Graduate
  1. Classical mechanics  1.1. Advanced Kinematics  1.1.1. Generalized coordinate systems  1.1.2. Parametric equations of motion  1.1.3. Non-inertial frames and fictitious forces  1.1.4. Covariant formulation of momentum  1.1.5. Action-angle variable  1.2. Lagrangian and Hamiltonian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Noether's theorem and conservation laws  1.2.4. Normalized Speed  1.2.5. Canonical conversion  1.2.6. Poisson bracket and Hamilton–Jacobi theory  1.2.7. Hamiltonian chaos and integrability  1.3. Rigid body mobility  1.3.1. Euler's equations of motion  1.3.2. Principal moments of inertia  1.3.3. Gyroscopic motion and precession  1.3.4. Inertia tensor  1.3.5. Stability of rotational speed  1.4. Nonlinear dynamics and chaos  1.4.1. Phase space and stability analysis  1.4.2. Poincaré sections and bifurcation theory  1.4.3. Strange Attractors and Fractals  1.4.4. Lyapunov exponent  1.4.5. KAM theorem and quasi-periodic motion
  2. Electromagnetism  2.1. Advanced Electrodynamics  2.1.1. Green's function and potential theory  2.1.2. Multipole expansion  2.1.3. Image charging method  2.1.4. Boundary conditions and uniqueness theorem  2.2. Electromagnetic wave propagation  2.2.1. Plane waves in dielectrics and conductors  2.2.2. Waveguides and cavity resonators  2.2.3. Radiation pressure and optical tweezers  2.2.4. Polarization and Jones calculus  2.3. Relativistic electrodynamics  2.3.1. Covariant formulation of electrodynamics  2.3.2. Lienard–Wiechert potentials  2.3.3. Synchrotron radiation and bremsstrahlung  2.3.4. Electromagnetic field tensor and Lorentz transformations  2.4. Plasma physics  2.4.1. Magnetohydrodynamics  2.4.2. Debye shielding and plasma oscillations  2.4.3. Alfvén waves and tokamak confinement  2.4.4. Plasma instabilities and turbulence
  3. Statistical mechanics and thermodynamics  3.1. Advanced Thermodynamics  3.1.1. Legendre transforms and thermodynamic potentials  3.1.2. Fluctuation–dissipation theorem  3.1.3. Onsager interpersonal relations  3.1.4. Critical events and phase transitions  3.2. Quantum statistical mechanics  3.2.1. Density Matrix and Ensemble Theory  3.2.2. Bose–Einstein condensates  3.2.3. Quantum phase transition  3.2.4. Fermi–Dirac and Bose–Einstein statistics  3.2.5. Partition functions and grand canonical ensembles
  4. Quantum mechanics  4.1. Advanced wave mechanics  4.1.1. WKB approximation  4.1.2. Path integral formulation  4.1.3. Quantum harmonic oscillator and coherent states  4.2. Angular momentum and spin  4.2.1. Spherical Harmonics  4.2.2. Clebsch–Gordan coefficient  4.2.3. Wigner–Eckart theorem  4.2.4. Spin–orbit coupling  4.3. Quantum scattering theory  4.3.1. Born approximation  4.3.2. Partial wave analysis  4.3.3. Optical theorem  4.3.4. S-matrix theory  4.4. Quantum field theory  4.4.1. Second Quantization  4.4.2. Feynman diagrams and propagators  4.4.3. Renormalization theory  4.4.4. Gauge theory and Yang–Mills fields  4.4.5. Spontaneous symmetry breaking and the Higgs mechanism
  5. General relativity and cosmology  5.1. Tensor calculus and differential geometry  5.1.1. Einstein field equations  5.1.2. Schwarzschild and Kerr metrics  5.1.3. Geodesics and Christoffel symbols  5.2. Cosmology and the Universe  5.2.1. The FLRW metric and cosmic inflation  5.2.2. Dark energy and structure formation  5.2.3. Cosmic microwave background radiation
  6. Condensed matter physics  6.1. Band structure and transport theory  6.1.1. Block theorem and the Kronig–Penney model  6.1.2. Fermi surface topology  6.1.3. Quantum Hall Effect  6.2. Superconductivity  6.2.1. BCS theory and Cooper pairs  6.2.2. Meissner effect and flux quantization  6.2.3. The Josephson Effect and SQUIDs  6.3. Topological phases of matter  6.3.1. Topological Insulators  6.3.2. Majorana fermions in topological phases of matter
  7. Nuclear and Particle Physics  7.1. Quantum Chromodynamics (QCD)  7.1.1. Quark–gluon plasma  7.1.2. Asymptotic freedom  7.1.3. Confinement and hadronization  7.2. Beyond the Standard Model  7.2.1. Grand Unified Theories  7.2.2. Supersymmetry and extra dimensions  7.2.3. Neutrino oscillations

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Nuclear and Particle Physics


Nuclear and particle physics is a fascinating field of physics that explores the smallest known building blocks of the universe and the forces that act on them. It deals with the fundamental aspects of matter and energy. Let's dive deep into this subject and understand its main components.

Fundamentals of Nuclear Physics

Atomic physics focuses on the study of atomic nuclei, which are located at the center of atoms. These nuclei are composed of protons and neutrons, collectively known as nucleons. The study of how these particles interact within the nucleus, what forces act on them, and how they contribute to the properties of the atom is the essence of atomic physics.

