Generalized su(1,1) algebra and the construction of nonlinear coherent states for P\"oschl-Teller potential

• URL: http://arxiv.org/abs/2005.11407v1
• Date: Fri, 22 May 2020 22:06:26 GMT
• Title: Generalized su(1,1) algebra and the construction of nonlinear coherent states for P\"oschl-Teller potential
• Authors: Abdessamad Belfakir and Yassine Hassouni
• Abstract summary: We show that a symmetry is present in the sequence of eigenvalues of one generator of the generalized su (1,1) algebra. We then construct the Barut-Girardello coherent states associated with the generalized su (1,1) algebra for a particle in a P"oschl-Teller potential.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a generalization structure of the su(1,1) algebra which depends on a function of one generator of the algebra, f(H). Following the same ideas developed to the generalized Heisenberg algebra (GHA) and to the generalized su(2), we show that a symmetry is present in the sequence of eigenvalues of one generator of the algebra. Then, we construct the Barut-Girardello coherent states associated with the generalized su(1,1) algebra for a particle in a P\"oschl-Teller potential. Furthermore, we compare the time evolution of the uncertainty relation of the constructed coherent states with that of GHA coherent states. The generalized su(1,1) coherent states are very localized.

Related papers

• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Chiral Virasoro algebra from a single wavefunction [14.735587711294299]
  When the edge is purely chiral, the Hilbert space of low-energy edge excitations can form a representation of a single Virasoro algebra. We propose a method to systematically extract the generators of the Virasoro algebra from a single ground state wavefunction.
  arXiv  Detail & Related papers  (2024-03-27T09:54:21Z)
• A formula for the overlap between Generalized Coherent States of any rank one simple Lie algebra [0.0]
  We show the emergence of a semi-classical behaviour from the set of coherent states. We verify that it always happens when some parameter, depending on the algebra and its representation, becomes large.
  arXiv  Detail & Related papers  (2023-11-28T00:18:59Z)
• An algebraic formulation of nonassociative quantum mechanics [0.0]
  We develop a version of quantum mechanics that can handle nonassociative algebras of observables. Our approach is naturally probabilistic and is based on using the universal enveloping algebra of a general nonassociative algebra.
  arXiv  Detail & Related papers  (2023-11-07T01:36:23Z)
• Algebras of actions in an agent's representations of the world [51.06229789727133]
  We use our framework to reproduce the symmetry-based representations from the symmetry-based disentangled representation learning formalism. We then study the algebras of the transformations of worlds with features that occur in simple reinforcement learning scenarios. Using computational methods, that we developed, we extract the algebras of the transformations of these worlds and classify them according to their properties.
  arXiv  Detail & Related papers  (2023-10-02T18:24:51Z)
• The Schmidt rank for the commuting operator framework [58.720142291102135]
  The Schmidt rank is a measure for the entanglement dimension of a pure bipartite state. We generalize the Schmidt rank to the commuting operator framework. We analyze bipartite states and compute the Schmidt rank in several examples.
  arXiv  Detail & Related papers  (2023-07-21T14:37:33Z)
• Extremal jumps of circuit complexity of unitary evolutions generated by random Hamiltonians [0.0]
  We investigate circuit complexity of unitaries generated by time evolution of randomly chosen strongly interacting Hamiltonians in finite dimensional Hilbert spaces. We prove that the complexity of $exp(-it H)$ exhibits a surprising behaviour -- with high probability it reaches the maximal allowed value on the same time scale as needed to escape the neighborhood of the identity consisting of unitaries with trivial (zero) complexity.
  arXiv  Detail & Related papers  (2023-03-30T17:05:06Z)
• Asymptotic Equipartition Theorems in von Neumann algebras [24.1712628013996]
  We show that the smooth max entropy of i.i.d. states on a von Neumann algebra has an rate given by the quantum relative entropy. Our AEP not only applies to states, but also to quantum channels with appropriate restrictions.
  arXiv  Detail & Related papers  (2022-12-30T13:42:35Z)
• Complete entropic inequalities for quantum Markov chains [17.21921346541951]
  We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality. We also establish the first general approximateization property of relative entropy.
  arXiv  Detail & Related papers  (2021-02-08T11:47:37Z)
• Generalization of group-theoretic coherent states for variational calculations [1.2599533416395767]
  We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We generate entanglement not found in the coherent states themselves, while retaining many of their desirable properties.
  arXiv  Detail & Related papers  (2020-12-22T16:50:25Z)
• Getting to the Bottom of Noether's Theorem [0.0]
  We show that Noether's theorem holds whenever we can map observables to generators in such a way that each observable generates a one- parameter group that preserves itself. We show this expresses a relation between quantum and statistical mechanics, closely connected to the principle that "inverse temperature is imaginary time"
  arXiv  Detail & Related papers  (2020-06-26T00:56:17Z)

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.