Theory of boseeinstein condensation in trapped gases physical. Intuitive picture of boseeinstein condensation bec. A boseeinstein condensate bec is a state of matter which is typically formed when a gas of. Starting from the simplest case with onecomponent bec of the weakly interacting bosons, we study the reduction of gpe to lower dimensions, the ground states of bec including the existence and uniqueness as well as. Extensions to nonuniform zerotemperature weakly interacting gas are due to gross 1719, ginzburg and pitaevskii 20, and pitaevskii 21.
Though the theory said such states of matter should exist, it wasnt until 1995 that eric a. Theory of bose einstein condensation in trapped gases. Bose einstein condensation remains, however, fundamental to. The idea that manyparticle states might represent the right path toward a quantum mechanical description of selfgravitating systems. The beginning of this thesis is devoted to a detailed introduction of the model which is based on an e. Quantum phase of a boseeinstein condensate with an. A new bose einstein condensate created at aalto university duration. Related content bose einstein condensates boris b kadomtsev and mikhail b kadomtsevhamiltonian formalism for nonlinear waves v e zakharov and evgenii a. Providing a useful introduction to one of the most exciting field of physics today, this text will be of interest to a growing community of physicists, and is easily accessible to nonspecialists alike.
Microscopic theory of boseeinstein condensation of. Boseeinstein condensates are an ideal testing ground for quantum field theory in real time and at finite temperatures basic topics of great importance for diverse physics systems. Soon after, the bose einstein condensate bec idea is extended to the whole interior and the gravostar solution is discussed 21. Starting from the simplest case with onecomponent bec of the weakly interacting bosons, we study the reduc. Starting from the simplest case with bec of weakly interacting bosons, we study the reduction of gpe to lower dimensions.
Pdf the theory of boseeinstein condensation of dilute gases. Could a black hole be a boseeinstein condensate of gravitons. Object eld equation of motion particle energy momentum wavelength dispersion relation optics atomic physics. Einstein, 1924, 1925 was observed in 1995 in a remarkable series of experiments on vapors of rubidium anderson et al. Theory of boseeinstein condensation in trapped gases. Einstein 192425 extended bose s idea to material particles predicted bec in an ideal quantum gas.
I acknowledge the use of materials and slides from w. Massive bosons consider a gas of massive, noninteracting, nonrelativistic, identical, spin0 bosons. Bose einstein condensation bec theory by einstein in 1925 based on the work by bose on photons in 1924 was finally observed in 1995 in lasercooled magnetically trapped ultracold bosonic atomic clouds with 3787 nuclei1. Mathematical theory and numerical methods for bose. We consider the case of spinless bosons so there is no spin factor in the density of states of section 4. Fundamental concepts of boseeinstein condensation this chapter introduces several key features associated with the bose einstein condensation bec phase transition. Perhaps the most striking feature of quantum mechanical theory is the fact. The history of the bose einstein condensate bec is considered from einstein s original conception, to londons revival with respect to superfluid 4he and to an explanation of todays concept of the bec as a result of broken gauge.
The book is meant to be introductory, but the authorsworld experts in transport phenomenaoffer sophisticated discussions of such nonequilibrium. It is thought to have played a part in the evolution of the early universe when the particles and forces formed, and the outer layers of a neutron star may well consist of a bec of exotic subatomic particles. Cambridge core condensed matter physics, nanoscience and mesoscopic physics universal themes of boseeinstein condensation edited by nick p. At low temperatures, bosons behave differently from fermions which obey the fermidirac statistics in a way that an unlimited number of them can condense into the same energy state. This apparently unusual property also gives rise to the special state of matter the bose einstein condensate. The early experiments on bose einstein condensation in dilute atomic gases accomplished three longstanding goals. Boseeinstein condensation in 1, 2 and 3 dimensions for. Universal themes of boseeinstein condensation edited by. But in bose condensation, the wave nature of each atom is precisely in phase with that of every other. It is an excellent text, a broad survey with some indepth discussions. The phenomenological theory, on the other hand, carries little signature of its microscopic origin, but the theory has turned out to be eminently suitable to describe the physics of space and timedependent superconductivity. K kelvin, coalesce into a single quantum mechanical entitythat is, one that can be described by a wave functionon a nearmacroscopic scale. Quantummechanical waves extend across the sample of condensate and can be observed with the naked eye.
