Related Experiment Video
Updated: May 7, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Ballistic spreading of entanglement in a diffusive nonintegrable system
1Physics Department, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review Letters
|October 8, 2013
Summary
Entanglement entropy spreads ballistically in nonintegrable spin chains, significantly faster than diffusive energy transport. This study reveals distinct dynamics for entanglement and energy in quantum systems.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- Understanding the dynamics of quantum information is crucial in nonintegrable systems.
- The behavior of entanglement entropy and energy transport often differs in complex quantum models.
Purpose of the Study:
- To investigate the time evolution of entanglement entropy in a one-dimensional nonintegrable spin chain.
- To compare the spreading speed of entanglement with the diffusion of energy in the same system.
Main Methods:
- Exact diagonalization of a quantum Ising spin chain with transverse and longitudinal fields.
- Analysis of the time evolution of entanglement entropy from random initial pure states.
Main Results:
- Entanglement entropy exhibits linear growth over time, indicating ballistic spreading.
- Energy transport in the system is found to be diffusive.
- Entanglement spreading is demonstrably faster than energy diffusion.
Conclusions:
- Nonintegrable spin chains display ballistic entanglement spreading.
- The distinct dynamics highlight faster quantum information propagation compared to energy transport.
Related Concept Videos
02:39Entropy
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
01:28Conservation of Linear Momentum for a System of Particles
In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
02:49Second Law of Thermodynamics
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
02:21Spontaneity
A spontaneous process is one that occurs naturally under certain conditions. A nonspontaneous process, on the other hand, will not take place unless it is “driven” by the continual input of energy from an external source. Processes have a natural tendency to occur in one direction under a given set of conditions. Water will naturally flow downhill (spontaneous process), but uphill flow (nonspontaneous process) requires outside intervention such as the use of a pump. Iron exposed to the earth’s...
01:16Electrostatic Boundary Conditions
Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
03:48Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion
Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...