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Register a new userCoulomb transition matrix with fractional values of interaction parameter
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Added by
Vladislav Kharchenko
Publication date
2021
fields
Physics
and research's language is
English
Authors
V.F. Kharchenko
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No Arabic abstract
Leaning upon the specific Fock symmetry of the Coulomb interaction potential in the four-dimensional momentum space we perform the analytical solution of the Lippman-Schwinger equation for the Coulomb transition matrix in the case of negative energy at fraction values of the interaction parameter. Analytical expressions for the three dimensional and partial Coulomb transition matrix with simplest factional values of the interaction parameter are obtained.
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With the use of the stereographic projection of momentum space into the four-dimensional sphere of unit radius. the possibility of the analytical solution of the three-dimensional two-body Lippmann-Schwinger equation with the Coulomb interaction at negative energy has been studied. Simple analytical expressions for the three-dimensional Coulomb transition matrix in the case of the repulsive Coulomb interaction and positive integer values of the Coulomb parameter have been obtained. The worked out method has been also applied for the generalized three-dimensional Coulomb transition matrix in the case of the attractive Coulomb interaction and negative integer values of the Coulomb parameter.
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The superconductor-insulator transition (SIT) in regular arrays of Josephson junctions is studied at low temperatures. Near the transition a Ginzburg-Landau type action containing the imaginary time is derived. The new feature of this action is that it contains a gauge field $Phi $ describing the Coulomb interaction and changing the standard critical behavior. The solution of renormalization group (RG) equations derived at zero temperature $T=0$ in the space dimensionality $d=3$ shows that the SIT is always of the first order. At finite temperatures, a tricritical point separates the lines of the first and second order phase transitions. The same conclusion holds for $d=2$ if the mutual capacitance is larger than the distance between junctions.
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