文档介绍：A new paradigm of condensed matter physics
beyond Landau’s theories
Xiao-Gang Wen
/˜wen
Condensed matter theory – a theory of matter
Some matter have shape (solids) and some have no shape (liquids)
• How to describe the different mechanical properties?
• Why? What is the origin of shape?
How to describe the mechanical properties?
The mechanical properties of solids and liquids are described by two
very famous equation.
• Navier equation
2 i ijk m
∂t u − Tm ∂j∂ku = 0
where ui is the displacement vector.
• Euler equation
2 2 2
∂t ρ− v ∂i ρ= 0
where ρ is the density.
Different mechanical properties are captured by the two different
equations.
The deformations (ui and δρ) can propagate → sound waves.
Different mechanical properties → different sound waves:
• Solids have two transverse modes and pression mode.
• Liquids have only pression mode.
Origin of shape (mechanical properties)
= origin of Euler/Navier equations
= origin of sound waves
= origin of phonons
Shape is originated anization of atoms
Many years after the Euler/Navier equation, atoms are discovered.
Different mechanical properties and different sound e from
anization of atoms:
liquid order → Euler equation
crystal order → Navier equation
Principle of emergence
All (low energy) properties from anization of atoms
Waves and phonons are collective motions of atoms
anizations are symmetry breaking
anizations = different phases
Definition of phases and quantum phases:
Singularities in free energy (T 6= 0) or ground state energy (T = 0)
imply phase transitions.
Landau symmetry breaking theory:
anizations = different symmetries
Phase transition = symmetry breaking
A A A
B’ B
Application of symmetry breaking states
• s (100BC) • Superconductors (1911)
Applications: Applications:
Compass (100BC ) Sensor (SQUID)
Motors (1900) High Q resonators (cell phone)
Data storage (1960) Strong ic field (MRI)
Spintronics (2000) The standard