Author | Zhang
Edit | Qian Ning
John bardeen (1908–1991) won two Nobel Prizes, both of which were related to condensed matter research. Condensed state is based on quantum theory. After the establishment of quantum field theory, theoretical physics has developed in two different directions: particle physics and condensed matter physics. Most people's eyes turn to the traditional high-energy particle physics under the guidance of reductionism, thinking that that is the orthodox direction of physics.
In fact, however, a large part of today's physicists are doing research on condensed matter physics, including both theoretical and experimental aspects. The theoretical part of condensed matter physics has many similarities with particle physics theory. The research from solid state to condensed state in the past hundred years has promoted the vigorous development of information technology in practice and brought people surprises again and again. Typical examples are transistors and superconductivity introduced in the last article. Condensed matter physics is unique in theory: the layer expansion theory followed by condensed matter research has made great contributions to scientific thought and philosophy; Symmetry breaking's thought in condensed matter is applied to the Higgs mechanism of obtaining mass in particle physics, which we will introduce in the next article.
Landau phase transition theory
Lev Landau (1908- 1968), a famous physicist in the former Soviet Union, is a master in the field of physics and has made great contributions in many fields of theoretical physics. In the eyes of China academic circles, Landau, like Feynman, is a legendary figure with outstanding academic achievements and maverick. Feynman is widely known for his autobiographical books, while Landau enjoys a high reputation in academic circles for his series of classic physics textbooks with large volumes. For Landau's story, such an article is endless. Please refer to Resources [1].
Figure 26-2: Young Landau is with Bohr, Heisenberg, Pauli and Gamov.
Landau's Fermi liquid and phase transition theory laid the foundation of the whole condensed matter physics. Fermi liquid theory allows us to continue to use single particle images in multi-particle condensed matter physics. In addition, Landau's phase transition theory is related to symmetry breaking's theory, which allows us to describe the macroscopic state of condensed state system with order parameters and classify different phases with symmetry. General matter has three states: solid, liquid and gas, which is what junior high school physics tells us. Later, the research results of modern physics expanded the concept of "three states of matter"-plasma state, Bose-Einstein condensed state, liquid crystal state and so on, as shown in Figure 26-3. Later, it expanded and subdivided into many different material "phases". The mutual transformation between material phases is called "phase transition".
Figure 26-3: Phase transition diagram (including liquid crystal and plasma)
Changes in solids, liquids and gases are accompanied by changes in volume and the release (or absorption) of heat. This kind of transformation is called "first-order phase transition", and their mathematical meaning is that at the phase transition point, the parameters in thermodynamics (such as chemical potential) remain unchanged, but their first derivative (volume, etc.). ) change. Later, the number of material phases and phase transitions observed in the experiment increased, and the concept of first-order phase transition was extended to "second-order" and "third-order" ... n-order phase transitions, which were distinguished by the n-order derivative of thermodynamic quantities.
These N-order phase transitions are collectively called "continuous phase transitions". Landau established the mathematical model of continuous phase transition and provided a unified description [2]. In his view, the continuous phase transition is characterized by the change of order degree of matter, which can be described by the change of order parameters. Or further, it can be seen as a change in the symmetry of the material structure.
The method of studying phase and phase transition according to the symmetry of matter and its breaking mode is called Landau paradigm. It can also be said that condensed matter physics was born in this way [3]. Physicists are increasingly aware that studying solids or liquids alone is far from meeting the needs of the actual situation. Especially after mixing with low temperature physics, the study of solid physics turned to the study of various systems composed of a large number of particles. The particles in these systems have a strong interaction. Under various physical conditions, they not only show solid state, liquid state, liquid crystal state and plasma state, but also show superfluid state, superconducting state, boson condensed state and fermion condensed state ... The study of these different states and their mutual transformation constitutes condensed physics.
Anderson challenged reductionism.
Another master who studied condensed matter physics and laid a groundbreaking foundation was American physicist philip anderson (1923-2020).
Anderson died this spring at the age of 97. He has made great contributions in symmetry breaking, high temperature superconductivity and many other fields. When he was working in Bell Laboratories in New Jersey, he first put forward the concepts and theories of localized state and extended state in condensed state. To this end, he and another American physicist John Hasbrouck van Vleck (1899- 1980) and British physicist neville francis morte (65438+).
