Related Experiment Video
Updated: Apr 29, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
9.0K
Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops
Atushi Tanaka1, Sang Wook Kim2, Taksu Cheon3
1Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan.
Summary
This study links exotic quantum holonomy in Hermitian systems to exceptional points in non-Hermitian quantum theory. It reveals how quantum kicked tops exhibit higher-order exceptional points and their stability under perturbations.
Area of Science:
- Quantum Physics
- Non-Hermitian Quantum Mechanics
- Quantum Chaos
Background:
- Exotic quantum holonomy arises in families of Hermitian cycles.
- Exceptional points (EPs) are critical points in non-Hermitian systems where eigenvalues and eigenvectors coalesce.
- Quantum kicked tops are a paradigmatic model for studying quantum chaos.
Purpose of the Study:
- To investigate the correspondence between exotic quantum holonomy and exceptional points in quantum kicked tops.
- To derive explicit expressions for adiabatic parameter dependencies of quasienergies and stationary states.
- To analyze the behavior of higher-order EPs under perturbations and their relation to holonomy stability.
Main Methods:
- Analysis of quantum kicked tops under specific conditions.
- Derivation of adiabatic parameter dependencies for quasienergies and stationary states.
- Investigation of complexified adiabatic parameters and perturbation theory to study EP behavior.
Main Results:
- An explicit expression for adiabatic parameter dependencies of quasienergies and stationary states, exhibiting anholonomies, was obtained.
- Quantum kicked tops with complexified adiabatic parameters were shown to possess higher-order EPs.
- These higher-order EPs bifurcate into lower-order EPs under small perturbations, demonstrating the stability of exotic holonomy against such bifurcation.
Conclusions:
- A direct link between exotic quantum holonomy and exceptional points in non-Hermitian quantum theory is established within the quantum kicked top model.
- The study provides insights into the nature and stability of exceptional points and their connection to topological properties of quantum systems.
- The findings contribute to understanding the interplay between topology, non-Hermiticity, and chaos in quantum mechanics.
More Related Videos
Related Concept Videos
03:06The Pauli Exclusion Principle
51.6K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
51.6K
02:43Quantum Numbers
39.8K
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
39.8K
01:29Higher Derivatives
335
In calculus, higher-order derivatives extend the idea of differentiation beyond the first derivative to capture successive rates of change. These derivatives provide detailed information about the behavior of functions and have important applications in both mathematics and physics. To illustrate these concepts, consider the example function\begin{equation*}f(x) = x^3 - x\end{equation*}which serves as a useful case study for exploring higher derivatives.The first derivative represents the slope...
335
01:34Woodward–Hoffmann Selection Rules and Microscopic Reversibility
2.2K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
2.2K
01:29Equipotential Surfaces and Field Lines
4.2K
Electric potential can be pictorially represented as a three-dimensional surface. On such a surface, the electric potential is constant everywhere. The equipotential surface is always perpendicular to the electric field lines, and while it is three-dimensional, it can be treated as an equipotential line in a two-dimensional case. These equipotential lines are also always perpendicular to electric field lines. The term equipotential is often used as a noun, referring to an equipotential line or...
4.2K
01:16Second Uniqueness Theorem
1.4K
Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
1.4K