Quantum solvability of quadratic Li'enard type nonlinear oscillators possessing maximal Lie point symmetries: An implication of arbitrariness of ordering parameters

• URL: http://arxiv.org/abs/2106.01882v1
• Date: Thu, 3 Jun 2021 14:27:20 GMT
• Title: Quantum solvability of quadratic Li'enard type nonlinear oscillators possessing maximal Lie point symmetries: An implication of arbitrariness of ordering parameters
• Authors: V. Chithiika Ruby and M. Lakshmanan
• Abstract summary: Two one-dimensional quadratic Li'enard type nonlinear oscillators are classified under the category of maximal (eight parameter) Lie point symmetry group. Classically, both the systems were also shown to be linearizable as well as isochronic.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we investigate the quantum dynamics of underlying two one-dimensional quadratic Li'enard type nonlinear oscillators which are classified under the category of maximal (eight parameter) Lie point symmetry group (J. Math. Phys.54 , 053506 (2013)). Classically, both the systems were also shown to be linearizable as well as isochronic. In this work, we study the quantum dynamics of the nonlinear oscillators by considering a general ordered position dependent mass Hamiltonian. The ordering parameters of the mass term are treated to be arbitrary to start with. We observe that the quantum version of these nonlinear oscillators are exactly solvable provided that the ordering parameters of the mass term are subjected to certain constraints imposed on the arbitrariness of the ordering parameters. We obtain the eigenvalues and eigenfunctions associated with both the systems. We also consider briefly the quantum versions of other examples of quadratic Li'enard oscillators which are classically linearizable.

Related papers

• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Non-equilibrium dynamics of charged dual-unitary circuits [44.99833362998488]
  interplay between symmetries and entanglement in out-of-equilibrium quantum systems is currently at the centre of an intense multidisciplinary research effort. We show that one can introduce a class of solvable states, which extends that of generic dual unitary circuits. In contrast to the known class of solvable states, which relax to the infinite temperature state, these states relax to a family of non-trivial generalised Gibbs ensembles.
  arXiv  Detail & Related papers  (2024-07-31T17:57:14Z)
• Solving the homogeneous Bethe-Salpeter equation with a quantum annealer [34.173566188833156]
  The homogeneous Bethe-Salpeter equation (hBSE) was solved for the first time by using a D-Wave quantum annealer. A broad numerical analysis of the proposed algorithms was carried out using both the proprietary simulated-anneaing package and the D-Wave Advantage 4.1 system.
  arXiv  Detail & Related papers  (2024-06-26T18:12:53Z)
• Geometric Interpretation of a nonlinear extension of Quantum Mechanics [0.0]
  We show that the non-linear terms can be viewed as giving rise to gravitational effects. We suggest that the two components of the wave function represent the system described by the Hamiltonian H in two different regions of spacetime.
  arXiv  Detail & Related papers  (2024-05-12T14:01:31Z)
• Liénard Type Nonlinear Oscillators and Quantum Solvability [0.0]
  Li'enard-type nonlinear oscillators with linear and nonlinear damping terms exhibit diverse dynamical behavior in both the classical and quantum regimes. The modified Emden equation categorized as Li'enard type-II exhibits isochronous oscillations at the classical level. The study on the quantum counterpart of the system provides a deeper understanding of the behavior in the quantum realm as a typical PT-symmetric system.
  arXiv  Detail & Related papers  (2024-05-02T11:26:52Z)
• Non-equilibrium quantum probing through linear response [41.94295877935867]
  We study the system's response to unitary perturbations, as well as non-unitary perturbations, affecting the properties of the environment. We show that linear response, combined with a quantum probing approach, can effectively provide valuable quantitative information about the perturbation and characteristics of the environment.
  arXiv  Detail & Related papers  (2023-06-14T13:31:23Z)
• Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations [31.986350313948435]
  We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations. We compare the quantum linear systems algorithms based methods and the quantum simulation methods arising from different numerical approximations.
  arXiv  Detail & Related papers  (2022-09-18T05:50:23Z)
• Quantum solvability of a nonlinear $\delta$-type mass profile system: Coupling constant quantization [1.3907460999698045]
  We consider a general ordered position-dependent mass Hamiltonian in which the ordering parameters of the mass term are treated as arbitrary. We observe that the quantum system admits bounded solutions but importantly the coupling parameter of the system gets quantized.
  arXiv  Detail & Related papers  (2022-07-29T08:21:09Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• On the classical and quantum dynamics of a class of nonpolynomial oscillators [0.0]
  We consider two one dimensional nonlinear oscillators, namely (i) Higgs oscillator and (ii) a $k$-dependent nonpolynomial rational potential. We observe that the quantum version of the Higgs oscillator is exactly solvable under appropriate restrictions of the ordering parameters. The three dimensional generalization of the quantum counterpart of the $k$-dependent nonpolynomial potential is found out to be quasi exactly solvable.
  arXiv  Detail & Related papers  (2020-08-17T07:52:37Z)
• Bistability in the dissipative quantum systems I: Damped and driven nonlinear oscillator [0.0]
  We revisit quantum dynamics of the damped and driven nonlinear oscillator. In the classical case this system has two stationary solutions (the limit cycles) in the certain parameter region, which is the origin of the celebrated bistability phenomenon.
  arXiv  Detail & Related papers  (2020-02-26T09:24:56Z)

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.