In theoretical physics, the hierarchy problem is the problem concerning the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 1024 times stronger than gravity.
In physics, a Feshbach resonance can occur upon collision of two slow atoms, when they temporarily stick together forming an unstable compound with short lifetime. It is a feature of many-body systems in which a bound state is achieved if the coupling(s) between at least one internal degree of freedom and the reaction coordinates, which lead to dissociation, vanish. The opposite situation, when a bound state is not formed, is a shape resonance. It is named after Herman Feshbach, a physicist at MIT.
In non-equilibrium thermodynamics, GENERIC is an acronym for General Equation for Non-Equilibrium Reversible-Irreversible Coupling. It is the general form of dynamic equation for a system with both reversible and irreversible dynamics. GENERIC formalism is the theory built around the GENERIC equation, which has been proposed in its final form in 1997 by Miroslav Grmela and Hans Christian Öttinger.
In physical cosmology, cosmological perturbation theory is the theory by which the evolution of structure is understood in the Big Bang model. Cosmological perturbation theory may be broken into two categories: Newtonian or general relativistic. Each case uses its governing equations to compute gravitational and pressure forces which cause small perturbations to grow and eventually seed the formation of stars, quasars, galaxies and clusters. Both cases apply only to situations where the universe is predominantly homogeneous, such as during cosmic inflation and large parts of the Big Bang. The universe is believed to still be homogeneous enough that the theory is a good approximation on the largest scales, but on smaller scales more involved techniques, such as N-body simulations, must be used. When deciding whether to use general relativity for perturbation theory, note that Newtonian physics is only applicable in some cases such as for scales smaller than the Hubble horizon, where spacetime is sufficiently flat, and for which speeds are non-relativistic.
The 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 model rose to prominence in the 1980s after it was found to capture the essence of the superfluid-insulator transition in a way that was much more mathematically tractable than fermionic metal-insulator models.
In physics, a quantum vortex represents a quantized flux circulation of some physical quantity. In most cases, quantum vortices are a type of topological defect exhibited in superfluids and superconductors. The existence of quantum vortices was first predicted by Lars Onsager in 1949 in connection with superfluid helium. Onsager reasoned that quantisation of vorticity is a direct consequence of the existence of a superfluid order parameter as a spatially continuous wavefunction. Onsager also pointed out that quantum vortices describe the circulation of superfluid and conjectured that their excitations are responsible for superfluid phase transitions. These ideas of Onsager were further developed by Richard Feynman in 1955 and in 1957 were applied to describe the magnetic phase diagram of type-II superconductors by Alexei Alexeyevich Abrikosov. In 1935 Fritz London published a very closely related work on magnetic flux quantization in superconductors. London's fluxoid can also be viewed as a quantum vortex.
The Gross–Pitaevskii equation describes the ground state of a quantum system of identical bosons using the Hartree–Fock approximation and the pseudopotential interaction model.
Stokesian dynamics is a solution technique for the Langevin equation, which is the relevant form of Newton's 2nd law for a Brownian particle. The method treats the suspended particles in a discrete sense while the continuum approximation remains valid for the surrounding fluid, i.e., the suspended particles are generally assumed to be significantly larger than the molecules of the solvent. The particles then interact through hydrodynamic forces transmitted via the continuum fluid, and when the particle Reynolds number is small, these forces are determined through the linear Stokes equations. In addition, the method can also resolve non-hydrodynamic forces, such as Brownian forces, arising from the fluctuating motion of the fluid, and interparticle or external forces. Stokesian Dynamics can thus be applied to a variety of problems, including sedimentation, diffusion and rheology, and it aims to provide the same level of understanding for multiphase particulate systems as molecular dynamics does for statistical properties of matter. For rigid particles of radius suspended in an incompressible Newtonian fluid of viscosity and density , the motion of the fluid is governed by the Navier–Stokes equations, while the motion of the particles is described by the coupled equation of motion:
The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to a relativistic description of bound systems in terms of quantum-mechanical wave functions. The quantization is based on the choice of light-front coordinates, where plays the role of time and the corresponding spatial coordinate is . Here, is the ordinary time, is one Cartesian coordinate, and is the speed of light. The other two Cartesian coordinates, and , are untouched and often called transverse or perpendicular, denoted by symbols of the type . The choice of the frame of reference where the time and -axis are defined can be left unspecified in an exactly soluble relativistic theory, but in practical calculations some choices may be more suitable than others.
