Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCoulomb transition matrix at negative energy and integer values of interaction parameter
47
0
0.0
(
0
)
Added by
Vladislav Kharchenko
Publication date
2019
fields
Physics
and research's language is
English
Authors
V. F. Kharchenko
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
We explore the quantum Coulomb problem for two-body bound states, in $D=3$ and $D=3-2epsilon$ dimensions, in detail, and give an extensive list of expectation values that arise in the evaluation of QED corrections to bound state energies. We describe the techniques used to obtain these expectation values and give general formulas for the evaluation of integrals involving associated Laguerre polynomials. In addition, we give formulas for the evaluation of integrals involving subtracted associated Laguerre polynomials--those with low powers of the variable subtracted off--that arise when evaluating divergent expectation values. We present perturbative results (in the parameter $epsilon$) that show how bound state energies and wave functions in $D=3-2epsilon$ dimensions differ from their $D=3$ dimensional counterparts and use these formulas to find regularized expressions for divergent expectation values such as $big langle bar V^3 big rangle$ and $big langle (bar V)^2 big rangle$ where $bar V$ is the $D$-dimensional Coulomb potential. We evaluate a number of finite $D$-dimensional expectation values such as $big langle r^{-2+4epsilon} partial_r^2 big rangle$ and $big langle r^{4epsilon} p^4 big rangle$ that have $epsilon rightarrow 0$ limits that differ from their three-dimensional counterparts $big langle r^{-2} partial_r^2 big rangle$ and $big langle p^4 big rangle$. We explore the use of recursion relations, the Feynman-Hellmann theorem, and momentum space brackets combined with $D$-dimensional Fourier transformation for the evaluation of $D$-dimensional expectation values. The results of this paper are useful when using dimensional regularization in the calculation of properties of Coulomb bound systems.
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.
We review the methods to combine several measurements, in the form of parameter values or $p$-values.
Recently, the celebrated Keldysh potential has been widely used to describe the Coulomb interaction of few-body complexes in monolayer transition-metal dichalcogenides. Using this potential to model charged excitons (trions), one finds a strong dependence of the binding energy on whether the monolayer is suspended in air, supported on SiO$_2$, or encapsulated in hexagonal boron-nitride. However, empirical values of the trion binding energies show weak dependence on the monolayer configuration. This deficiency indicates that the description of the Coulomb potential is still lacking in this important class of materials. We address this problem and derive a new potential form, which takes into account the three atomic sheets that compose a monolayer of transition-metal dichalcogenides. The new potential self-consistently supports (i) the non-hydrogenic Rydberg series of neutral excitons, and (ii) the weak dependence of the trion binding energy on the environment. Furthermore, we identify an important trion-lattice coupling due to the phonon cloud in the vicinity of charged complexes. Neutral excitons, on the other hand, have weaker coupling to the lattice due to the confluence of their charge neutrality and small Bohr radius.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
