Related Experiment Video
Updated: Apr 25, 2026
09:25
Author Spotlight: Exploring Intrinsically Disordered Protein Dynamics Through NMR Relaxation Experiments
Published on: November 1, 2024
2.2K
Eigenvalue statistics of reduced density matrix during driving and relaxation
M Mierzejewski1, T Prosen2, D Crivelli1
1Institute of Physics, University of Silesia, 40-007 Katowice, Poland.
Physical Review Letters
|August 29, 2014
Summary
We investigated a one-dimensional correlated metal
Area of Science:
- Condensed matter physics
- Quantum dynamics
Background:
- Studying quantum systems driven by external fields is crucial for understanding non-equilibrium phenomena.
- Reduced density matrices are key to characterizing subsystem properties in many-body systems.
Purpose of the Study:
- To analyze the statistical properties of subsystems in a driven one-dimensional correlated metal.
- To investigate the applicability of universal statistical ensembles and thermal distributions.
Main Methods:
- Numerical exact diagonalization of the reduced density matrix (ρ).
- Analysis of eigenvalue statistics and spectra of log(ρ).
Main Results:
- Subsystem statistics follow Gaussian unitary and orthogonal ensembles for driven and equilibrium states, respectively.
- Spectra of modestly driven subsystems align with Gibbs thermal distributions.
Conclusions:
- Universal statistical behavior is observed in both generic and integrable one-dimensional correlated metals.
- Driven quantum systems can exhibit thermal properties governed by time-dependent energy.
More Related Videos
Related Concept Videos
01:28Atomic Nuclei: Types of Nuclear Relaxation
1.1K
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...
1.1K
01:23Atomic Nuclei: Nuclear Relaxation Processes
1.1K
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.
1.1K
01:12Reduced Mass Coordinates: Isolated Two-body Problem
2.5K
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
2.5K
01:14Atomic Nuclei: Nuclear Spin State Population Distribution
1.7K
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
1.7K
01:24Reynolds Transport Theorem
1.9K
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...
1.9K
01:10Entropy Change in Reversible Processes
2.4K
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.
2.4K