Fractional Quantum Hall Effect: Emergent Particles with Fractional Charge
The Fractional Quantum Hall Effect (FQHE) is a quantum phenomenon observed in two-dimensional electron systems subjected to very strong magnetic
Quantum Hall Effect: Quantized Resistance in 2D Systems
The Quantum Hall Effect occurs in two-dimensional electron systems placed under strong magnetic fields at very low temperatures. In this
Topological Insulators: Edge States Protected by Topology
Topological insulators are a class of materials that act as insulators in their bulk but conduct electricity on their surfaces
Chiral Symmetry: The Physics of Handedness
Chiral symmetry is a type of symmetry that distinguishes between left-handed and right-handed versions of particles or fields, especially in
Spontaneous Symmetry Breaking: Hidden Order Behind Emergent Phenomena
Spontaneous symmetry breaking (SSB) occurs when the underlying laws (equations or Lagrangians) of a system are symmetric, but the state
Gauge Symmetry: The Foundation of Modern Field Theories
Gauge symmetry is a type of symmetry in which certain transformations can be performed on the fields of a physical
Noether’s Theorem: Symmetry Leads to Conservation
Noether’s Theorem is one of the most profound and unifying principles in theoretical physics. It states that every continuous symmetry
Symplectic Geometry: The Mathematical Backbone of Classical Mechanics
Symplectic geometry is a branch of mathematics that studies geometric structures fundamental to the formulation of classical mechanics, especially in
Action: The Quantity Nature Minimizes
In physics, action is a fundamental concept in the formulation of mechanics, especially in Lagrangian mechanics. It is defined as
Lagrangian Mechanics: Motion from Energy Differences
Lagrangian mechanics is a powerful reformulation of classical mechanics that uses energy principles—specifically, the difference between kinetic and potential energy—to