In addition to his outstanding contribution to physics itself, 1972, Anderson published a famous paper "More is Different" in Science magazine [4], aiming at the reductionism that everything belongs to the simplest particle, and put forward the emergence of different branches formed by different material levels. The Declaration of Independence, regarded as condensed matter physics, brought another perspective to the whole scientific community, expressing Anderson's challenge and transcendence to the traditional scientific methods of mankind.
The traditional scientific research method is reductionism, and science in ancient Greece began with "tracing back to the source" or "reduction". The so-called reductionism is to decompose a complex system into a combination of components, and the behavior of a complex system can be understood and described by the behavior of its components. For example, matter is made up of molecules, molecules are made up of atoms, and atoms are made up of deeper elementary particles, which recursively form smaller and smaller levels in the material structure. The method of reductionism is to answer questions step by step, expecting a deeper structure to explain the essence of the previous level. In this way, the route of scientific evolution seems to come down to a reductive route, and finally it can be traced back to a "ultimate problem".
However, Anderson put forward a different view. He believes that "there are many differences", reduction can't reconstruct the universe, and some behaviors can't fully explain the whole behavior. High-level material laws are not necessarily the application of low-level laws, but not only the basic laws at the bottom. Every level needs a brand-new basic conceptual framework and has its basic principles. In other words, Anderson taught us another perspective of understanding the world, which is different from reductionism, that is, the view of "layer exhibition theory" (or holism). Hierarchical development theory neither belongs to reductionism nor opposes reductionism, but complements reductionism and forms a more complete scientific method.
In Many Are Different, Anderson takes symmetry breaking in condensed matter as an example to expound the theory of layer spreading.
Phase transition-symmetry and symmetry breaking
The concept of symmetry is not difficult to understand. Geometric symmetry can be seen everywhere in nature, artificial architecture, art and other fields. Lattices in solids are geometrically symmetric structures with repeated spatial states. If the whole crystal moves by a lattice constant a, the result is still the original system. In other words, the lattice structure has the symmetry that the system remains unchanged under the transformation of spatial translation A. Therefore, symmetry means that the system remains unchanged under some transformation. Besides spatial translation transformation, there are other kinds of transformations, such as spatial rotation and spatial inversion. In addition to various transformations in three-dimensional space, there are also translation or anti-evolution transformations in time and other abstract or internal transformations. Various transformations correspond to different symmetries.
There is a Noether theorem in physics, which was discovered by German mathematician emmy noether (1882- 1935). It links the conservation law in physics with symmetry [5]. For example, the law of conservation of energy corresponds to time symmetry; Conservation of momentum corresponds to spatial translation symmetry; Conservation of angular momentum corresponds to rotational symmetry and so on. I won't go into details here. See reference [6].
The world is not only symmetrical, but also asymmetrical. Observe the world around us: people's left face and right face are not exactly the same. Most people's hearts are on the left, most DNA molecules are right-handed, and the earth is not a completely regular sphere ... It is precisely because of these asymmetric elements in symmetry that symmetry and asymmetry meet harmoniously, creating our colorful world.
Even in the case of symmetry, there are different grades. For example, a regular triangle should be more symmetrical than an isosceles triangle; Spherical masks are more symmetrical than ellipsoidal masks. In addition, the symmetry of the object state will also change, from low to high, or from high to low.
Figure 26-4: Phase Transition and symmetry breaking
Landau relates the phase transition in condensed matter physics to the change of symmetry in material structure. He called the symmetry process from high symmetry to low symmetry "symmetry breaking". Correspondingly, inverse phase transition means "symmetry recovery". However, how to judge the "level" of symmetry? What needs to be reminded in particular is that sometimes we equate "symmetry" with "order", but in fact, the "high and low" degree of these two concepts is just the opposite. The more orderly the structure, the lower the symmetry. Here is a simple example to illustrate.
The upper part of Figure 26-4 shows the change of molecular structure during the process of "solid liquid crystal liquid state". The symmetry of these three, which is higher or lower?
Solid water molecules are arranged in order to form a neat and beautiful lattice or pattern (lattice); In liquid crystal, the three-dimensional lattice is broken and becomes one-dimensional crystal. Then, as the temperature continues to rise, the one-dimensional ordered structure is also destroyed and becomes a disordered liquid: the water molecules in the liquid are doing random and irregular Brownian motion-there is no fixed direction, no fixed position, and they are in a completely disordered state, and they look the same in any direction and at any point. And this is what we call the "highest" symmetry state, that is, the symmetry of liquid is high, but it is disordered. Compared with liquid state, the order degree of liquid crystal and solid state gradually increases, and the symmetry gradually decreases.
