fermi-Dirac statistics and non-standard theories such as fractional exclusion statistics for anyons and Tsallis nonextensive statistics. The present work is an attempt to account for the heavy electron distribution within incomplete statistics (IS) which is developed for complex systems with interactions which make the statistics incomplete such that 1 1 = ∑ = w i q i p . The parameter q, when different from unity, characterizes the incompleteness of the statistics. It is shown that the correlated electrons can be described with the help of IS with q related to the coupling constant J in the context of Kondo model.
Journal of Low Temperature Physics, 2008
In the Bose-Einstein condensation of interacting atoms or molecules such as 87 Rb, 23 Na and 7 Li... more In the Bose-Einstein condensation of interacting atoms or molecules such as 87 Rb, 23 Na and 7 Li, the theoretical understanding of the transition temperature is not always obvious due to the interactions or zero point energy which cannot be exactly taken into account. The S-wave collision model fails sometimes to account for the condensation temperatures. In this work, we look at the problem within the nonextensive statistics which is considered as a possible theory describing interacting systems. The generalized energy U q and the particle number N q of boson gas are given in terms of the nonextensive parameter q. q>1 (q<1) implies repulsive (attractive) interaction with respect to the perfect gas. The generalized condensation temperature T cq is derived versus T c given by the perfect gas theory. Thanks to the observed condensation temperatures, we find q ≈ 0.1 for 87 Rb atomic gas, q ≈ 0.95 for 7 Li and q ≈ 0.62 for 23 Na. It is concluded that the effective interactions are essentially attractive for the three considered atoms, which is consistent with the observed temperatures higher than those predicted by the conventional theory.
... A. Avetisyan. Local field effects in superradiance and superradiance without inversion from a... more ... A. Avetisyan. Local field effects in superradiance and superradiance without inversion from a thin film of three-level atoms. Author(s): AA Bogdanov; IV Ryzhov; Evgeni D. Trifonov; AI Zaitsev; Viktor A. Malyshev. Transmitted and ...
We comment on the problem of energy translation invariance of probability distribution and presen... more We comment on the problem of energy translation invariance of probability distribution and present some observations. It is shown that a probability distribution can be invariant in the thermodynamic limit if there is no long term interaction or correlation and no relativistic effect. So this invariance should not be considered as a universal theoretical property. Some peculiarities within the invariant
Reports on Mathematical Physics, 2009
Physica A: Statistical Mechanics and its Applications, 2004
This is a study of the information evolution of complex systems by a geometrical consideration. W... more This is a study of the information evolution of complex systems by a geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale reÿnement. Due to the incompleteness of the state number counting at any scale on fractal support, the incomplete normalization i p q i =1 is applied throughout the paper, where q is the fractal dimension divided by the dimension of the smooth Euclidean space in which the fractal structure of the phase space is embedded. It is shown that the information growth is nonadditive and is proportional to the trace-form i pi − i p q i which can be connected to several nonadditive entropies. This information growth can be extremized to give power-law distributions for these nonequilibrium systems. It can also be used for the study of the thermodynamics derived from Tsallis entropy for nonadditive systems which contain subsystems each having its own q. It is argued that, within this thermodynamics, the Stefan-Boltzmann law of blackbody radiation can be preserved.
Physica A: Statistical Mechanics and its Applications, 2007
This work is an extension of the incomplete probability theory from the simple case of monofracta... more This work is an extension of the incomplete probability theory from the simple case of monofractals previously studied to the more general case of multifractals which can occur in the phase space without equiprobable partition. PACS numbers : 05.20.-y (Classical statistical mechanics) 05.45.Df (Fractals) 02.50.-r (Probability theory, stochastic processes, and statistics)
Journal of Low Temperature Physics, 2008
Heavy electrons in superconducting materials are widely studied with the Kondo lattice t-J model.... more Heavy electrons in superconducting materials are widely studied with the Kondo lattice t-J model. Numerical results have shown that the Fermi surface of these correlated particles undergoes a flattening effect according to the coupling degree J. This behaviour is not easy to understand from the theoretical point of view within standard Fermi-Dirac statistics and non-standard theories such as fractional exclusion statistics for anyons and Tsallis nonextensive statistics. The present work is an attempt to account for the heavy electron distribution within incomplete statistics (IS) which is developed for complex systems with interactions which make the statistics incomplete such that 1 1 = ∑ = w i q i p . The parameter q, when different from unity, characterizes the incompleteness of the statistics. It is shown that the correlated electrons can be described with the help of IS with q related to the coupling constant J in the context of Kondo model.
Journal of Low Temperature Physics, 2008
In the Bose-Einstein condensation of interacting atoms or molecules such as 87 Rb, 23 Na and 7 Li... more In the Bose-Einstein condensation of interacting atoms or molecules such as 87 Rb, 23 Na and 7 Li, the theoretical understanding of the transition temperature is not always obvious due to the interactions or zero point energy which cannot be exactly taken into account. The S-wave collision model fails sometimes to account for the condensation temperatures. In this work, we look at the problem within the nonextensive statistics which is considered as a possible theory describing interacting systems. The generalized energy U q and the particle number N q of boson gas are given in terms of the nonextensive parameter q. q>1 (q<1) implies repulsive (attractive) interaction with respect to the perfect gas. The generalized condensation temperature T cq is derived versus T c given by the perfect gas theory. Thanks to the observed condensation temperatures, we find q ≈ 0.1 for 87 Rb atomic gas, q ≈ 0.95 for 7 Li and q ≈ 0.62 for 23 Na. It is concluded that the effective interactions are essentially attractive for the three considered atoms, which is consistent with the observed temperatures higher than those predicted by the conventional theory.
... A. Avetisyan. Local field effects in superradiance and superradiance without inversion from a... more ... A. Avetisyan. Local field effects in superradiance and superradiance without inversion from a thin film of three-level atoms. Author(s): AA Bogdanov; IV Ryzhov; Evgeni D. Trifonov; AI Zaitsev; Viktor A. Malyshev. Transmitted and ...