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. Conclusions i below a critical temperature t c bose einstein condensation takes place. I a mean eld approach leads to the grosspitaevskii equation which has to be ful lled by the singleparticle wave functions in order to minimize the total energy in the system. Gross pitaevskii equation for the order parameter and beyond cnrinfm. Numerical solution of the grosspitaevskii equation for. 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. Only 50% of pairs are bose einstein condensed at zero temperature strongly interacting gas. This phase transition predicts a winnertakesall phenomena in complex networks and can be mathematically mapped to the mathematical model explaining boseeinstein condensation in physics. We show that spatial bose einstein condensation of noninteracting bosons occurs in dimension d 2 over discrete structures with inhomogeneous topology and with no need of external confining potentials. It makes special reference to the physics of ultracold atomic gases. Grosspitaevskii dynamics for boseeinstein condensates. Apr 03, 2003 the book is an introductory text to the physics of bose einstein condensation. Conclusions i below a critical temperature t c boseeinstein condensation takes place.
Boseeinstein condensation and superfluidity paperback. Numerical simulations for boseeinstein condensation bec cdn. Boseeinstein condensation bec refers to a prediction of quantum statistical. Stringari this book is an introductory text to the physics of boseeinstein condensation. Nov 20, 2015 bose einstein condensation vulgarisation. A faster way to make boseeinstein condensates mit news. In this chapter, wave turbulence wt in boseeinstein condensates bec and nonlinear optics is considered.
We study the numerical solution of the timedependent grosspitaevskii equation gpe describing a boseeinstein condensate bec at zero or very low temperature. I a mean eld approach leads to the gross pitaevskii equation. Boseeinstein condensation in inhomogeneous josephson. Computing ground states of spin2 boseeinstein condensates. Theory of boseeinstein condensation in trapped gases lptms. Boseeinstein condensation, journal of research of the. Pdf theory of boseeinstein condensation for trapped atoms. Equation for order parameter is properly derived by replacing v with effective potential where is relevant coupling constant of problem. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum phenomena, particularly wavefunction interference. The authors also make sense of key experiments from the past twenty years with a.
Ultracold atomic gases is a rapidly developing area of physics that attracts many young researchers around the world. Boseeinstein condensation of strontium, simon stellmer, meng khoon tey, bo huang, rudolf grimm, and florian schreck phys. Lecture 20 bose einstein condensation in an ideal bose gas. This phenomenon, first predicted by einstein in 1925, has been realized experimentally in 1995 in a remarkable series of experiments whose importance has been recognized by the award of the 2001 nobel prize in physics. Boseeinstein condensation in 1924 published in 1925, einstein predicted a novel kind of condensation in a gas of noninteracting bosons he considered n particles in a box of volume v and reasoned that the number of particles in the lowest quantum state p 0 would. The obtained results give an opportunity to investigate the dynamics of solitons under the action of various perturbations. Smith, boseeinstein condensation in dilute bose gases, cambridge university press 2002 l. Various properties of these systems are discussed, including the density profiles and the energy of the ground state configurations, the. Bose einstein condensation is a fundamental phenomenon of nature. The averaged lagrangian of solitons of the boseeinstein condensation is determined. The aim of the infmcnr research and development center on boseeinstein condensation bec is to promote theoretical research on the various phenomena related to boseeinstein condensation and to the physics of cold atomic gases in traps. Boseeinstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 nobel prize. In a fermi gas, boseeinstein condensation of pairs was measured by ramping the scattering length to the bec side and detecting the resulting bimodal distribution condensation of pairs measured at unitarity 1a0 as a function of temperature.
Lecture 23 classical nonideal gas the mayer cluster expansion. Boseeinstein condensation bec is a phase transition where a. Pdf theory of boseeinstein condensation in trapped gases. This phenomenon, first predicted by einstein in 1925 has been realized experimentally in 1995 in a remarkable series of experiments whose importance has been recognized by the award of the 2001 nobel prize in physics.
Boseeinstein condensation in networks is a phase transition observed in complex networks that can be described by the bianconibarabasi model. A good reference is the book boseeinstein condensation in. In preparation for the numerics we scale the 3d grosspitaevskii equation and obtain a fourparameter model. Bose 1924 quantum statistical treatment of photons i a. Boseeinstein condensation in 1, 2 and 3 dimensions for. Gross pitaevskii gp equation for order parameter plays role analogous to maxwell equations in classical electrodynamics. Stringari approximate solutions of the nonlinear schrodinger equation for ground and excited states of boseeinstein condensates 165 kb r. Grosspitaevskii dynamics of boseeinstein condensates and. A boseeinstein condensate bec is a state of matter also called the fifth state of matter which is typically formed when a gas of bosons at low densities is cooled to temperatures very close to absolute zero 273. Lectures on the boseeinstein condensation valentin a. Analytic solution of grosspitaevskii equation tsuzuki, 1971 maximum soliton velocity v fixed by sound velocity c. Dodd zerotemperature, meanfield theory of atomic boseeinstein condensates 298 kb. Various theoretical approaches to describing the physics of interacting bosons and of interacting fermi gases, giving rise to.
Einstein 192425 extended bose s idea to material particles predicted bec in an ideal quantum gas i w. Boseeinstein condensation in 1, 2 and 3 dimensions for massive and massless bosons in a box i. Einstein, 1924, 1925 was observed in 1995 in a remarkable series of experiments on vapors of rubidium anderson et al. Series of monographs on physics oxford university press 2003 theory of boseeinstein condensation in trapped gases. Fermidirac and bose einstein statistics basic introduction duration. This book is an introductory text to the physics of bose einstein condensation. Width of the soliton fixed by healing length width becomes larger and larger as v approaches the sound velocity energy of moving soliton. This file is licensed under the creative commons attributionshare alike 3. This volume introduces the basic concepts of boseeinstein condensation and superfluidity. Analytic solution of gross pitaevskii equation tsuzuki, 1971 maximum soliton velocity v fixed by sound velocity c. Physics stack exchange is a question and answer site for active researchers, academics and students of physics.
