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Statistical Mechanics Lecture 2

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Undetected location. NO YES. Home Subjects Chemistry Physical Chemistry. Statistical Mechanics: Fundamentals and Modern Applications. Selected type: Hardcover. Added to Your Shopping Cart. This is a dummy description. Statistical Mechanics reflects the latest techniques and developments in statistical mechanics.

Covering a variety of concepts and topics - molecular dynamic methods, renormalization theory, chaos, polymer chain folding, oscillating chemical reactions, and cellular automata. Permissions Request permission to reuse content from this site. Classical Statistical Mechanics. Quantum Statistical Mechanics. Angular momentum — operators, eigenvalues and eigenstates of angular momentum; parity and rotational invariance; the hydrogen atom; angular momentum quantum numbers. Time-independent perturbation theory — non-degenerate eigenvalues; first and second order corrections; degenerate perturbation theory; the variational principle.

Crystal symmetry — lattice, basis, unit cell of a crystal; Miller indices; lattice planes and spacings; the reciprocal lattice and Brillouin zones; Bragg and Laue diffraction; structure factor; atomic form factor; neutron and x-ray diffraction; powder and single crystal diffraction. Sound propagation in solids — normal mode dispersion for linear atomic chains; acoustic and optical phonon modes; Born von Karman boundary conditions; density of states; lattice quantization and phonons; Einstein and Debye models of heat capacity.

Electronic properties — free electron theory; density of states; the Fermi energy; Fermi surfaces; conductivity and heat capacity; the nearly-free electron model; band gaps; the Bloch theorem; the Kronig-Penny model. Distinctions between metals, semiconductors and insulators; aspects of condensed matter physics. PH - Statistical Mechanics. Basic postulates of statistical mechanics — macrostates and microstates; distinguishable and indistinguishable particles; distribution functions.


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Temperature and entropy — state probabilities; the Boltzmann relation; the canonical ensemble; the partition function; Gibbs' entropy formula; the Third Law of thermodynamics; information theory; irreversible processes and the arrow of time. Density of states and heat capacity in black body radiation. Ideal classical gases — the Maxwell-Boltzmann distribution; rotational and vibrational heat.

Free electron gases — the Fermi energy and distribution function; Pauli paramagnetism; electronic contributions to heat capacity. Phonons — phonon contributions to heat capacity; the Debye approximation; the phonon gas; thermal conductivity of insulators. Phase transitions — the Weiss model of ferromagnetism; order-disorder transitions.

The hydrogen atom — central potential approximation; radial wavefunctions; quantum numbers; energy levels and degeneracy; electron spin and total angular momentum; spin-orbit coupling and fine structure; Zeeman splitting. Helium atom — Coulomb repulsion and exchange; singlet-triplet splitting. Electronic configuration and the periodic table — alkali metals; residual electrostatic interaction; LS-coupling scheme; Hund's rules; hyperfine structure and isotope shift.

Spectroscopy — selection rules for electric dipole interaction; Zeeman and Stark effects; inner shell transitions and x-ray spectra; modern atomic physics experiments. PH - Cosmology. Computation and its physical consequences — Turing machines; the physical Church-Turing thesis; the halting problem; computational complexity; emergence. Introduction to information theory — quantifying information; Shannon entropy; correlations and mutual information.

Thermodynamics of information — Maxwell's demons; Szilard Engines; Landaur's erasure; energetic limits of computation. Quantum Information — quantum bits; quantum gates; quantum non-locality; quantum entanglement. Quantum technologies — sampling of iconic quantum technologies like quantum bomb detection and quantum teleportation. Superconductivity — Drude theory of conduction in normal metals; superconductor properties; the Meissner effect; perfect diamagnetism; type I and type II superconductors; the London equation; Ginzburg-Landau theory; the superconducting phase transition; gauge symmetries and spontaneous symmetry breaking; the Abrikosov flux lattice; macroscopic coherent states; field operators; off-diagonal long-range order; the Josephson effect and its application in the Superconducting Quantum Interference Device SQUID ; introduction to the BCS theory.

Superfluids — superfluid helium-4; macroscopic wave functions, flow quantization; rotating superfluids and vortices; phonon and roton excitations; the Tisza-Landau two-fluid model; superfluid helium-3; unconventional superconductivity. PH - Fluid Mechanics.

