Bose-Einstein Condensation in Nonlinear System

Temperature Dependence of the Excitation Energy 23 Chapter 4 Calculation of Entropy 31 Chapter 5 Specific Heat 41 Chapter 6 Bose-Einstein Condensate of Dressed Bosons 59 Chapter 7  Transition and Phase Diagram 71 Chapter 8 Two-fluid Mechanism Caused by Nonlinear Energy Form 77 Chapter 9 Properties of the Solutions 91 Chapter 10 Contribution of Dressed Bosons in Several Phenomena 99 Chapter 11 Thermodynamic Functions 109 Chapter 12 Discussion and Conclusions 113 Appendixes Mathematical Programs 129 References 163 Index 169  , which depends upon the other dressed boson numbers.Consequently, the energy of the dressed boson with quantum level i varies depending on the distribution of dressed boson number.This nonlinear dependence yields level inversion; that is to say, which momentum level of the dressed boson has a minimum energy depends upon the choice of the distribution of dressed boson number.The level with momentum zero has minimum energy for some distribution.However, when the distribution of dressed boson number changes into a specific distribution, a level with a non-zero momentum has minimum energy.This level inversion produces Bose condensation of the dressed bosons with non-zero momentum.The stability of the moving superfluid component is established on the basis of this level inversion.Many other surprising effects arise from the nonlinearity.In almost all cases for many body problems, the total energy is nonlinearly dependent upon the distribution function of quasi-particle number.Accordingly, the developed method explained in this book is widely applicable to investigation of the statistical physics of many body problems.This work started about 35 years ago.