Superradiation of Dirac particles in KN ds black hole

In this article, we process the approximate wave function of the Dirac particle outside the horizon of the KN ds black hole to obtain V, and then derive V (including real and imaginary parts). We deal with the real and imaginary parts separately. When V (real part or imaginary part) has a maximum value, there may be a potential barrier outside the field of view to have a chance to produce superradiation.

Origin Invariant Full Optical Rotation Tensor in the Length Dipole Gauge without London Atomic Orbitals

<div> <div> <div> <p>We present an origin-invariant approach to compute the full optical rotation tensor (Buckingham/Dunn tensor) in the length dipole gauge without recourse to London atomic orbitals, called LG(OI). The LG(OI) approach is simpler and less computationally demanding than the more common LG-London and modified velocity gauge (MVG) approaches and it can be used with any approximate wave function or density functional method. We report an implementation at coupled cluster with single and double excitations level (CCSD), for which we present the first simulations of the origin-invariant Buckingham/Dunn tensor in the length gauge. With this method, we attempt to decouple the effects of electron correlation and basis set incompleteness on the choice of gauge for optical rotation calculations on simple test systems. The simulations show a smooth convergence of the LG(OI) and MVG results with the basis set size towards the complete basis set limit. However, these preliminary results indicate that CCSD may not be close to a complete description of the electron correlation effects on this property even for small molecules, and that basis set incompleteness may be a less important cause of discrepancy between choices of gauge than electron correlation incompleteness. </p> </div> </div> </div>

Origin Invariant Full Optical Rotation Tensor in the Length Dipole Gauge without London Atomic Orbitals

<div> <div> <div> <p>We present an origin-invariant approach to compute the full optical rotation tensor (Buckingham/Dunn tensor) in the length dipole gauge without recourse to London atomic orbitals, called LG(OI). The LG(OI) approach is simpler and less computationally demanding than the more common LG-London and modified velocity gauge (MVG) approaches and it can be used with any approximate wave function or density functional method. We report an implementation at coupled cluster with single and double excitations level (CCSD), for which we present the first simulations of the origin-invariant Buckingham/Dunn tensor in the length gauge. With this method, we attempt to decouple the effects of electron correlation and basis set incompleteness on the choice of gauge for optical rotation calculations on simple test systems. The simulations show a smooth convergence of the LG(OI) and MVG results with the basis set size towards the complete basis set limit. However, these preliminary results indicate that CCSD may not be close to a complete description of the electron correlation effects on this property even for small molecules, and that basis set incompleteness may be a less important cause of discrepancy between choices of gauge than electron correlation incompleteness. </p> </div> </div> </div>

Approximate Lie Symmetry Conditions of Autoparallels and Geodesics

This paper is devoted to the study of approximate Lie point symmetries of general autoparallel systems. The significance of such systems is that they characterize the equations of motion of a Riemannian space under an affine parametrization. In particular, we formulate the first-order symmetry determining equations based on geometric requirements and stipulate that the underlying Riemannian space be approximate in nature. Lastly, we exemplify the results by application to some approximate wave-like manifolds.

Origin Invariant Optical Rotation in the Length Dipole Gauge without London Atomic Orbitals

<div> <div> <div> <p>We present an approach to perform origin-invariant optical rotation calculations in the length dipole gauge without recourse to London atomic orbitals, called LG(OI). The LG(OI) approach works with any approximate wave function or density functional method, but here we focus on the implementation with the coupled cluster (CC) with single and double excitations method because of the lack of production-level alternatives. Preliminary numerical tests show the efficacy of the LG(OI) procedure, and indicate that conventional CC-LG calculations with the origin in the center of mass of a molecule may still carry significant origin dependence. </p> </div> </div> </div>

Origin Invariant Optical Rotation in the Length Dipole Gauge without London Atomic Orbitals

<div> <div> <div> <p>We present an approach to perform origin-invariant optical rotation calculations in the length dipole gauge without recourse to London atomic orbitals, called LG(OI). The LG(OI) approach works with any approximate wave function or density functional method, but here we focus on the implementation with the coupled cluster (CC) with single and double excitations method because of the lack of production-level alternatives. Preliminary numerical tests show the efficacy of the LG(OI) procedure, and indicate that conventional CC-LG calculations with the origin in the center of mass of a molecule may still carry significant origin dependence. </p> </div> </div> </div>