Related Experiment Video
Updated: Jan 9, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
480
Opening Krylov Space to Access All-Time Dynamics via Dynamical Symmetries
Nicolas Loizeau1, Berislav Buča1,2,3, Dries Sels4,5
1University of Copenhagen, Niels Bohr Institute, Copenhagen, Denmark.
Physical Review Letters
|November 30, 2025
Summary
Researchers developed a new method to derive dynamical symmetries in quantum many-body systems. This approach helps understand system dynamics and relates operator growth to thermalization in chaotic systems.
Area of Science:
- Quantum Many-Body Physics
- Atomic Physics
- Condensed Matter Physics
Background:
- Solving quantum many-body dynamics is a major challenge.
- Dynamical symmetries characterize system evolution but are hard to derive.
Purpose of the Study:
- To present a novel method for deriving dynamical symmetries in infinite closed quantum systems.
- To connect operator growth to thermalization and observable decay.
Main Methods:
- Introduced an emergent open boundary condition on the Krylov chain.
- Partitioned Krylov space into system and environment degrees of freedom.
- Used nonlocal operators as an effective bath for local operators.
Main Results:
- Successfully derived dynamical symmetries numerically and analytically.
- Demonstrated the method's practicality with numerical examples.
- Derived analytical results for two idealized cases.
Conclusions:
- The new method provides a powerful approach for computing complex many-body dynamics.
- Directly relates operator growth hypothesis to thermalization and exponential decay in chaotic systems.
Related Concept Videos
01:30Dynamics of Circular Motion
23.2K
An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed acceleration is called centripetal acceleration. This acceleration acts along the radius of the curved path (thus is also referred to as radial acceleration).
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
23.2K
01:28Symmetry in Maxwell's Equations
4.1K
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
4.1K
01:17Dynamics Of Circular Motion: Applications
9.4K
Suppose a car moves on flat ground and turns to the left. The centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. For this, a minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway. Let's now consider banked curves, where the slope of the road helps in negotiating the curve. The greater the angle of the curve, the faster one can take the curve. It is common for race tracks for...
9.4K
01:08Equation of Rotational Dynamics
14.6K
Angular variables are introduced in rotational dynamics. Comparing the definitions of angular variables with the definitions of linear kinematic variables, it is seen that there is a mapping of the linear variables to the rotational ones. Linear displacement, velocity, and acceleration have their equivalents in rotational motion, which are angular displacement, angular velocity, and angular acceleration. Similar to the rotational variables, a mapping exists from Newton's second law of motion...
14.6K
01:19Euler Equations of Motion
575
Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...
575
01:30Kinematic Equations for Rotation
726
In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...
726