Related Experiment Video
Updated: Apr 24, 2026
08:51
Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers
Published on: August 18, 2017
9.6K
Exploring chaos in the Dicke model using ground-state fidelity and Loschmidt echo
Utso Bhattacharya1, Sayak Dasgupta1, Amit Dutta1
1Department of Physics, Indian Institute of Technology, 208016, Kanpur.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 13, 2014
Summary
We investigated quantum chaos in the Dicke Hamiltonian model. Measures like ground-state fidelity and Loschmidt echo reveal the system
Area of Science:
- Quantum physics
- Atomic physics
- Quantum chaos
Background:
- The Dicke Hamiltonian describes light-matter interactions in quantum systems.
- Understanding quantum critical behavior is crucial for quantum technologies.
- Quantum chaos explores chaotic dynamics in quantum systems.
Purpose of the Study:
- To investigate quantum critical behavior in a finite-atom Dicke Hamiltonian.
- To identify signatures of quantum chaos using specific measures.
- To analyze the system's behavior in the superradiant phase.
Main Methods:
- Utilizing ground-state fidelity as a measure of quantum chaos.
- Employing the Loschmidt echo and time-averaged Loschmidt echo.
- Analyzing system dynamics as a function of coupling strength and time.
Main Results:
- Ground-state fidelity exhibits aperiodic oscillations with coupling strength.
- Loschmidt echo shows rapid decay and aperiodic oscillations in the superradiant phase.
- Time-averaged Loschmidt echo confirms chaotic nature and incorporates fidelity information.
Conclusions:
- The studied Dicke Hamiltonian exhibits classically chaotic behavior in the superradiant phase.
- Ground-state fidelity and Loschmidt echo are effective indicators of quantum chaos.
- The time-averaged Loschmidt echo provides a robust signature of chaos.
Related Concept Videos
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
1.2K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.2K
01:12Fermi Level Dynamics
1.1K
The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
1.1K
01:14NMR Spectrometers: Resolution and Error Correction
988
When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
988
01:30Atomic Emission Spectroscopy: Interference
780
In atomic emission spectroscopy (AES), high-temperature atomizers excite a broad range of elements and molecules that generate complex emissions from sources such as oxides, hydroxides, and flame combustion products in the flame or plasma. Several strategies can be employed to minimize spectral interferences caused by overlapping emission lines or bands. These include increasing instrument resolution, choosing alternative emission lines, optimally placing the detector in low-background regions,...
780
01:27π Electron Effects on Chemical Shift: Overview
1.5K
An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0,...
1.5K
01:06Nuclear Overhauser Enhancement (NOE)
1.3K
Irradiation of a spin-active nucleus causes an increase or decrease in the signal intensity of neighboring nuclei that are not necessarily chemically bonded or involved in J-coupling. This phenomenon, called the nuclear Overhauser enhancement (NOE), results from through-space interactions between the nuclear spins. The NOE effect decreases with increasing internuclear distance and is generally not observed beyond 4 angstroms. In NOE, dipole-dipole interactions between neighboring spin-active...
1.3K