Related papers: Quantum catastrophes from an algebraic perspective

Quantum catastrophes from an algebraic perspective

URL: http://arxiv.org/abs/2008.13717v1
Date: Mon, 31 Aug 2020 16:33:34 GMT
Title: Quantum catastrophes from an algebraic perspective
Authors: A. Leviatan and N. Gavrielov
Abstract summary: We study the properties of quantum cusp and butterfly catastrophes from an algebraic viewpoint. The classical properties are determined by using coherent states to construct the complete phase diagrams associated with Landau potentials exhibiting such catastrophes.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We study the properties of quantum cusp and butterfly catastrophes from an algebraic viewpoint. The analysis employs an interacting boson model Hamiltonian describing quantum phase transitions between specific quadrupole shapes by interpolating between two incompatible dynamical symmetry limits. The classical properties are determined by using coherent states to construct the complete phase diagrams associated with Landau potentials exhibiting such catastrophes.The quantum properties are determined by analyzing the spectra, transition rates and symmetry character of the eigenstates of critical Hamiltonians.

Related papers

Hilbert space geometry and quantum chaos [39.58317527488534]
We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
arXiv Detail & Related papers (2024-11-18T19:00:17Z)
Attractive-repulsive interaction in coupled quantum oscillators [14.37149160708975]
We find an interesting symmetry-breaking transition from quantum limit cycle oscillation to quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from quantum homogeneous to inhomogeneous steady state. Remarkably, we find the generation of entanglement associated with the symmetry-breaking transition that has no analogue in the classical domain.
arXiv Detail & Related papers (2024-08-23T10:45:19Z)
A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution [18.47824812164327]
We introduce the concept of imaginary-time Lindbladian evolution as an alternative framework. This new approach defines gapped quantum phases in open systems through the spectrum properties of the imaginary-Liouville superoperator.
arXiv Detail & Related papers (2024-08-06T14:53:40Z)
Parameter space geometry of the quartic oscillator and the double well potential: Classical and quantum description [0.0]
A novel semiclassical treatment based on a Fourier decomposition allows to construct classical analogues of the quantum metric tensor. A detailed comparison is presented between exact quantum numerical results, a perturbative quantum description and the semiclassical analysis.
arXiv Detail & Related papers (2023-08-23T00:55:35Z)
Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter [0.0]
Topological phases are characterized by their entanglement properties. We propose to leverage the power of synthetic quantum systems for measuring entanglement via the Entanglement Hamiltonian.
arXiv Detail & Related papers (2021-10-08T06:13:51Z)
Anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the two-dimensional limit of the vibron model [0.0]
An excited-state quantum phase transition might also stem from the lowering of the energy of the corresponding energy functional. One such example occurs in the 2D limit of the vibron model, once an anharmonic term in the form of a bosonic number operator is added to the Hamiltonian. In the present work, we characterize it in the symmetric, previously overlooked phase of the model making use of quantities such as the effective frequency, the expected value of the quantum number operator, the participation ratio, the density of states, and the quantum fidelity susceptibility.
arXiv Detail & Related papers (2021-06-21T12:31:17Z)
Multiple ground-state instabilities in the anisotropic quantum Rabi model [0.0]
We study the anisotropic variant of the quantum Rabi model with different coupling strengths of the rotating and counter-rotating wave terms. The anisotropy preserves the parity symmetry of the original model. We find analytically that the ground-state and the first excited state can cross several times.
arXiv Detail & Related papers (2021-01-29T04:21:08Z)
Quantum particle across Grushin singularity [77.34726150561087]
We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
arXiv Detail & Related papers (2020-11-27T12:53:23Z)
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)
Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
arXiv Detail & Related papers (2020-01-16T17:44:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.