Components of an atom

An atom consists of a nucleus and orbiting electrons. The nucleus is small and dense, containing positively charged protons and neutral neutrons. Here is a visual representation of an atom:

Nucleus Electron

Electrons orbit the nucleus, while protons and neutrons reside inside the nucleus.

Nature of nuclear forces

Within the nucleus, protons and neutrons are held together by strong nuclear forces. These forces must be strong enough to overcome the electrostatic repulsion between protons due to their positive charge. The strong force is one of the four fundamental forces of nature and acts over very short distances. Understanding these forces helps explain the stability of the nucleus, fission, and fusion processes.

F_strong(nuclear) >> F_electromagnetic

This means that the strong nuclear force (F strong ) is much greater than the electromagnetic force between protons (F electromagnetic ).

Radioactivity and nuclear reactions

Nuclear physics also investigates radioactivity, a natural phenomenon in which unstable nuclei release energy by emitting radiation. There are three main types of radioactive decay:

  1. Alpha decay
  2. Beta decay
  3. Gamma decay

Alpha decay

In alpha decay, a nucleus releases an alpha particle, which consists of 2 protons and 2 neutrons. This type of decay decreases the atomic number by 2 and the mass number by 4.

^{A}_{Z}X → ^{A-4}_{Z-2}Y + ^{4}_{2}He

Beta decay

During beta decay, a neutron turns into a proton, releasing an electron (beta particle) and an antineutrino. This increases the atomic number by 1 without any change in the mass number.

^{A}_{Z}X → ^{A}_{Z+1}Y + e^- + &bar;ν_e

Gamma decay

Gamma decay involves the release of a gamma-ray photon from an excited nucleus. It usually follows other types of decay when the nucleus transitions from an excited state to a lower energy state.

^{A}_{Z}X* → ^{A}_{Z}X + γ

Nuclear Fission and Fusion

Nuclear fission

Fission is the process in which a heavy nucleus splits into two smaller nuclei, releasing a few neutrons and a large amount of energy. This is the principle behind nuclear reactors.

^{235}_{92}U + n → ^{141}_{56}Ba + ^{92}_{36}Kr + 3n + E

Nuclear fusion

Fusion is the process in which two lighter nuclei combine to form a heavier nucleus. This process releases energy and powers stars, including our Sun.

^{2}_{1}H + ^{3}_{1}H → ^{4}_{2}He + n + E
Fragmentation Merger Heavy nuclei -> Small nucleus Light nuclei -> Heavy nuclei

Basics of Particle Physics

Particle physics explores the fundamental components of matter and energy, often called elementary particles. It is a field that goes beyond the atomic level to study subatomic particles with the help of accelerators and particle detectors.

Elementary particles

Particles are classified into two main categories:

  • Fermions - The building blocks of matter. This category includes quarks and leptons.
  • Bosons - Carriers of forces. These include the photon, W and Z bosons, the gluon and the Higgs boson.

Fermions

Fermions have half-integer spin and they obey the Pauli exclusion principle:

Spin 1/2

Fermions include:

  1. Quarks: These combine to form protons and neutrons. Examples: up, down, charm, strange, top, bottom.
  2. Leptons: Simple particles, including electrons, muons, and neutrinos.

Bosons

Bosons have integer spin and include the force carrier particles:

Spin 1

Types of bosons:

  • Photon (γ) – Electromagnetic force
  • Gluon (g) - The strong force
  • W and Z bosons - The weak force
  • Higgs boson - Mass production via the Higgs field

Standard model of particle physics

The Standard Model is a theory that describes fundamental particles and their interactions, except for gravity. It is a framework that classifies particles based on their properties such as charge, spin, mass, and types of interactions.

Quarks Leptons Bosons

Interactions in the Standard Model

The conversation includes the following:

  1. Strong interaction: Gluons mediate it, confining quarks within protons, neutrons.
  2. Electromagnetic interaction: Photons mediate this and it is a long-range interaction affecting charged particles.
  3. Weak interaction: Responsible for processes such as beta decay; mediated by W and Z bosons. Characterized by short range.

Experiments and applications

Nuclear and particle physics experiments are conducted in laboratories around the world, with technologies such as particle accelerators and detectors helping to explore atomic and subatomic particles in depth.

Particle accelerators

These facilities accelerate particles to very high speeds, creating collision conditions similar to those just after the Big Bang. Some well-known accelerators are:

  • Large Hadron Collider (LHC): Located at CERN in Switzerland, it is used to search for particles like the Higgs boson.
  • Fermilab: Located in the United States, it formerly housed the Tevatron collider.

Applications of Nuclear and Particle Physics

Understanding nuclear and particle physics leads to advances in a variety of fields:

  • Medical applications: Techniques such as MRI, PET scans, and radiation therapy for cancer use the principles of nuclear physics.
  • Energy production: Nuclear reactors generate electricity through controlled fission reactions.
  • Understanding the universe: Particle physics helps explain cosmic phenomena and structures such as neutron stars and black holes.

Conclusion

Nuclear and particle physics are central to understanding the universe. The field is constantly evolving as scientists strive for deeper insights into the fundamental rules and particles that govern everything around us. From the subatomic realm to cosmological phenomena, this branch of physics is vital in advancing our understanding of the natural world.


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