Open symbols show the relative depth of the spatial modulation of the bls. Generalized theory of boseeinstein condensation nuclear fusion for hydrogenmetal system yeong e. Einstein generalized boses theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted. Kim journal of condensed matter nuclear science 4 2011 188201. Boseeinstein condensation a state of matter in which atoms or particles are chilled to such low energies that they condense into a single quantum state. It seems more plausible that the gravitons inside a black hole may be in a bose einstein condensate state than that everything inside a black hole is a boseeinstein condensate of gravitons. Generalized theory of boseeinstein condensation nuclear. Starting from the simplest case with onecomponent bec of the weakly interacting bosons, we study the reduction of gpe to lower dimensions, the. Boseeinstein condensation network theory wikipedia. Bose einstein condensation theory gases materials science. The theory of real systems with boseeinstein condensate was advanced by bogolubov 16 who considered uniform weakly nonideal.
Meanfield theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Pdf in 1924 bose introduced a counting rule for the states of a gas of photons which explained plancks law for thermal radiation at one stroke. Bose einstein condensation is a fundamental phenomenon of nature. Boseeinstein condensation in 1, 2 and 3 dimensions for massive and massless bosons in a box i. New light on old paradoxes the creation of bose einstein con. Boseeinstein condensate bec, a state of matter in which separate atoms or subatomic particles, cooled to near absolute zero 0 k. Chapter 3 boseeinstein condensation of an ideal gas pdf 281kb. Bose 1924 quantum statistical treatment of photons. The rst theoretical description of boseeinstein condensation bec in an ideal gas dates from 1924, when einstein published his articles on the quantum the ory of an ideal gas. Ketterle nobel lecture 2001 and his talk given at mits teachers program 240603.
Numerical analysis of boseeinstein condensation in a. Bose einstein condensation with neutral atoms, there was another possibility. Boseeinstein condensate theory of deuteron fusion in metal. Extensions to nonuniform zerotemperature weakly interacting gas are due to gross 1719, ginzburg and. Boseeinstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 nobel prize. Kim department of physics purdue university west lafayette, indiana 47907, usa june 18, 2011 abstract generalized theory of boseeinstein condensation nuclear fusion becnf is used to carry out. This phase transition predicts a winnertakesall phenomena in complex networks and can be mathematically mapped to the mathematical model explaining boseeinstein condensation in physics. Filled symbols show the average bls intensity proportional to the total density of the condensate. Superfluid helium4 is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong. The theory of real systems with boseeinstein condensate was advanced by bogolubov 16 who considered uniform weakly nonideal lowtemperature bose gas. Pdf theory of boseeinstein condensation in trapped gases.
The subjects we will study in this chapter include an order parameter, spontaneous. Wieman 1995 produced the rst gaseous condensate nobel price of physics 2001. Moreover, quantitative theoretical predictions can be made for comparison with such experiments. The theory of boseeinstein condensation of dilute gases. Growth dynamics of a boseeinstein condensate in a dimple. Kim department of physics purdue university west lafayette, indiana 47907, usa june 18, 2011 abstract generalized theory of boseeinstein condensation nuclear fusion. Analysis of some classical and quantum aspects of black. Nevertheless, such a mathematical model provides the simplest example for the realization of bose einstein condensation. Boseeinstein condensation in this section we discuss the thermodynamic properties of the ideal bose gas. Development of boseeinstein condensate theory of deuteron fusion in metal is based upon a single hypothesis that deuterons in metal are mobile and hence are capable of forming bose einstein condensates. Boseeinstein condensation in dilute gases will be useful to newcomers to the field and will help researchers with diverse backgrounds communicate with each other.