Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass

• URL: http://arxiv.org/abs/2106.08467v1
• Date: Tue, 15 Jun 2021 22:23:33 GMT
• Title: Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass
• Authors: Bruno G. da Costa, Genilson A. C. da Silva, Ignacio S. Gomez
• Abstract summary: We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator. From the supersymmetric partner Hamiltonians we obtain the eigenstates and the eigenvalues along with the ladders operators.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner Hamiltonians and the shape invariance technique we obtain the eigenstates and the eigenvalues along with the ladders operators, thus showing a preservation of the supersymmetric structure in terms of the deformed counterpartners. The deformed space in supersymmetry allows to characterize position-dependent effective mass, uniform field interactions and to obtain a generalized uncertainty relation (GUP) that behaves as a distinguishability measure for the coherent states, these latter satisfying a periodic evolution of the GUP corrections.

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)
• Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
  entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
  arXiv  Detail & Related papers  (2024-04-04T14:45:28Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• 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)
• Exact solution and coherent states of an asymmetric oscillator with position-dependent mass [0.0]
  Deformed oscillator with position-dependent mass is studied in classical and quantum formalisms. Open trajectories in phase space are associated with scattering states and continuous energy spectrum. An oscillation of the time evolution of the uncertainty relationship is also observed, whose amplitude increases as the deformation increases.
  arXiv  Detail & Related papers  (2023-02-04T14:16:23Z)
• Duality symmetry conjugates of the quantum Rabi model : effective bosonic, fermionic and coupling-only dynamical properties [0.0]
  In this article, two symmetry operators, characterized as "duality" symmetry operators, have been introduced which transform the quantum Rabi Hamiltonian into duality conjugates. The closed $SU(2)$ Lie algebra provides the standard eigenvalues and eigenstates of the parity symmetry operator. It is established that Jaynes-Cummings and anti-Jaynes-Cummings operators are duality symmetry conjugates.
  arXiv  Detail & Related papers  (2021-12-23T13:08:20Z)
• Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices [14.450949607717437]
  We experimentally realize an extended Su-Schrieffer-Heeger model with broken chiral symmetry. Our results demonstrate that inversion symmetry protects the quantized Zak phase, but edge states can disappear in the topological nontrivial phase. Our photonic lattice provides a useful platform to study the interplay among topological phases, symmetries, and the bulk-boundary correspondence.
  arXiv  Detail & Related papers  (2021-09-28T13:35:44Z)
• Aspects of quantum states asymmetry for the magnetic dipolar interaction dynamics [0.0]
  We study asymmetry properties of quantum states in relation to the Hamiltonian responsible for the magnetic dipolar interaction dynamics. Because the MDI Hamiltonian has a null eigenvalue, the group generator-based asymmetry measure does not adequately quantify the state susceptibility.
  arXiv  Detail & Related papers  (2021-01-03T03:35:32Z)
• Group Theoretical Approach to Pseudo-Hermitian Quantum Mechanics with Lorentz Covariance and $c \rightarrow \infty $ Limit [0.0]
  The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation. The key feature of the formulation is that it is not unitary but pseudo-unitary, exactly in the same sense as the Minkowski spacetime representation. Explicit wavefunction description is given without any restriction of the variable domains, yet with a finite integral inner product.
  arXiv  Detail & Related papers  (2020-09-12T23:48:52Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• Covariant Quantum Mechanics and Quantum Spacetime [0.0]
  The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation. Explicit wavefunction description is given without any restriction of the variable domains, yet with a finite integral inner product.
  arXiv  Detail & Related papers  (2020-02-04T08:55:56Z)

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.