Shulou(Shulou.com)11/24 Report--

We will arrive at Lesser Snow in a few days.

Before you know it, Beijing is getting cold.

Not long ago in the summer

Still looking forward to the coolness of autumn and winter

I didn't expect that when winter comes,

Begin to miss the warmth of spring and summer again.

In this cold winter

The most important thing I want to do is go to the seaside for a holiday.

After all, there are only 212 days left before next summer vacation!

I am happy in the beach, sunshine and sea breeze.

Why don't you do the preview from now on?

As a qualified roll king (rookie)

When you go to the seaside, you can't share knowledge with your peers.

Such a sunny journey

Anyone who listens to it will envy!

Mention of marine knowledge

How can there be less marine animals?

They leave graceful curved tracks in the ocean.

And...

Is there a secret of quantum dynamics in their motion?

The Motion characteristics of Part I Ocean Elves-- Levi Flight We all know that the characteristics of many creatures can be described mathematically.

The seeds in the mature sunflower plate form two sets of spirals in opposite directions, one clockwise and the other counterclockwise. And the number of these two sets of spirals happens to be the Fibonacci series (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144). The two adjacent numbers in the

Photo Source: pixabay

Photo Source: Zhihu besides, the strange shape of pagoda cuisine is one of the examples of fractal geometric patterns.

Photo Source: pixabay, what characteristics of marine life can be expressed mathematically? Let's take sharks as an example to explore.

In life, our course of action is often determined by our thoughts, such as going out to school in the morning, going to work, going to canteens and restaurants at mealtime, and so on. Have you ever thought about the sports behavior of sharks?

Photo Source: pixabay is a ferocious predator in the ocean, and sharks need to "cook" efficiently.

So how can sharks exercise to make a quick and accurate "dry meal"? Let's first consider the simplest case-random motion. Maybe sharks just swim around at random?

At this time, we have to mention the classic Brownian motion.

In 1827, when Robert Brown, a British botanist, looked at pollen grains suspended in water with a microscope, he found that these pollen grains moved randomly in a continuous, rapid and irregular manner, which was called "Brownian motion".

The movement of pollen in water Pollen Grains in Water-Brownian Motion animated gif (gifs.com) Brownian motion refers to the never-ending and irregular movement of particles suspended in liquid or gas.

Brownian motion | the sample path of On the Brownian Motion-Mati è re et R é volution (matierevolution.fr) Brownian motion is very special. It is a continuous function of time t, which is continuous everywhere but not differentiable everywhere [2].

The probability distribution of the spatial position of a large number of Brown particles at t time shows a normal distribution.

Does the motion of sharks conform to the characteristics of Brownian motion?

Theoretical analysis shows that compared with simple Brownian motion, Le'vy Flights can increase the predation efficiency of marine organisms such as sharks.

Levy flight, named after mathematician P. Le'vy, is a random walk, which is essentially a random probability distribution. Its step size accords with the characteristics of Levy distribution and can be described by the following distribution functions.

Among them, 1 < μ ≤ 3 LJ is the flight step.

French mathematician Paul Pierre L é vy | Image source [10] like all random processes, Levy's random motion originates from the diffusion process. Therefore, L é vy random motion principle can be used in random methods and to simulate random and pseudo-random natural phenomena. In particular, they show an abnormal diffusion phenomenon: there is still a "microstructure" in the system. Therefore, L é vy random motion is related to chaos theory.

Levy flight has the characteristics of gradual power law (that is, it obeys heavy-tailed distribution), conforms to the generalized central limit theorem, and has the characteristics of random fractal.

Levi Flight | Picture Source: cuckoo algorithm (implemented by C++). CSDN Levi Flight is a random walk with a Levi distribution and a heavy-tailed probability distribution. That is, when it is defined as walking in a space with a size greater than 1, the step performed is an isotropic random direction, which means that there is a relatively high probability of a big stride in the process of random walking. This is also the obvious difference between Levi's flight and Brownian motion.

Comparison of Brownian motion and Levy's flight trajectory [5] the term "Levi flight" was coined by Beno ú t Mandelbrot, who used it as a specific definition of step distribution. For cases where the step size distribution is Cauchy distribution, he uses the term Cauchy flight; when it is a normal distribution, he uses the Rayleigh flight term (which is not an example of heavy-tailed probability distribution).

Later researchers expanded the use of the term "Le'vy flight" to include random walks that occur on discrete grids rather than continuous spaces.

Image source: pixabay tracked the movements of a variety of marine organisms, including silk sharks, yellowfin tuna, bluefin, swordfish, sea turtles and penguins, and researchers found that when marine creatures are in a shortage of food around them, their movement strategies show the characteristics of Levy's flight, and predators can "dry rice" more efficiently.

Image source: pixabay is not only suitable for the trajectory of marine life, Levi flight is also used in the flight behavior of flies, microbial behavior and even economics.

Part II the key to unlocking quantum phenomena-Quantum Simulation read here, you may think that Levi's flight is amazing, but its charm is not only that. Levi's flight statistics can even be applied to fluid dynamics in quantum systems.

Before we understand the specific role of Levy's flight, let's take a look at what methods are generally used to study quantum systems.

