Related Experiment Video
Updated: Jul 28, 2025
11:38
Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions
Published on: April 19, 2018
8.0K
Eigenvalue Crossing as a Phase Transition in Relaxation Dynamics.
Gianluca Teza1, Ran Yaacoby1, Oren Raz1
1Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel.
Physical Review Letters
|June 2, 2023
Summary
A novel dynamical phase transition, analogous to equilibrium phase transitions, is revealed by a crossing of relaxation operator eigenvalues. This phenomenon is observable in a four-state colloidal system and analytically proven in a 1D Ising model.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Physics
- Soft Matter Physics
Background:
- Systems relax to equilibrium after parameter changes.
- Dynamical phase transitions are difficult to observe in experiments.
- Eigenvalue analysis of relaxation operators is key to understanding system dynamics.
Purpose of the Study:
- To identify and characterize a singularity in system dynamics analogous to a first-order equilibrium phase transition.
- To demonstrate the experimental observability of this dynamical transition in a colloidal system.
- To provide analytical proof for the survival of this phenomenon in a many-body model.
Main Methods:
- Analysis of relaxation operator eigenvalues.
- Theoretical modeling of a four-state colloidal system.
- Analytical proof for a one-dimensional Ising model in the thermodynamic limit.
Main Results:
- A crossing between the second and third eigenvalues of the relaxation operator leads to a dynamical singularity.
- This singularity mimics a first-order equilibrium phase transition.
- The transition is experimentally observable in a feasible four-state colloidal system.
- Analytical proof confirms the phenomenon's validity in the thermodynamic limit for a 1D Ising model.
Conclusions:
- A new type of dynamical phase transition has been identified and characterized.
- Experimental observation is feasible in colloidal systems, bridging theory and experiment.
- The findings offer insights into non-equilibrium dynamics and phase transitions.
More Related Videos
Related Concept Videos
02:31Phase Transitions
19.3K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
19.3K
01:10Entropy Change in Reversible Processes
2.6K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.6K
01:28Atomic Nuclei: Types of Nuclear Relaxation
334
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
334
01:23Atomic Nuclei: Nuclear Relaxation Processes
686
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis.
686
02:39Phase Transitions: Melting and Freezing
12.5K
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
12.5K
02:33Phase Transitions: Sublimation and Deposition
17.3K
Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
17.3K