Described in mathematical language, if the spatial coordinates are translated in liquid state, the properties of the system will not change, which shows that there is a high degree of symmetry to the space. However, when water turns into ice, the system can only remain unchanged if it moves an integer multiple of the lattice constant a in some spatial directions. Therefore, from liquid to solid, the symmetry of matter decreases, that is, it is broken, from continuous translational symmetry to discrete translational symmetry. Or: the solid state breaks the continuous translational symmetry of the liquid state, that is, the crystal is the product of any translational symmetry breaking of the liquid. Compared with liquid, the particle density of crystal appears periodic modulation in space, so it is more orderly, and the change of periodic modulation from scratch can characterize the phase transition of substance from liquid crystallization to solid.
Symmetry breaking can be divided into two categories: dominant symmetry breaking and spontaneous symmetry breaking. The reason for the first kind of "symmetry breaking" is determined by the laws of nature, because some physical systems themselves do not have the symmetry corresponding to some physical laws. The famous example of symmetry breaking is "CP destruction in weak interaction" discovered by Li Zhengdao and Yang Zhenning.
Physicists are more interested in the second kind of spontaneous symmetry breaking. In this case, the physical system still follows some symmetry, but the lower energy states (including vacuum states) of the physical system do not have this symmetry. Famous examples of this symmetry breaking are BCS theory in superconducting physics introduced in our last article, and Higgs mechanism in the standard model of elementary particles to be introduced in the next article.
Spontaneous symmetry breaking
To make "spontaneous symmetry breaking" more clear, that is to say, physical laws have some symmetry, but the solution of one of its equations, that is, the actual state of the physical system, does not have this symmetry. In this way, all the real situations we see in the world are some special situations after the spontaneous symmetry breaking, so it can only reflect a small part of the physical laws. In Figure 26-5, several examples in daily life are given to illustrate the "breaking" of symmetry.
Figure 26-5: obvious symmetry breaking and spontaneous symmetry breaking in nature.
Figure 26-5a shows a stone on a hillside. The hillside causes the asymmetry of gravity potential energy, which makes the stone roll to the right. This is an obvious symmetry breaking. In the case of Figure 26-5b, a pencil stands upright on the table, and the force it receives is symmetrical in all directions, so the probability of it falling in any direction is equal. But the pencil will only drop in one direction, destroying its original rotational symmetry. This kind of destruction is not caused by the asymmetry of physical laws or the surrounding environment, but by the unstable factors of the pencil itself, so it is called spontaneous symmetry breaking. The process of crystallization of water droplets into snowflake patterns in Figure 26-5c also belongs to spontaneous symmetry breaking.
Yoichiro Nambu, a Japanese-American physicist (192 1-20 15) first introduced the concept of "symmetry breaking" from condensed matter physics to particle physics [7]. Therefore, the South shared the 2008 Nobel Prize in Physics with two other Japanese physicists, Kobayashi Makoto (1944-) and Maskawa Junxiu (1940-), who discovered the origin of the positive and negative matter symmetry breaking.
References:
[1]. Zhang's blog science network: "Silicon Fires Start a prairie fire" -2 1- Landau with strange personality /home.php? Space and time. uid=67722 1。 Do = blog & id = 724191
[2]. Yu Lu and Hao Bailin. Phase transition and critical phenomena, Science Press, 1992.
[3].L.D. Landau, on the theory of phase transition, 1937, published in: zh.eksp.teor.fiz.7 (1937)19-32, phys.z.sow jetion/.
[4]. Anderson, more different, Science Volume 177, pp. 393-396 (1972).
[5]. Yvette Cosman-Schwartzbach (20 10). Noether theorem: the law of invariance and conservation in the twentieth century. The origin and research of the history of mathematics and physical science. Springer Publishing House.
[6]. Zhang Science Network blog: Unification Road -8- Symmetry and Conservation /home.php? Space and time. uid=67722 1。 Do = blog & id = 882465
[7]. Y. Nanbu; Jona Lacino, G. (April 196 1). "The dynamic model of elementary particles is based on the analogy with superconductivity. I ". Physical review122: 345–358.