In recent years, the fields of quantum computing, quantum information and quantum simulation have attracted more and more public attention.

Similar to other simulation methods, quantum simulation is to compare a variety of quantum phenomena and classical phenomena in nature by artificially controlling the quantum system of variables. In 1982, Feynman proposed the concept of quantum simulator for this purpose.

American physicist Richard Philip Feynman (Richard Phillips Feynman) | Image source How Richard Feynman Convinced The Naysayers 60 Years Ago That Gravitational Waves Are Real-The Quantum Labyrinth for traditional supercomputers, due to the limitation of scale and speed, simulating the dynamics of a complex quantum system is a very difficult task.

But for the quantum simulator, the dynamics of simulating complex quantum systems is like a fish in water, and it can realize the evolution of arbitrary quantum states.

Quantum computer is very similar to quantum simulator, but different emphasis is emphasized. We pay more attention to the computing function of quantum computer and the comparative simulation function of quantum simulator.

Photo Source: pixabay We know that in nature, the evolution of quantum systems is difficult to accurately control and change, so it is difficult for us to control variables, so it is difficult to study the properties of quantum dynamics under different parameters.

In this case, quantum simulation is an effective method to study the behavior of quantum dynamics. in the process of quantum simulation, we can artificially accurately control the parameters of the quantum system, and the high-throughput adjustment parameters can be scanned and repeated many times. Under such conditions, we can explore the properties of quantum systems from many angles and study them systematically.

Generally speaking, quantum simulation is often used in the scientific research of various fields, such as time crystal quantum simulation, quantum multi-mention localization simulation thermodynamics, statistical mechanics, topology, field theory and quantum chemistry simulation.

Dynamic simulation of Part III quantum magnet-Levy flight quantum simulator is very powerful, but if we do not have the ability to perform the same calculation, how can we verify the results of the quantum simulator?

The observation of the quantum system shows that the long-term behavior of the quantum system can be expressed by the Bernoulli equation which describes the fluid behavior.

The researchers simulated the dynamics of long-range quantum magnets in 51 systems with individually controlled ions through a quantum simulator.

Among them, the quantum state of a single ion in the quantum system is controlled by a tightly focused and controllable laser beam, which can locate any ion and interact with the ion at the same time.

Photo Source: pixabay here, Levi flight once again plays an important role. In this quantum system, the simulation of the dynamic process of quantum magnets is controlled by the distribution of Levy flight.

By changing the power index of Levy's flight, it is found that after an initial stage dominated by quantum mechanical effects, the system can actually be described by familiar equations in fluid dynamics (from normal diffusion to abnormal hyperdiffusion).

As we described earlier, an important feature of Levi's flight is that the probability distribution is heavy-tailed, which means that there is a relatively high probability of big strides in the process of random walking. Here, it shows that the long-distance interaction has a strong effect on transport.

This method also provides an effective way to verify the results of the quantum simulator: after a certain point in time, the quantum system will follow the laws of classical fluid dynamics. Compared with the classical law of hydrodynamics, if there is a strong deviation, it shows that the quantum simulator can not work properly.

When we go to the beach in the future

While letting the sea take away your sorrow

You might as well think about the Levi flight that you learned today.

In the process of watching the big fish eat the small ones

Unwittingly grasped the secret of quantum dynamics!

Will you get more contented happiness?

reference

[0] the original cover image is from pixabay.

[1] Brownian Motion-Zhihu

Jiang Peihua, Zhou Qiaoyan, Lan Tianya, Liu Kexin. Probability properties of several changing forms of Brownian motion and their applications [J]. Journal of Nantong University (Natural Science Edition), 2022, 21 (01): 88-94.

[3] Viswanathan, G., Buldyrev, S., Havlin, S. Et al. Optimizing the success of random searches. Nature 401,911,914 (1999).

Xu Jian. Research on Multi-objective Collaborative Optimization of production Planning and scheduling based on Levy Flight improved MOPSO [D]. Hangzhou University of Electronic Science and Technology, 2021.DOI:10.27075 / d.cnki.ghzdc.2021.000548.

[5] Brockmann, D.C., Hufnagel, L. & Geisel, T. The scaling laws of human travel. Nature 439,462-465 (2006).

[6] Bartumeus, F., da Luz, M. G. E., Viswanathan, G. & Catalan, J. Animalsearch strategies: a quantitative random-walk analysis. Ecology 86, 3078-3087 (2005).

[7] Schuster, F. L. & Levandowsky, M. Chemosensory responses of Acanthamoebacastellani: Visual analysis of random movement and responses to chemicalsignals. J. Eukaryot. Microbiol. 43,150158 (1996).

[8] Fan Heng. Quantum computation and quantum simulation. Acta Phys. Sin., 2018, 67 (12): 120301.

[9] Feynman R P 1982 Int. J. Theor. Phys. 21 467

Wang Shuhong, Jiang Xun. Paul Pierre Levy, the originator of Levy's flight [J]. Science, 2019, 71 (05): 50-54.

[11] Levy distribution (Levi Distribution) and Levy fligt (Levi Flight), CSDN

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop). Authors: Norma, Garrett

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