Oscillatory states of quantum Kapitza pendulum

• URL: http://arxiv.org/abs/2208.02488v3
• Date: Thu, 12 Jan 2023 08:59:13 GMT
• Title: Oscillatory states of quantum Kapitza pendulum
• Authors: Wei He, Chang-Yong Liu
• Abstract summary: We study quantum mechanics problem described by the Schr"odinger equation with Kapitza pendulum potential. For the oscillatory states spatially localize around the two stable saddle positions of the potential, we obtain the perturbative eigenvalues and corresponding piecewise wavefunctions.
• Score: 4.4884981459499524
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study quantum mechanics problem described by the Schr\"{o}dinger equation with Kapitza pendulum potential, that is the asymmetric double-well potential on the circle. For the oscillatory states spatially localize around the two stable saddle positions of the potential, we obtain the perturbative eigenvalues and corresponding piecewise wavefunctions. The spectrum is computed by extending the angle coordinate to the complex plane so that the quantization condition is formulated as contour integral along a path extending in the imaginary direction. Quantum tunneling between the wells is computed.

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)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Quantum vibrational mode in a cavity confining a massless spinor field [91.3755431537592]
  We analyse the reaction of a massless (1+1)-dimensional spinor field to the harmonic motion of one cavity wall. We demonstrate that the system is able to convert bosons into fermion pairs at the lowest perturbative order.
  arXiv  Detail & Related papers  (2022-09-12T08:21:12Z)
• A Potential Based Quantization Procedure of the Damped Oscillator [0.0]
  We formulate the quantization of the dissipative oscillator, which aids understanding of the above mentioned. We arrive at such an irreversible quantum theory by which the quantum losses can be described.
  arXiv  Detail & Related papers  (2022-04-06T15:17:03Z)
• Quantum Entanglement of Non-Hermitian Quasicrystals [7.371841894852217]
  We present a class of experimentally realizable models for non-Hermitian quasicrystal chains. We numerically determine the metal-insulator transition point. Inspired by entanglement spectrum, we further analytically prove that a duality exists between the two phase regions.
  arXiv  Detail & Related papers  (2021-12-26T16:17:04Z)
• Effect of Emitters on Quantum State Transfer in Coupled Cavity Arrays [48.06402199083057]
  We study the effects of atoms in cavities which can absorb and emit photons as they propagate down the array. Our model is equivalent to previously examined spin chains in the one-excitation sector and in the absence of emitters.
  arXiv  Detail & Related papers  (2021-12-10T18:52:07Z)
• Quantum coherence, correlations and nonclassical states in the two-qubit Rabi model with parametric oscillator [0.0]
  Quantum coherence and quantum correlations are studied in a strongly interacting system composed of two qubits and a parametric medium. We employ the adiabatic approximation approach to analytically solve the system. The reconstructed states are observed to be nearly pure generalized Bell states.
  arXiv  Detail & Related papers  (2021-06-12T11:16:40Z)
• Comment on `Exact solution of the position-dependent effective mass and angular frequency Schr\"odinger equation: harmonic oscillator model with quantized confinement parameter' [0.0]
  In a recent paper, Jafarov, Nagiyev, Oste and Van der Jeugt, construct a confined model of the non-relativistic quantum harmonic oscillator. By using a point canonical transformation starting from the constant-mass Schr"odinger equation for the Rosen-Morse II potential, it is shown here that similar results can be easily obtained without quantizing the confinement parameter.
  arXiv  Detail & Related papers  (2021-05-06T14:20:06Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Phase-space propagation and stability analysis of the 1-dimensional Schr\"odinger equation for finding bound and resonance states of rotationally excited H$_2$ [0.0]
  A mathematical phase-space representation of the 1-dimensional Schr"odinger equation is employed to obtain bound and resonance states of the rotationally excited H$$ molecule. The structure of the phase-space tangent field is analyzed and related to the behavior of the wave function in classically allowed and forbidden regions.
  arXiv  Detail & Related papers  (2020-05-29T21:51:16Z)

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.