Related Experiment Video
Updated: Jul 16, 2025
12:25
2D and 3D Matrices to Study Linear Invadosome Formation and Activity
Published on: June 2, 2017
10.1K
Unveiling order from chaos by approximate 2-localization of random matrices
Nicolas Loizeau1, Flaviano Morone1, Dries Sels1,2
1Department of Physics, New York University, New York, NY 10003.
Summary
Generic quantum Hamiltonians can be approximated as 2-local, meaning they only involve pairwise interactions. This finding holds even for complex systems and suggests a link between quantum chaos and geometric locality.
Area of Science:
- Quantum physics
- Many-body systems
- Quantum information theory
Background:
- Quantum many-body systems possess a tensor product structure, enabling decomposition into independent subsystems.
- The compatibility of a Hamiltonian with a specific tensor product structure is a key research question.
Purpose of the Study:
- To determine if an arbitrary Hamiltonian can be represented in a 2-local form in a suitable basis.
- To investigate the robustness of such 2-local Hamiltonians against perturbations.
Main Methods:
- Analytical calculations
- Numerical simulations
- Analysis of coupling adjacency structures
Main Results:
- Generic Hamiltonians can be accurately approximated as 2-local (pairwise interactions) in a specific basis.
- These 2-local Hamiltonians exhibit robustness against perturbations in coupling constants (not fine-tuned).
- A potential mechanism for the emergence of geometric locality from quantum chaos is proposed.
Conclusions:
- Arbitrary quantum Hamiltonians can be effectively described by 2-local interactions in an appropriate basis.
- The discovered 2-local structure offers insights into the relationship between quantum chaos and system geometry.
Related Concept Videos
00:59Propagation of Uncertainty from Random Error
724
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
724
01:17Wald-Wolfowitz Runs Test II
267
The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...
267
01:09Random Variables
12.3K
A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
12.3K
01:08Vector Algebra: Method of Components
14.0K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
In many applications, the magnitudes and directions of...
14.0K
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
01:19Routh-Hurwitz Criterion II
291
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
291