Statistical mechanics Statistical mechanics In quantum field theory and statistical mechanics, the 1/N expansion is a particular perturbative analysis of quantum field theories with an SO(N) or SU(N) internal symmetry. ...more on Wikipedia about "1/N expansion"
In physics, atomic theory is a theory of the nature of matter. It states that all matter is composed of atoms. The philosophical background of the atomic theory is called atomism. The theory applies to the common phases of matter, namely solids, liquids and gasses, as directly experienced on Earth. Strictly speaking, it is not the appropriate theory for plasmas or neutron stars where unusual environments such as extremes of temperature or density prevent atoms from forming. ...more on Wikipedia about "Atomic theory"
A Bethe lattice or Cayley tree is a connected cycle-free graph where each node is connected to z neighbours, where z is called the coordination number. It can be seen as a tree-like structure emanating from a central node, with all the nodes arranged in shells around the central one. The central node may be called the root or origin of the lattice. The number of nodes in the k'th shell is given by ...more on Wikipedia about "Bethe lattice"
The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...more on Wikipedia about "Boltzmann constant"
In physics, the Boltzmann distribution predicts the distribution function for the fractional number of particles Ni / N occupying a state i with energy Ei: ...more on Wikipedia about "Boltzmann distribution"
The Boltzmann equation, devised by Ludwig Boltzmann, describes the statistical distribution of particles in a fluid. It is one of the most important equations of non-equilibrium statistical mechanics, the area of statistical mechanics that deals with systems far from thermodynamic equilibrium; for instance, when there is an applied temperature gradient or electric field. The Boltzmann equation is used to study how a fluid transports physical quantities such as heat and charge, and thus to derive transport properties such as electrical conductivity, Hall conductivity, viscosity, and thermal conductivity. ...more on Wikipedia about "Boltzmann equation"
In physics, the Boltzmann factor is a weighting factor determining the relative probability of a system in thermodynamic equilibrium at a temperature (T). ...more on Wikipedia about "Boltzmann factor"
There's a bit of shortopedia in all of us. Statistical_mechanics
An ideal Bose gas is a quantum-mechanical version of a classical ideal gas. It is composed of bosons, which have an integral value of spin, and obey Bose-Einstein statistics. The statistical mechanics of bosons were developed by Satyendra Nath Bose for photons, and extended to massive particles by Albert Einstein who realized that an ideal gas of bosons would form a condensate at a low enough temperature, unlike a classical ideal gas. This condensate is known as a Bose-Einstein condensate. ...more on Wikipedia about "Bose gas"
(Bose-Einstein statistics) :For other topics related to Einstein see Einstein (disambiguation). ...more on Wikipedia about "Bose-Einstein statistics"
A canonical ensemble in statistical mechanics is an ensemble of dynamically similar systems, each of which can share its energy with a large heat reservoir, or heat bath. Equivalently, the members of the ensemble can be considered loosely-coupled to each other so that they can share the total energy. The distribution of the total energy amongst the possible dynamical states (i.e. the members of the ensemble) is given by the partition function. A generalization of this is the grand canonical ensemble, in which the systems may share particles as well as energy. By contrast, in the microcanonical ensemble, the energy of each individual system is fixed. ...more on Wikipedia about "Canonical ensemble"
The correlation function in statistical mechanics is measure of the order in a system. ...more on Wikipedia about "Correlation function (statistical mechanics)"
In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part. The coupling constant determines the strength of the interaction part with respect to the kinetic part, or between two sectors of the interaction part. For example, the electric charge of a particle is a coupling constant. ...more on Wikipedia about "Coupling constant"
In physics, a critical point is the point of termination of a phase equilibrium curve, which separates two distinct phases. At this point, the phases are no longer distinguishable. ...more on Wikipedia about "Critical point (physics)"
This article is about physics. For other uses of the term cutoff, see cutoff (disambiguation). ...more on Wikipedia about "Cutoff"
The density matrix renormalization group (DMRG) is a numerical technique originally intended to obtain the ground state of a quantum manybody system with high accuracy. It is a variational method, and its efficiency does not decrease when the system is strongly correlated. The method has been extended to equilibrium statistical mechanics and non-equilibrium systems. Its main disadvantage is that only 1D and tree-like systems are suitable to obtain the maximum power of the method. ...more on Wikipedia about "Density matrix renormalization group"