Equations of flow — Pascal's theorem; the Bernoulli equation; Euler's equation; the Navier-Stokes equation; vorticity and divergence. Compressible and incompressible fluids — flow around objects; potential flow; viscosity, Reynolds number; laminar flow and turbulence; Kolmogorov scaling. Dynamical phenomena — sound waves; shock fronts; Rankine-Hugoniot relations; shallow-water equations; surface waves; conservation of potential vorticity.

PH - Chaotic Dynamical Systems. Phase planes and critical points; free and damped oscillators; prey-predator models; extensions to three-dimensional phase space and beyond, e. Discrete dynamics — 1D and 2D maps; fixed points and stability; period doubling; shift map and logistic map. Chaos theory — sensitivity to initial conditions the butterfly effect ; Lyapunov exponents; limits to predictability; strange attractors and fractal dimensions; the Kepler problem. Stable and unstable manifolds — homoclinic and heteroclinic tangle; lobes and turnstile transport; particle motion in 2D incompressible fluids.

Semiconductor-based device fabrication — ion implantation; diffusion and oxidation processes; epitaxy; thin film deposition; material and device characterization; lithography; etching and cleaning. Magnetic, organic and bioMEMS devices — fabrication and characterization techniques. Waveguide optics — optical fibres; crystal optics.

An Advanced Approach with Applications

Light sources and detectors — optoelectronic interactions in semiconductors; photovoltaic devices; liquid crystal optics; flat panel displays. PH - Biophysics. Introduction to biophysics — working principles of common biophysical models; chemical bonds; structure and dynamics of biomolecules. Structure calculations and computer simulations. Thermodynamics and kinetics of molecular interactions.

Single-molecule biophysics. Physics and medicine. Scattering theory — formulation of scattering experiments; Born approximations; Green's function methods; bound and free states; resonances; Fermi's golden rule. Many-body quantum mechanics — quantum postulates for many-body systems; quantum entanglement; the Einstein-Podolsky-Rosen paradox and Bell's inequalities; the many-worlds interpretation of quantum mechanics. Identical particles — exchange symmetry; bosons and fermions; creation and annihilation operators, and second quantization; coherent states; the Pauli exclusion principle; quantum field theories.

Quantum electrodynamics — the electromagnetic Hamiltonian; gauge symmetry and the Aharanov-Bohm effect; Dirac's equation; quantization of the electromagnetic field; photons; electromagnetic radiation; electromagnetic shifts of electronic energy levels.

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Statistical Physics

Basic theories and models for condensed-matter physics — approaches to the many-body problem; collective phenomena. Structure and bonding - order and disorder; types of bonding and structure; electrons in periodic potentials; the Bloch theorem; tight-binding models; 1D chain models; band structures of real materials; optical transitions and photoemission.

Interactions — effective medium approximations for electron-electron interactions; Hartree-Fock theory; exchange and correlation energy; electron fluids and electrostatic screening; the exclusion principle and quasiparticles. Transport and scattering — crystal momentum; neutron scattering; electron-phonon scattering; optical conductivity; Drude theory, plasmons; transport in electric and magnetic fields; quantization of orbits, cyclotron resonance; the de Haas-van Alphen effect; Fermi surfaces; magnetoresistance oscillation; the quantum Hall effect.

Semiconductors — thermal equilibrium of quasiparticles; field effect transistor; p-n junctions, LED; excitons; semiconductor heterostrutures; quantum wells; semiconductor lasers.

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Magnetism — origin of magnetic moments and interactions; ferromagnetism; itinerant magnetism; the Stoner model; strongly interacting systems; Mott insulators. PH - Surfaces and Interfaces. Thermodynamics of surface phenomena — electronic structures; phase transitions; elementary excitations; physisorption and chemisorption; energy transfer.

Schottky barrier and band offsets in semiconductors; band engineering. Analytical techniques — scanning tunneling microscopy; electron diffraction methods; photoemission; ballistic electron emission microscopy. PH - Nanoscale Physics.


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  8. Electron gases in 2D and multilayer systems. Quantum transport in 1D — magnetotunneling; quantum capacitance; quantum conductance. Quantum dots and artificial atoms — eigenenergies and eigenstates; single particle conductance; Coulomb blockade; Kondo effect; the Aharanov-Bohm effect.

    Statistical Mechanics: Fundamentals and Modern Applications (Wilde - PDF Free Download

    PH - Nuclear Physics. Properties of nuclei — nuclear radii, masses, and abundances; binding energies; spins and electromagnetic moments. Nuclear structure — deuterons; nucleon-nucleon scattering and exchange forces; the semi-empirical mass formula; the Fermi gas model; the shell model; liquid drop models with vibrational and rotational excitations; collective structure.