Quantum Superexponential Oscillator

• URL: http://arxiv.org/abs/2003.10740v1
• Date: Tue, 24 Mar 2020 09:58:33 GMT
• Title: Quantum Superexponential Oscillator
• Authors: Peter Schmelcher
• Abstract summary: We show that the ground state exhibits a remarkable metamorphosis of decentering, asymmetrical squeezing and the development of a tail. A corresponding spectral analysis shows that, surprisingly, to a good approximation the spectrum is equidistant.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the spectral and eigenstate properties of the quantum superexponential oscillator. Our focus is on the quantum signatures of the recently observed transition of the energy dependent period of the corresponding classical superexponential oscillator. We show that the ground state exhibits a remarkable metamorphosis of decentering, asymmetrical squeezing and the development of a tail. Analyzing the central moments up to high order a characteristic transition from exponentially decaying moments to increasing moments is unraveled. A corresponding spectral analysis shows that, surprisingly, to a good approximation the spectrum is equidistant. A closer look, however, reveals a spectral scaling behaviour below the transition point which is replaced by irregular oscillations above the transition energy. Excited bound states are analyzed up to the continuum threshold. We discuss future perspectives and possible experimental realizations of the superexponential oscillator.

Related papers

• Does the oscillatory behavior of the Momentum Spectrum depend on the basis in the Post-Transient Stage? [0.0]
  Pair creation by a spatially homogeneous, time-dependent electric field is studied within the framework of quantum electrodynamics. We employ the standard Bogoliubov transformation approach to compute the single-particle distribution function in an adiabatic basis.
  arXiv  Detail & Related papers  (2024-10-17T21:34:25Z)
• Point-Calibrated Spectral Neural Operators [54.13671100638092]
  We introduce Point-Calibrated Spectral Transform, which learns operator mappings by approximating functions with the point-level adaptive spectral basis. Point-Calibrated Spectral Neural Operators learn operator mappings by approximating functions with the point-level adaptive spectral basis.
  arXiv  Detail & Related papers  (2024-10-15T08:19:39Z)
• Measurement-Induced Spectral Transition [0.0]
  noisy quantum dynamics exposed to weak measurements exhibit a spectral transition between gapless and gapped phases. We show that the gapless and gapped phases respectively correspond to the volume-law and area-law phases of the entanglement entropy for the dominant Lyapunov vector.
  arXiv  Detail & Related papers  (2024-06-26T10:33:28Z)
• 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)
• Orbit quantization in a retarded harmonic oscillator [0.0]
  We analytically predict the value of the first Hopf bifurcation, unleashing a self-oscillatory motion. When the system is driven very far from equilibrium, a multiscale strange attractor displaying intrinsic and robust intermittency is uncovered.
  arXiv  Detail & Related papers  (2023-01-25T04:47:06Z)
• 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)
• Observation of a superradiant phase transition with emergent cat states [18.801683138820948]
  Superradiant phase transitions (SPTs) are important for understanding light-matter interactions at the quantum level. We report an experimental demonstration of the SPT featuring the emergence of a highly nonclassical photonic field.
  arXiv  Detail & Related papers  (2022-07-12T13:12:23Z)
• Quantum time dilation in a gravitational field [39.58317527488534]
  We investigate how the superposition principle affects the gravitational time dilation observed by a simple clock. We show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the emission rate of an atom in a classical mixture of these packets.
  arXiv  Detail & Related papers  (2022-04-22T10:02:21Z)
• Spectral Properties of Confining Superexponential Potentials [0.0]
  Superexponential potentials with an oscillating power show a rich spectral structure with varying amplitudes and wave vectors. In the parity symmetric case doublets of near degenerate energy eigenvalues emerge in the spectrum. The corresponding eigenstates are strongly localized in the outer wells of the potential and occur as even-odd pairs.
  arXiv  Detail & Related papers  (2021-03-17T16:38:00Z)
• Experimental Adiabatic Quantum Metrology with the Heisenberg scaling [21.42706958416718]
  We propose an adiabatic scheme on a perturbed Ising spin model with the first order quantum phase transition. We experimentally implement the adiabatic scheme on the nuclear magnetic resonance and show that the achieved precision attains the Heisenberg scaling.
  arXiv  Detail & Related papers  (2021-02-14T03:08:54Z)
• 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)

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.