Exactness of SWKB for Shape Invariant Potentials
- URL: http://arxiv.org/abs/2005.06683v2
- Date: Tue, 30 Jun 2020 21:32:44 GMT
- Title: Exactness of SWKB for Shape Invariant Potentials
- Authors: Asim Gangopadhyaya, Jeffry V. Mallow, Constantin Rasinariu, Jonathan
Bougie
- Abstract summary: Supersymmetry based semiclassical method produces exact spectra for shape invariant potentials.
In this paper we prove that this exactness follows from their additive shape invariance.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The supersymmetry based semiclassical method (SWKB) is known to produce exact
spectra for conventional shape invariant potentials. In this paper we prove
that this exactness follows from their additive shape invariance.
Related papers
- Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networks [43.88179780450706]
We investigate the impact of weight space permutation symmetries on variational inference.
We devise a symmetric symmetrization mechanism for constructing permutation invariant variational posteriors.
We show that the symmetrized distribution has a strictly better fit to the true posterior, and that it can be trained using the original ELBO objective.
arXiv Detail & Related papers (2024-08-10T09:06:34Z) - Crystalline invariants of fractional Chern insulators [6.267386954898001]
We show how ground state expectation values of partial rotations can be used to extract crystalline invariants.
For the topological orders we consider, we show that the Hall conductivity, filling fraction, and partial rotation invariants fully characterize the system.
arXiv Detail & Related papers (2024-05-27T17:59:59Z) - Study on a Quantization Condition and the Solvability of Schrödinger-type Equations [0.0]
We study a quantization condition in relation to the solvability of Schr"odinger equations.
The SWKB quantization condition provides quantizations of energy.
We show explicit solutions of the Schr"odinger equations with the classical-orthogonal-polynomially quasi-exactly solvable potentials.
arXiv Detail & Related papers (2024-03-29T14:56:34Z) - On reconstruction of states from evolution induced by quantum dynamical
semigroups perturbed by covariant measures [50.24983453990065]
We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures.
Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
arXiv Detail & Related papers (2023-12-02T09:56:00Z) - Generalized Langer Correction and the Exactness of WKB for all
Conventional Potentials [0.0]
We show that the Langer correction generates the exact quantization condition for all conventional potentials.
We also prove that this correction is related to the previously proven exactness of SWKB for these potentials.
arXiv Detail & Related papers (2022-12-22T20:03:51Z) - Equivariant bifurcation, quadratic equivariants, and symmetry breaking
for the standard representation of $S_n$ [15.711517003382484]
Motivated by questions originating from the study of a class of shallow student-teacher neural networks, methods are developed for the analysis of spurious minima in classes of equivariant dynamics related to neural nets.
It is shown that spurious minima do not arise from spontaneous symmetry breaking but rather through a complex deformation of the landscape geometry that can be encoded by a generic $S_n$-equivariant bifurcation.
Results on generic bifurcation when there are quadratic equivariants are also proved; this work extends and clarifies results of Ihrig & Golubitsky and Chossat, Lauterback &
arXiv Detail & Related papers (2021-07-06T06:43:06Z) - Universal Approximation Theorem for Equivariant Maps by Group CNNs [14.810452619505137]
This paper provides a unified method to obtain universal approximation theorems for equivariant maps by CNNs.
As its significant advantage, we can handle non-linear equivariant maps between infinite-dimensional spaces for non-compact groups.
arXiv Detail & Related papers (2020-12-27T07:09:06Z) - Exactness of Semiclassical Quantization Rule for Broken Supersymmetry [0.0]
We show that the long-conjectured exactness of the supersymmetry-based semiclassical quantization condition for broken supersymmetry is a consequence of the additive shape invariance for the corresponding potentials.
arXiv Detail & Related papers (2020-12-03T13:48:46Z) - Deformed Shape Invariant Superpotentials in Quantum Mechanics and
Expansions in Powers of $\hbar$ [0.0]
We show that the method developed by Gangopadhyaya, Mallow, and their coworkers can be generalized to deformed shape invariant potentials in supersymmetric quantum mechanics.
The extended method is illustrated by several examples, corresponding both to $hbar$-independent superpotentials and to a superpotential explicitly depending on $hbar$.
arXiv Detail & Related papers (2020-09-30T09:55:38Z) - Bulk detection of time-dependent topological transitions in quenched
chiral models [48.7576911714538]
We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction.
This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
arXiv Detail & Related papers (2020-01-16T17:44:52Z) - SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from
Symmetric PEPS [55.41644538483948]
Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projectedangled Pair States (PEPS)
Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder.
Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence.
arXiv Detail & Related papers (2019-12-31T16:30:25Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.