Phase-space propagation and stability analysis of the 1-dimensional
Schr\"odinger equation for finding bound and resonance states of rotationally
excited H$_2$
- URL: http://arxiv.org/abs/2006.00095v3
- Date: Mon, 30 Aug 2021 13:06:14 GMT
- Title: Phase-space propagation and stability analysis of the 1-dimensional
Schr\"odinger equation for finding bound and resonance states of rotationally
excited H$_2$
- Authors: Juan S. Molano, Carlos A. Arango
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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$_2$ 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. In this phase-space representation, bound states
behave like unstable orbits meanwhile resonance states behave similarly to
asymptotically stable cycles. The lattice of quantum states of the
energy-momentum diagram for H$_2$ is calculated allowing to have a global view
of the energy as function of the quantum numbers. The arc length and winding
number of the phase-space trajectories, as functions of the energy, are used to
obtain the energy eigenvalues of bound and resonance states of H$_2$
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) - Probing pair correlations in Fermi gases with Ramsey-Bragg interferometry [41.94295877935867]
We propose an interferometric method to probe pair correlations in a gas of spin-1/2 fermions.
The method consists of a Ramsey sequence where both spin states of the Fermi gas are set in a superposition of a state at rest and a state with a large recoil velocity.
The off-diagonal long-range order is directly reflected in the behavior of the interferometric signal for long interrogation times.
arXiv Detail & Related papers (2023-12-21T15:46:29Z) - Observation of a finite-energy phase transition in a one-dimensional
quantum simulator [39.899531336700136]
We show the first experimental demonstration of a finite-energy phase transition in 1D.
By preparing initial states with different energies in a 1D trapped-ion quantum simulator, we study the finite-energy phase diagram of a long-range interacting quantum system.
arXiv Detail & Related papers (2023-10-30T18:00:01Z) - 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) - Identical damped harmonic oscillators described by coherent states [0.0]
We take a single coherent state and compute the relative entropy of coherence, $C_r$, in the energy, position and momentum bases.
Coherence is computed for a superposition of two coherent states, a cat state, and also a superposition of two cat states in the energy basis as a function of separation.
Considering a system of two non-interacting DHOs, the effect of quantum statistics is studied on the coherence of reduced single-particle states.
arXiv Detail & Related papers (2022-09-02T09:48:36Z) - Oscillatory states of quantum Kapitza pendulum [4.4884981459499524]
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.
arXiv Detail & Related papers (2022-08-04T06:34:58Z) - Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered.
Operators of the form $hatcal H=hatA+ihatB$ are described.
Rigorous analytical analysis is performed for both wave and Green's functions.
arXiv Detail & Related papers (2020-10-13T15:50:49Z) - Scattering Amplitude Together with Thermodynamic Properties in the
Poschl-Teller Double Ring-Shaped Coulomb Potential [0.0]
We obtain the exact solution to the Dirac equation with the Poschl-Teller double ring-shaped Coulomb (PTDRSC) potential for any spin-orbit quantum number K.
The relativistic scattering amplitude for spin 1/2 particles in the field of this potential has been studied.
arXiv Detail & Related papers (2020-09-05T14:11:31Z) - Dynamical Zeeman resonance in spin-orbit-coupled spin-1 Bose gases [5.624813092014403]
The Bose-Einstein condensate is assumed to be in some superposed state of Zeeman sublevels and subject to a sudden shift of the trapping potential.
It is shown that the time-averaged center-of-mass oscillation and the spin polarizations of the Bose-Einstein condensate exhibit remarkable resonant peaks when the Zeeman fields are tuned to certain strengths.
arXiv Detail & Related papers (2020-07-28T11:23:39Z) - Exploring 2D synthetic quantum Hall physics with a quasi-periodically
driven qubit [58.720142291102135]
Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties.
We experimentally study a synthetic quantum Hall effect with a two-tone drive.
arXiv Detail & Related papers (2020-04-07T15:00:41Z)
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.