Inter-dimensional Degeneracies in van der Waals Clusters and Quantum Monte Carlo Computation of Rovibrational States

Quantum Monte Carlo estimates of the spectrum of rotationally invariant states of noble gas clusters suggest inter-dimensional degeneracy in $N-1$ and $N+1$ spacial dimensions. We derive this property by mapping the Schr\"odinger eigenvalue problem onto an eigenvalue equation in which $D$ appears as a continuous variable. We discuss implications for quantum Monte Carlo and dimensional scaling methods

Soliton Solutions and Conservation Laws for a Self-interacting Scalar Field in ϕ4\phi^{4} Theory

We calculate soliton solutions to the scalar field equation of motion that arises for the 4th-order extended Lagrangian ($\phi^{4}$ theory) in quantum field theory using the extended hyperbolic tangent and the sine-cosine methods. Using the former technique, ten complex soliton waves are obtained; we graphically represent three of these profiles using density plots. In the latter case, two real soliton solutions are obtained, of which, we demonstrate the wave profile for the positive case. Using the multiplier method, we calculate conservation laws in $(1 + 1)$-, $(2 + 1)$-, and $(3 + 1)$-dimensions producing three, six, and ten conservation laws respectively. Lastly, we reflect on the application of conservation laws in particle physics and phenomenology.Comment: 19 pages, 2 figure

Conservation Laws for a Thermal Reservoir Model in Open Quantum Systems

We construct Lie point symmetries, a closed-form solution and conservation laws using a non-Noetherian approach for a specific case of the Gorini-Kossakowski-Sudarshan-Lindblad equation that has been recast for the study of non-relativistic free particles in a thermal reservoir environment. Conservation laws are constructed subsequently using the Ibragimov method via a solution to the adjoint form of the equation of motion via its corresponding scalaing symmetry. A general computational framework for obtaining all conserved vectors is exhibited some triplets of conserved quantities are calculated in full.Comment: 11 page