 | A major contributor to this article appears to have a close connection with its subject.(December 2011) |
Peter Kramer (born 1933 in Quedlinburg) is a German physicist.
| A major contributor to this article appears to have a close connection with its subject.(December 2011) |
Peter Kramer (born 1933 in Quedlinburg) is a German physicist.
Kramer studied physics at the University of Münster, the University of Tübingen, the University of Bristol and the University of Marburg. He received his PhD in 1964 in Marburg and in 1968 his Habilitation in Tübingen. He was a postdoc at the UNAM in Mexico City, where he collaborated with Marcos Moshinsky. He was a professor at the Institute for Theoretical Physics in Tübingen from 1970 until 1998 when he retired. He has also served as a Dean and a Vice President at the University of Tübingen. Kramer married in 1962 and has two children.
Kramer's work is concerned with applications of groups and representations in mathematical physics. His early work was in nuclear physics. In the early eighties he and his student Roberto Neri developed a mathematical model for quasiperiodic tesselations of three-dimensional space. Their paper was submitted in 1983 and published in 1984, [1] the same year that Dan Shechtman and his co-workers announced the experimental discovery of an alloy with icosahedral quasi-crystalline structure. [2] [3] Shechtman was awarded the 2011 Nobel Prize in chemistry for his work.
More recently, Kramer has become interested in cosmology and three-dimensional space forms. His scientific œuvre contains more than 200 publications. [4]
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the subject deals with "condensed" phases of matter: systems of many constituents with strong interactions between them. More exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theories to develop mathematical models.
The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces, and operators on these spaces. In brief, values of physical observables such as energy and momentum were no longer considered as values of functions on phase space, but as eigenvalues; more precisely as spectral values of linear operators in Hilbert space.
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold.
Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P, and T that is observed to be an exact symmetry of nature at the fundamental level. The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.
Quantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?" The correspondence principle states that classical mechanics is the classical limit of quantum mechanics, specifically in the limit as the ratio of Planck's constant to the action of the system tends to zero. If this is true, then there must be quantum mechanisms underlying classical chaos. If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, how can exponential sensitivity to initial conditions arise in classical chaos, which must be the correspondence principle limit of quantum mechanics?
The year 1984 in science and technology involved some significant events.
An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types is aperiodic if copies of these tiles can form only non-periodic tilings.
Paul Joseph Steinhardt is an American theoretical physicist whose principal research is in cosmology and condensed matter physics. He is currently the Albert Einstein Professor in Science at Princeton University, where he is on the faculty of both the Departments of Physics and of Astrophysical Sciences.
In theoretical physics, thermal quantum field theory or finite temperature field theory is a set of methods to calculate expectation values of physical observables of a quantum field theory at finite temperature.
Dan Shechtman is the Philip Tobias Professor of Materials Science at the Technion – Israel Institute of Technology, an Associate of the US Department of Energy's Ames National Laboratory, and Professor of Materials Science at Iowa State University. On April 8, 1982, while on sabbatical at the U.S. National Bureau of Standards in Washington, D.C., Shechtman discovered the icosahedral phase, which opened the new field of quasiperiodic crystals.
In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. The system cannot lose energy to the environment and come to rest because it is already in its quantum ground state. Because of this, the motion of the particles does not really represent kinetic energy like other motion; it has "motion without energy". Time crystals were first proposed theoretically by Frank Wilczek in 2012 as a time-based analogue to common crystals – whereas the atoms in crystals are arranged periodically in space, the atoms in a time crystal are arranged periodically in both space and time. Several different groups have demonstrated matter with stable periodic evolution in systems that are periodically driven. In terms of practical use, time crystals may one day be used as quantum computer memory.
Alan Lindsay Mackay FRS is a British crystallographer, born in Wolverhampton.
An icosahedral twin is a nanostructure appearing for atomic clusters and also nanoparticles with some thousands of atoms. These clusters are twenty-faced, made of twenty interlinked tetrahedra crystals, typically joined along triangular faces having three-fold symmetry. One can think of their formation as a kind of atom-scale self-assembly. A related, more common structure has five units similarly arranged with twinning, which were known as "fivelings" in the 19th century, more recently as "decahedral multiply twinned particles", "pentagonal particles" or "star particles". A variety of different methods lead to icosahedral form at size scales where surface energies are more important those from the bulk.
Laurie Mark Brown is an American theoretical physicist and historian of quantum field theory and elementary particle physics.
In solid state physics, the magnetic space groups, or Shubnikov groups, are the symmetry groups which classify the symmetries of a crystal both in space, and in a two-valued property such as electron spin. To represent such a property, each lattice point is colored black or white, and in addition to the usual three-dimensional symmetry operations, there is a so-called "antisymmetry" operation which turns all black lattice points white and all white lattice points black. Thus, the magnetic space groups serve as an extension to the crystallographic space groups which describe spatial symmetry alone.
Theo Willem Jan Marie Janssen, better known as Ted Janssen, was a Dutch physicist and Full Professor of Theoretical Physics at the Radboud University Nijmegen. Together with Pim de Wolff and Aloysio Janner, he was one of the founding fathers of N-dimensional superspace approach in crystal structure analysis for the description of quasi periodic crystals and modulated structures. For this work he received the Aminoff Prize of the Royal Swedish Academy of Sciences in 1988 and the Ewald Prize of the International Union of Crystallography in 2014. These achievements were merit of his unique talent, combining a deep knowledge of physics with a rigorous mathematical approach. Their theoretical description of the structure and symmetry of incommensurate crystals using higher dimensional superspace groups also included the quasicrystals that were discovered in 1982 by Dan Schechtman, who received the Nobel Prize in Chemistry in 2011. The Swedish Academy of Sciences explicitly mentioned their work at this occasion.
Denis Gratias, born on 22 September 1947 in Paris (France) is a French scientist, emeritus research director at the CNRS. His speciality is materials science, in particular crystallography. Since the discovery of quasicrystals by Dan Shechtman in 1982, he has contributed to their description, notably by developing theoretical models. He is a correspondent member at the French Academy of Sciences since 1994.
Max Dresden was a Dutch-American theoretical physicist and historian of physics. He is known for his research in "statistical mechanics, superconductivity, quantum field theory, and elementary particle physics."
Werner Fischer is a German mineralogist and mathematical crystallographer.
Dov I. Levine is an American-Israeli physicist, known for his research on quasicrystals, soft condensed matter physics, and statistical mechanics out of equilibrium.
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