Acoustic theory. Acoustic theory is the field relating to mathematical description of sound waves.
It is derived from fluid dynamics. See acoustics for the engineering approach. The propagation of sound waves in a fluid (such as water) can be modeled by an equation of motion (conservation of momentum) and an equation of continuity (conservation of mass). With some simplifications, in particular constant density, they can be given as follows: where is the acoustic pressure and is the acoustic fluid velocity vector, Antenna (radio) Atomic theory. BCS theory. History In 1957 Bardeen and Cooper assembled these ingredients and constructed such a theory, the BCS theory, with Robert Schrieffer.
The theory was first published in April 1957 in the letter, "Microscopic theory of superconductivity". The demonstration that the phase transition is second order, that it reproduces the Meissner effect and the calculations of specific heats and penetration depths appeared in the December 1957 article, "Theory of superconductivity". They received the Nobel Prize in Physics in 1972 for this theory. The 1950 Landau-Ginzburg theory of superconductivity is not cited in either of the BCS papers. In 1986, high-temperature superconductivity was discovered (i.e. superconductivity at temperatures considerably above the previous limit of about 30 K; up to about 130 K). Overview At sufficiently low temperatures, electrons near the Fermi surface become unstable against the formation of Cooper pairs.
More details Underlying evidence L. Dirac hole theory. Dirac hole theory is a theory in quantum mechanics, named after English theoretical physicist Paul Dirac.
The theory posits that the continuum of negative energy states, that are solutions to the Dirac equation, are filled with electrons, and the vacancies in this continuum (holes) are manifested as positrons with energy and momentum that are the negative of those of the state. The discovery of the positron in 1929 gave a considerable support to the Dirac hole theory. While Enrico Fermi, Niels Bohr and Wolfgang Pauli were skeptical about the theory, other physicists, like Guido Beck and Kurt Sitte, made use of Dirac hole theory in alternative theories of beta decay. Gian Wick extended Dirac hole theory to cover neutrinos, introducing the anti-neutrino as a hole in a neutrino Dirac sea. Landau theory. Landau theory in physics was introduced by Lev Landau in an attempt to formulate a general theory of continuous (i.e. second-order) phase transitions. Mean-field formulation (no long-range correlation) Landau was motivated to suggest that the free energy of any system should obey two conditions: it is analyticit obeys the symmetry of the Hamiltonian Given these two conditions, one can write down (in the vicinity of the critical temperature, Tc) a phenomenological expression for the free energy as a Taylor expansion in the order parameter.
Ising Model Example M-theory. M-theory is a theory in physics that unifies all consistent versions of superstring theory.
The existence of such a theory was first conjectured by Edward Witten at the string theory conference at the University of Southern California in the summer of 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Background Quantum gravity and strings Classical mechanics. Diagram of orbital motion of a satellite around the earth, showing perpendicular velocity and acceleration (force) vectors.
In physics, classical mechanics and quantum mechanics are the two major sub-fields of mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.
It is also widely known as Newtonian mechanics. Perturbation theory (quantum mechanics) In the theory of quantum electrodynamics (QED), in which the electron–photon interaction is treated perturbatively, the calculation of the electron's magnetic moment has been found to agree with experiment to eleven decimal places.
In QED and other quantum field theories, special calculation techniques known as Feynman diagrams are used to systematically sum the power series terms. The problem of non-perturbative systems has been somewhat alleviated by the advent of modern computers. It has become practical to obtain numerical non-perturbative solutions for certain problems, using methods such as density functional theory. Quantum field theory. Theory of relativity. The theory of relativity, or simply relativity in physics, usually encompasses two theories by Albert Einstein: special relativity and general relativity. Concepts introduced by the theories of relativity include: Measurements of various quantities are relative to the velocities of observers.
In particular, space contracts and time dilates.Spacetime: space and time should be considered together and in relation to each other.The speed of light is nonetheless invariant, the same for all observers. Scattering theory. Top: the real part of a plane wave travelling upwards.
Bottom: The real part of the field after inserting in the path of the plane wave a small transparent disk of index of refraction higher than the index of the surrounding medium. This object scatters part of the wave field, although at any individual point, the wave's frequency and wavelength remain intact. In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles.
Prosaically, wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow. Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil. See also String theory. String theory was first studied in the late 1960s as a theory of the strong nuclear force before being abandoned in favor of the theory of quantum chromodynamics.
Subsequently, it was realized that the very properties that made string theory unsuitable as a theory of nuclear physics made it a promising candidate for a quantum theory of gravity. Five consistent versions of string theory were developed until it was realized in the mid-1990s that they were different limits of a conjectured single 11-dimensional theory now known as M-theory. Many theoretical physicists, including Stephen Hawking, Edward Witten and Juan Maldacena, believe that string theory is a step towards the correct fundamental description of nature: it accommodates a consistent combination of quantum field theory and general relativity, agrees with insights in quantum gravity (such as the holographic principle and black hole thermodynamics) and has passed many non-trivial checks of its internal consistency.