Functional integration method for quantum magnets and 1D-random potential problem, with application to the infrared dynamics

1991 ◽  
Vol 61 (1) ◽  
pp. 199-211
Author(s):  
I. V. Kolokolov
Keyword(s):  
Potential Problem ◽  
Integration Method ◽  
Random Potential ◽  
Functional Integration ◽  
Quantum Magnets ◽  
Functional Integration Method

Solution of Some Differential Equations of Quantum Physics by the Numerical Functional Integration Method

2003 ◽  
Vol 3 (4) ◽  
pp. 560-578
Author(s):  
Y. Y. Lobanov ◽  
E. P. Zhidkov
Keyword(s):  
Differential Equations ◽  
Quantum Physics ◽  
Metric Spaces ◽  
Integration Method ◽  
Open Quantum Systems ◽  
Functional Integration ◽  
Method Comparison ◽  
Binding Energies ◽  
Functional Integrals ◽  
Functional Integration Method

Abstract The application of the numerical functional integration method to the solution of differential equations in quantum physics is discussed. We have developed a method of numerical evaluation of functional integrals in abstract complete separable metric spaces, which proves to have important advantages over the conventional Monte Carlo method of path integration. One of the considered applications is the investigation of open quantum systems (OQS), i.e., systems interacting with their environment. The density operator of OQS satisfies the known Lindblad differential equation. We have obtained the expression for matrix elements of this operator in the form of the double conditional Wiener integral and considered its application to some problems of nuclear physics. Another application is the solution of the Scr¨odinger equation with imaginary time and anticommuting variables for studying many-fermion systems. We have developed a numerical method based on functional integration over ordered subspaces. The binding energies of some nuclei are computed using this method. Comparison of the results with those obtained by other authors and with experimental values is presented.

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