Microrheology is a technique used to measure the rheological properties of a medium, such as microviscosity, via the measurement of the trajectory of a flow tracer. It is a new way of doing rheology, traditionally done using a rheometer. There are two types of microrheology: passive microrheology and active microrheology. Passive microrheology uses inherent thermal energy to move the tracers, whereas active microrheology uses externally applied forces, such as from a magnetic field or an optical tweezer, to do so. Microrheology can be further differentiated into 1- and 2-particle methods.
In the context of the physical and mathematical theory of percolation, a percolation transition is characterized by a set of universal critical exponents, which describe the fractal properties of the percolating medium at large scales and sufficiently close to the transition. The exponents are universal in the sense that they only depend on the type of percolation model and on the space dimension. They are expected to not depend on microscopic details such as the lattice structure, or whether site or bond percolation is considered. This article deals with the critical exponents of random percolation.
The kicked rotator, also spelled as kicked rotor, is a paradigmatic model for both Hamiltonian chaos and quantum chaos. It describes a free rotating stick in an inhomogeneous "gravitation like" field that is periodically switched on in short pulses. The model is described by the Hamiltonian
Metadynamics is a computer simulation method in computational physics, chemistry and biology. It is used to estimate the free energy and other state functions of a system, where ergodicity is hindered by the form of the system's energy landscape. It was first suggested by Alessandro Laio and Michele Parrinello in 2002 and is usually applied within molecular dynamics simulations. MTD closely resembles a number of newer methods such as adaptively biased molecular dynamics, adaptive reaction coordinate forces and local elevation umbrella sampling. More recently, both the original and well-tempered metadynamics were derived in the context of importance sampling and shown to be a special case of the adaptive biasing potential setting. MTD is related to the Wang–Landau sampling.
The Vicsek model is a mathematical model used to describe active matter. One motivation of the study of active matter by physicists is the rich phenomenology associated to this field. Collective motion and swarming are among the most studied phenomena. Within the huge number of models that have been developed to catch such behavior from a microscopic description, the most famous is the model introduced by Tamás Vicsek et al. in 1995.
In quantum field theory, and in the significant subfields of quantum electrodynamics (QED) and quantum chromodynamics (QCD), the two-body Dirac equations (TBDE) of constraint dynamics provide a three-dimensional yet manifestly covariant reformulation of the Bethe–Salpeter equation for two spin-1/2 particles. Such a reformulation is necessary since without it, as shown by Nakanishi, the Bethe–Salpeter equation possesses negative-norm solutions arising from the presence of an essentially relativistic degree of freedom, the relative time. These "ghost" states have spoiled the naive interpretation of the Bethe–Salpeter equation as a quantum mechanical wave equation. The two-body Dirac equations of constraint dynamics rectify this flaw. The forms of these equations can not only be derived from quantum field theory they can also be derived purely in the context of Dirac's constraint dynamics and relativistic mechanics and quantum mechanics. Their structures, unlike the more familiar two-body Dirac equation of Breit, which is a single equation, are that of two simultaneous quantum relativistic wave equations. A single two-body Dirac equation similar to the Breit equation can be derived from the TBDE. Unlike the Breit equation, it is manifestly covariant and free from the types of singularities that prevent a strictly nonperturbative treatment of the Breit equation.
Interatomic potentials are mathematical functions to calculate the potential energy of a system of atoms with given positions in space. Interatomic potentials are widely used as the physical basis of molecular mechanics and molecular dynamics simulations in computational chemistry, computational physics and computational materials science to explain and predict materials properties. Examples of quantitative properties and qualitative phenomena that are explored with interatomic potentials include lattice parameters, surface energies, interfacial energies, adsorption, cohesion, thermal expansion, and elastic and plastic material behavior, as well as chemical reactions.
In solid state physics, the Luttinger–Ward functional, proposed by Joaquin Mazdak Luttinger and John Clive Ward in 1960, is a scalar functional of the bare electron-electron interaction and the renormalized one-particle propagator. In terms of Feynman diagrams, the Luttinger–Ward functional is the sum of all closed, bold, two-particle irreducible diagrams, i.e., all diagrams without particles going in or out that do not fall apart if one removes two propagator lines. It is usually written as or , where is the one-particle Green's function and is the bare interaction.
Spin squeezing is a quantum process that decreases the variance of one of the angular momentum components in an ensemble of particles with a spin. The quantum states obtained are called spin squeezed states. Such states have been proposed for quantum metrology, to allow a better precision for estimating a rotation angle than classical interferometers. Recently, it was shown that these states cannot provide a better precision.
A fracton is an emergent topological quasiparticle excitation which is immobile when in isolation. Many theoretical systems have been proposed in which fractons exist as elementary excitations. Such systems are known as fracton models. Fractons have been identified in various CSS codes as well as in symmetric tensor gauge theories.
