Bose–Hubbard modelThe Bose–Hubbard model gives a description of the physics of interacting spinless bosons on a lattice. It is closely related to the Hubbard model that originated in solid-state physics as an approximate description of superconducting systems and the motion of electrons between the atoms of a crystalline solid. The model was introduced by Gersch and Knollman in 1963 in the context of granular superconductors. (The term 'Bose' in its name refers to the fact that the particles in the system are bosonic.
Weyl semimetalWeyl fermions are massless chiral fermions embodying the mathematical concept of a Weyl spinor. Weyl spinors in turn play an important role in quantum field theory and the Standard Model, where they are a building block for fermions in quantum field theory. Weyl spinors are a solution to the Dirac equation derived by Hermann Weyl, called the Weyl equation. For example, one-half of a charged Dirac fermion of a definite chirality is a Weyl fermion. Weyl fermions may be realized as emergent quasiparticles in a low-energy condensed matter system.
Position operatorIn quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle. When the position operator is considered with a wide enough domain (e.g. the space of tempered distributions), its eigenvalues are the possible position vectors of the particle. In one dimension, if by the symbol we denote the unitary eigenvector of the position operator corresponding to the eigenvalue , then, represents the state of the particle in which we know with certainty to find the particle itself at position .
Dimensional reductionDimensional reduction is the limit of a compactified theory where the size of the compact dimension goes to zero. In physics, a theory in D spacetime dimensions can be redefined in a lower number of dimensions d, by taking all the fields to be independent of the location in the extra D − d dimensions. For example, consider a periodic compact dimension with period L. Let x be the coordinate along this dimension. Any field can be described as a sum of the following terms: with An a constant.
Extra dimensionsIn physics, extra dimensions are proposed additional space or time dimensions beyond the (3 + 1) typical of observed spacetime, such as the first attempts based on the Kaluza–Klein theory. Among theories proposing extra dimensions are: Large extra dimension, mostly motivated by the ADD model, by Nima Arkani-Hamed, Savas Dimopoulos, and Gia Dvali in 1998, in an attempt to solve the hierarchy problem. This theory requires that the fields of the Standard Model are confined to a four-dimensional membrane, while gravity propagates in several additional spatial dimensions that are large compared to the Planck scale.
Brane cosmologyBrane cosmology refers to several theories in particle physics and cosmology related to string theory, superstring theory and M-theory. Brane The central idea is that the visible, three-dimensional universe is restricted to a brane inside a higher-dimensional space, called the "bulk" (also known as "hyperspace"). If the additional dimensions are compact, then the observed universe contains the extra dimension, and then no reference to the bulk is appropriate.
Cavity optomechanicsCavity optomechanics is a branch of physics which focuses on the interaction between light and mechanical objects on low-energy scales. It is a cross field of optics, quantum optics, solid-state physics and materials science. The motivation for research on cavity optomechanics comes from fundamental effects of quantum theory and gravity, as well as technological applications. The name of the field relates to the main effect of interest: the enhancement of radiation pressure interaction between light (photons) and matter using optical resonators (cavities).
Louis de BroglieLouis Victor Pierre Raymond, 7th Duc de Broglie (də_ˈbroʊɡli, also USdə_broʊˈɡliː,_də_ˈbrɔɪ, də bʁɔj or də bʁœj; 15 August 1892 – 19 March 1987) was a French physicist and aristocrat who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis, he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave–particle duality, and forms a central part of the theory of quantum mechanics.
Pauli groupIn physics and mathematics, the Pauli group on 1 qubit is the 16-element matrix group consisting of the 2 × 2 identity matrix and all of the Pauli matrices together with the products of these matrices with the factors and : The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli. The Pauli group on qubits, , is the group generated by the operators described above applied to each of qubits in the tensor product Hilbert space .
Double-well potentialThe so-called double-well potential is one of a number of quartic potentials of considerable interest in quantum mechanics, in quantum field theory and elsewhere for the exploration of various physical phenomena or mathematical properties since it permits in many cases explicit calculation without over-simplification. Thus the "symmetric double-well potential" served for many years as a model to illustrate the concept of instantons as a pseudo-classical configuration in a Euclideanised field theory.
