Exactly solvable models of nonlinear dynamical systems driven by colored Ornstein-Uhlenbeck and Rayleigh noise

1993 ◽  
Vol 97 (3) ◽  
pp. 1370-1381
Author(s):  
A. F. Konstantinov ◽  
V. M. Loginov
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Nonlinear Dynamical ◽  
Exactly Solvable

Singularities in the complex time plane and exactly solvable dynamical systems

1994 ◽  
Vol 72 (3-4) ◽  
pp. 147-151 ◽  
Author(s):  
W.-H. Steeb ◽  
Assia Fatykhova
Keyword(s):  
Differential Equation ◽  
Quantum Mechanics ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Numerical Study ◽  
Complex Time ◽  
Nonlinear Dynamical ◽  
Singularity Structure ◽  
Exactly Solvable ◽  
Solvable Dynamical Systems

A powerful tool in the study of nonlinear dynamical systems is the investigation of the singularity structure in the complex time plane. In most cases the singularity structure can only be found numerically. Here we give two models that can be solved exactly, i.e., we can give the singularities in the complex time plane. The two models play a central role in quantum mechanics. Then we compare them with the numerical study of the nonlinear differential equation.

scholarly journals Interaction between Different Kinds of Quantum Phase Transitions

2021 ◽  
Vol 3 (2) ◽  
pp. 253-261
Author(s):  
Angel Ricardo Plastino ◽  
Gustavo Luis Ferri ◽  
Angelo Plastino
Keyword(s):  
Phase Transitions ◽  
Nuclear Physics ◽  
Body Problem ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Many Body ◽  
Pairing Interaction ◽  
Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

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