Fermi, varenna, july 2008 boseeinstein 1925 the idea is that something happens, similar to the isothermal compression of a vapor across the saturation. Meanfield theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Boseeinstein condensation is a fundamental phenomenon of nature. Boseeinstein 1925 the idea is that something happens, similar to the isothermal compression of a vapor across the saturation volume. Boseeinstein condensation network theory wikipedia. Stringari this book is an introductory text to the physics of bose einstein condensation. Theory of boseeinstein condensation in trapped gases. Stringari boseeinstein condensation, oxford university press 2003 systematically employed in this course. Equation for order parameter becomes grosspitaevskii. Dynamics of boseeinstein condensates in trapped atomic. We introduce the concept of a bosonic spin liquid condensate slc, where spinful bosons in a lattice form a boseeinstein condensate bec which is a total spin singlet and does not break the spin rotation symmetry. Dodd zerotemperature, meanfield theory of atomic boseeinstein condensates 298 kb mark edwards, r.
Sandro stringari university of trento 1 introduction to boseeinstein condensation 3. Smith, boseeinstein condensation in dilute gases, cambridge university, 01 complexvalued wave function. Models considered include 2d and 3d gross pitaevskii equations, nordheim quantum kinetic equation, boltzmann equation and 1d nonlinear equation for optical wt in nematic liquid crystals. Boseeinstein condensation of an ideal gas an ideal gas consisting of noninteracting bose particles is a. Boseeinstein condensates confined in traps exhibit unique features which have been the object of extensive experimental and theoretical studies in the last few years. At a hair above absolute zero, previously frenetic atoms morph into an almost zombielike state, moving as one wavelike formation, in a quantum form of matter known as a boseeinstein condensate. The book is an introductory text to the physics of boseeinstein condensation. Lecture 22 superfluid 4 he, bec in trapped atomic gases, classical gas with internal degrees of freedom. Stringari boseeinstein condensation, oxford university press 2003 ultracold atomic fermi gases e. In this paper i will discuss some issues concerning the behaviour of the order parameter and the dynamic and superfluid effects exhibited by such systems. Boseeinstein condensation in this section we discuss the thermodynamic properties of the ideal bose gas. Models considered include 2d and 3d grosspitaevskii equations, nordheim quantum kinetic equation, boltzmann equation and 1d nonlinear equation for optical wt in nematic liquid crystals. The interacting bose gas with repulsive potential is considered in the polymer representation and some of the yet unsolved mathematical questions for establishing the existence of bose condensation in this setting are discussed. In a related context, dilute boseeinstein condensates bec have been recently produced experimentally 57.
Smith, boseeinstein condensation in dilute gases, cambridge university, 01. Written by world renowned experts in the field, this book gives a comprehensive overview of exciting developments in bose einstein condensation and superfluidity from a theoretical perspective. Boseeinstein condensation in inhomogeneous josephson arrays. The condensate is actually a new state of matter, where quantummechanical wave functions. A good reference is the book bose einstein condensation in dilute gases by pethick and smith. Grosspitaevskii equation in boseeinstein condensates. Bose einstein condensate plural bose einstein condensates. Only 50% of pairs are boseeinstein condensed at zero temperature strongly interacting gas. Pitaevskii is a researcher at the cnr trento research center on boseeinstein condensation and at the kapitza institute for physical problems in moscow. Massive bosons consider a gas of massive, noninteracting, nonrelativistic, identical, spin0 bosons.
Sandro stringari university of trento 1 introduction to boseeinstein condensation 4. In this chapter, wave turbulence wt in bose einstein condensates bec and nonlinear optics is considered. Providing a useful introduction to one of the most exciting field of physics today, this text will be of interest. We consider the case of spinless bosons so there is no spin factor in the density of states of section 4. Josephson junction arrays provide a physical realization of this mechanism. You may do so in any reasonable manner, but not in. The dynamics of these compressible nonlinear quantum. We show that spatial boseeinstein condensation of noninteracting bosons occurs in dimension d 2 over discrete structures with inhomogeneous topology and with no need of external confining potentials. Wieman 1995 produced the rst gaseous condensate nobel price of physics 2001 about bose einstein condensation bec history of bec 4 28 c. In a fermi gas, bose einstein condensation of pairs was measured by ramping the scattering length to the bec side and detecting the resulting bimodal distribution condensation of pairs measured at unitarity 1a0 as a function of temperature. Written by world renowned experts in the field, this book gives a comprehensive overview of exciting developments in boseeinstein condensation and superfluidity from a theoretical perspective. Pdf the phenomenon of boseeinstein condensation of dilute gases in. The total number of bosons in a given state with energy is given by n z. This book is an introductory text to the physics of boseeinstein condensation.
Bose einstein condensate bec, a state of matter in which separate atoms or subatomic particles, cooled to near absolute zero 0 k. Bose einstein condensates portant, since bec in lower dimensions is not as simple as in 3d. Boseeinstein condensation in trapped gases university of illinois. Numerical simulations for boseeinstein condensation bec. Since the first boseeinstein condensates were successfully produced in 1995 by researchers in colorado and by wolfgang ketterle and colleagues at. Boseeinstein condensation and superfluidity international. Lecture 21 bose einstein condensation specific heat and entropy. Fermidirac and boseeinstein statistics basic introduction duration.