Follow the link for more information. A variety of topics in physics such as crystallography, waves – Max Cooper – Emergence, elasticity, magnetism, etc. References to “condensed” state can be traced to earlier sources. For example, in the introduction to his 1947 book Kinetic Theory of Liquids, Yakov Frenkel proposed that “The kinetic theory of liquids must accordingly be developed as a generalization and extension of the kinetic theory of solid bodies.

One of the first studies of condensed states of matter was by English chemist Humphry Davy, in the first decades of the nineteenth century. In 1823, Michael Faraday, then an assistant in Davy’s lab, successfully liquefied chlorine and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and oxygen. By 1908, James Dewar and Heike Kamerlingh Onnes were successfully able to liquefy hydrogen and then newly discovered helium, respectively. Paul Drude in 1900 proposed the first theoretical model for a classical electron moving through a metallic solid. However, despite the success of Drude’s free electron model, it had one notable problem: it was unable to correctly explain the electronic contribution to the specific heat and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures. In 1911, three years after helium was first liquefied, Onnes working at University of Leiden discovered superconductivity in mercury, when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value.

Drude’s classical model was augmented by Wolfgang Pauli, Arnold Sommerfeld, Felix Bloch and other physicists. The mathematics of crystal structures developed by Auguste Bravais, Yevgraf Fyodorov and others was used to classify crystals by their symmetry group, and tables of crystal structures were the basis for the series International Tables of Crystallography, first published in 1935. In 1879, Edwin Herbert Hall working at the Johns Hopkins University discovered a voltage developing across conductors transverse to an electric current in the conductor and magnetic field perpendicular to the current. Magnetism as a property of matter has been known in China since 4000 BC. The first attempt at a microscopic description of magnetism was by Wilhelm Lenz and Ernst Ising through the Ising model that described magnetic materials as consisting of a periodic lattice of spins that collectively acquired magnetization. A magnet levitating over a superconducting material.

A magnet levitating above a high-temperature superconductor. The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description of superconductivity and the Kondo effect. The quantum Hall effect: Components of the Hall resistivity as a function of the external magnetic field:fig.

The study of phase transition and the critical behavior of observables, termed critical phenomena, was a major field of interest in the 1960s. The effect was observed to be independent of parameters such as system size and impurities. In 1981, theorist Robert Laughlin proposed a theory explaining the unanticipated precision of the integral plateau. Shortly after, in 1982, Horst Störmer and Daniel Tsui observed the fractional quantum Hall effect where the conductance was now a rational multiple of a constant. Theoretical condensed matter physics involves the use of theoretical models to understand properties of states of matter. These include models to study the electronic properties of solids, such as the Drude model, the Band structure and the density functional theory. Theoretical understanding of condensed matter physics is closely related to the notion of emergence, wherein complex assemblies of particles behave in ways dramatically different from their individual constituents.

The metallic state has historically been an important building block for studying properties of solids. In 1912, The structure of crystalline solids was studied by Max von Laue and Paul Knipping, when they observed the X-ray diffraction pattern of crystals, and concluded that crystals get their structure from periodic lattices of atoms. In 1928, Swiss physicist Felix Bloch provided a wave function solution to the Schrödinger equation with a periodic potential, called the Bloch wave. Calculating electronic properties of metals by solving the many-body wavefunction is often computationally hard, and hence, approximation methods are needed to obtain meaningful predictions. 65, Walter Kohn, Pierre Hohenberg and Lu Jeu Sham proposed the density functional theory which gave realistic descriptions for bulk and surface properties of metals.

Some states of matter exhibit symmetry breaking, where the relevant laws of physics possess some symmetry that is broken. A common example is crystalline solids, which break continuous translational symmetry. Goldstone’s theorem in quantum field theory states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone bosons. Phase transition refers to the change of phase of a system, which is brought about by change in an external parameter such as temperature.

Classical phase transition occurs at finite temperature when the order of the system was destroyed. For example, when ice melts and becomes water, the ordered crystal structure is destroyed. Two classes of phase transitions occur: first-order transitions and continuous transitions. For the later, the two phases involved do not co-exist at the transition temperature, also called critical point.

Landau theory, which works in the so-called mean field approximation. However, it can only roughly explain continuous phase transition for ferroelectrics and type I superconductors which involves long range microscopic interactions. Near the critical point, the fluctuations happen over broad range of size scales while the feature of the whole system is scale invariant. Renormalization group methods successively average out the shortest wavelength fluctuations in stages while retaining their effects into the next stage.

Thus, the changes of a physical system as viewed at different size scales can be investigated systematically. Experimental condensed matter physics involves the use of experimental probes to try to discover new properties of materials. Image of X-ray diffraction pattern from a protein crystal. Several condensed matter experiments involve scattering of an experimental probe, such as X-ray, optical photons, neutrons, etc. The choice of scattering probe depends on the observation energy scale of interest. Coulomb and Mott scattering measurements can be made by using electron beams as scattering probes.

Similarly, positron annihilation can be used as an indirect measurement of local electron density. In experimental condensed matter physics, external magnetic fields act as thermodynamic variables that control the state, phase transitions and properties of material systems. Quantum oscillations is another experimental method where high magnetic fields are used to study material properties such as the geometry of the Fermi surface. Einstein condensate observed in a gas of ultracold rubidium atoms. The blue and white areas represent higher density. Ultracold atom trapping in optical lattices is an experimental tool commonly used in condensed matter physics, and in atomic, molecular, and optical physics. Einstein condensate, a novel state of matter originally predicted by S.