Density of states (DOS) is a property in statistical and condensed matter physics that quantifies how closely packed energy levels are in some physical system. It is often expressed as a function g(E) of the internal energy E, or a function g(k) of the wavevector k. It is usually used with electronic energy levels in a solid. In 3 dimensions, for example, the density of states in reciprocal space ( k-space) is , where V is the volume of the solid. ...more on Wikipedia about "Density of states"
In statistical mechanics, the partition function provides a link between the microscopic properties of atoms and molecules (e.g. size, shape and characteristic energy levels) and the bulk thermodynamic properties of matter. In order to understand the partition function, how it can be derived, and why it works, it is important to recognize that these bulk thermodynamic properties reflect the average behavior of the atoms and molecules. For example, the pressure of a gas is really just the average force per unit area exerted by its particles as they collide with the container walls. It doesn't matter which particular particles strike the wall at any given time or even the force with which a given particle strikes the wall. In addition it is not necessary to consider the fluctuations in pressure as different numbers of particles hit the walls, since the magnitude of these fluctuations is likely to be extremely small. Only the average force produced by all the particles over time is important in determining the pressure. Similarly for other properties, it is the average behavior that is important. The partition function provides a way to determine the most likely average behavior of atoms and molecules given information about the microscopic properties of the material. ...more on Wikipedia about "Derivation of the partition function"
In mathematics, and in statistical mechanics in physics, a Markov process is said to show detailed balance if the transition rates between each pair of states i and j in the state space obey ...more on Wikipedia about "Detailed balance"
In theoretical physics, a disorder operator is an operator that creates a discontinuity of the ordinary order operators or a monodromy for their values. ...more on Wikipedia about "Disorder operator"
In physics, an effective field theory is an approximate theory (usually a quantum field theory) that contains the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, but ignores the substructure and the degrees of freedom at shorter distances (or, equivalently, higher energies). ...more on Wikipedia about "Effective field theory"
In physics, in kinetic theory the Einstein relation is a previously unexpected connection revealed by Einstein in his 1905 paper on Brownian motion: ...more on Wikipedia about "Einstein relation (kinetic theory)"
It's real shortopedia feeling! Statistical_mechanics
In statistical mechanics, the ensemble average is defined as the mean of a quantity that is a function of the micro-state of a system (the ensemble of possible states), according to the distribution of the system on its micro-states in this ensemble. ...more on Wikipedia about "Ensemble average"
In physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e., that all accessible microstates are equally probable over long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same. ...more on Wikipedia about "Ergodic hypothesis"
In physics, the Fermi energy (EF) of a system of non-interacting fermions is the smallest possible increase in the ground state energy when exactly one particle is added to the system. It is equivalent to the chemical potential of the system in the ground state at absolute zero. The Fermi energy is one of the central concepts of condensed matter physics. ...more on Wikipedia about "Fermi energy"
A Fermi gas is a collection of non-interacting fermions. It is the quantum mechanical version of an ideal gas, for the case of fermionic particles. Electrons in metals and semiconductors and neutrons in a neutron star can be approximately considered Fermi gases. The energy distribution of the fermions in a Fermi gas in thermal equilibrium is determined by their density, the temperature and the set of available energy states, via Fermi-Dirac statistics. By the Pauli principle, no quantum state can be occupied by more than one fermion, so the total energy of the Fermi gas at zero temperature is larger than the product of the number of particles and the single-particle ground state energy. For this reason, the pressure of a Fermi gas is nonzero even at zero temperature, in contrast to that of a classical ideal gas. This so-called degeneracy pressure stabilizes a neutron star (a Fermi gas of neutrons) or a White Dwarf star (a Fermi gas of electrons) against the inward pull of gravity. ...more on Wikipedia about "Fermi gas"
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