Related Experiment Video
Updated: Jun 23, 2025
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
8.5K
Iterative Construction of Conserved Quantities in Dissipative Nearly Integrable Systems
Iris Ulčakar1,2, Zala Lenarčič1
1Jožef Stefan Institute, 1000 Ljubljana, Slovenia.
Physical Review Letters
|June 21, 2024
Summary
Researchers developed a new iterative scheme to study driven dissipative nearly integrable systems. This method stabilizes quantum integrability effects and approximates stationary states using a generalized Gibbs ensemble, enabling easier calculations for large systems.
Area of Science:
- Quantum many-body physics
- Statistical mechanics
Background:
- Integrable systems are rare solvable models in quantum mechanics.
- Real-world systems deviate from perfect integrability, leading to transient effects.
- Coupling systems to baths and driving can stabilize integrable effects in stationary states, approximated by generalized Gibbs ensembles.
Purpose of the Study:
- To develop an exact analytical method for describing driven dissipative nearly integrable models.
- To overcome the challenges in analyzing these complex quantum systems.
- To enable efficient calculations for large, thermodynamically relevant systems.
Main Methods:
- Development of an iterative scheme.
- Utilizing integrability breaking perturbations (baths) to identify key conserved quantities.
- Employing a truncated generalized Gibbs ensemble description.
Main Results:
- The proposed iterative scheme provides a highly efficient description of driven dissipative nearly integrable systems.
- The method stabilizes integrable effects up to arbitrary times.
- The scheme allows for the construction of unknown conserved quantities.
Conclusions:
- The developed iterative scheme offers a powerful tool for studying quantum many-body systems.
- This approach facilitates easier calculations in thermodynamically large systems.
- The method can be used to discover new conserved quantities in complex quantum models.
Related Concept Videos
01:14Conservation of Energy in Control Volume
830
Consider a turbine operating under steady-flow conditions. The control volume is drawn around the turbine, with fluid entering at one point and exiting at another. The turbine extracts energy from the fluid, which performs mechanical work (shaft work).
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to:
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to:
830
01:24Reynolds Transport Theorem
1.1K
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
1.1K
01:16Conservation of Mass in Finite Cotrol Volume
1.3K
The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
1.3K
01:20Continuity Equation
841
The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area can be written as the surface integral of the current density.
841
00:54Conservation of Energy
9.2K
The terms 'conserved quantity' and 'conservation law' have specific scientific meanings in physics, which differ from the meanings associated with their everyday use. For example, in everyday usage, water could be conserved by not using it, by using less of it, or by re-using it. However, in scientific terms, a conserved quantity of a system stays constant, changes by a definite amount that is transferred to other systems, and is converted into other forms of that...
9.2K
01:20Convolution Properties I
145
Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
145