Mathematical theory and numerical methods for boseeinstein. Boseeinstein condensation and boseeinstein condensation in dilute gases both cover the basic theory at the level of the grosspitaevskii and bogoliubovde gennes equations. Derivation of the grosspitaevskii equation for the dynamics of. Stringari boseeinstein condensation, oxford university press 2003 systematically employed in this course. These atoms then all achieve a collective quantum state, similar to a huge quantum wave, called the boseeinstein condensate. Roomtemperature boseeinstein condensation of cavity. Dynamics of collapsing and exploding boseeinstein condensates. Physicists are able to cool some gases down to less than onemillionth of a degree above absolute zero by stopping their atoms with lasers and magnetic fields. Mar 14, 2002 the early experiments on boseeinstein condensation in dilute atomic gases accomplished three longstanding goals.
But pitaevskii and stringari s book places less emphasis on what one might call the. The gross pitaevskii equation is discussed at the level of an advanced course on statistical physics. The main aim of this paper is to study the bifurcation solutions associated with the spinor bose einstein condensates. The new numerical method is explicit, unconditionally stable, time reversible, time transverse invariant, and of spectral accuracy in space and second. Grosspitaevskii equation in boseeinstein condensates. From the timedependent grosspitaevskii equation we can look at the dynamics of the boseeinstein condensate. The early experiments on boseeinstein condensation in dilute atomic gases accomplished three longstanding goals.
Below t c,thecondensatepopula tionvarieswithtemperatureas n0 n 1. Bose in 1924 predicted a different statistics for the light quanta and derived plancks radiation formula through very simple arguments. The boseeinstein condensate bec is a macroscopic quantum state of matter. But pitaevskii and stringari s book places less emphasis on what one might call the atomic physics aspects of dilute alkali gases. Your story matters citation erdos, laszlo, benjamin schlein, and horngtzer yau. 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. Conclusions i below a critical temperature t c boseeinstein condensation takes place. Boseeinstein condensate bec, a state of matter which is formed by cooling a gas of extremely low density,about one hundred thousandth the density of normal air,to super low temperatures. Evolution of cosmological perturbations in boseeinstein. Variational solutions of the grosspitaevskii equations vctor m. Derivation of the grosspitaevskii equation for the dynamics. Boseeinstein condensation bec refers to a prediction of quantum statistical.
Linear response theory for gross pitaevskii equation. The gross pitaevskii equation and boseeinstein condensates 249 of the system is the creation of vortices, which can be seen as small twisters inside the liquid that behave quite differently. Boseeinstein condensates bec have been reported in li, rb, and na atoms. 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. The oneparticle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the gp minimizer.
Russian, born in saratov russia january 18, 1933 s. At very low temperatures, all particles in a dilute bose gas condense to the same quantum ground state, forming a boseeinstein condensate bec, i. Since the grosspitaevskii equation is a nonlinear partial differential equation, exact solutions are hard to come by. Under investigation in this paper is a variablecoefficient grosspitaevskii equation which describes the boseeinstein condensate. First, cooling of neutral atoms into their motional ground state, thus. Now, polaritons are shown to condense at room temperature using a microcavity within an. Basic meanfield theory for boseeinstein condensates. Boseeinstein condensation and superfluidity ebook, 2016. Assuming the unscaled potential to be sufficiently weak, we prove complete boseeinstein condensation for the ground state and for manybody states with finite excitation energy in the limit of large n with a uniform. About bose einstein condensation bec history of bec 4 28 c stefan kienzle. Based on the principle of hamilton dynamics and the principle of lagrangian dynamics, a general pattern formation equation for the spinor boseeinstein condensates is established. Based on the principle of hamilton dynamics and the principle of lagrangian dynamics, a general pattern formation equation for the spinor bose einstein condensates is established. Pitaevskii, sandro stringari from waterstones today. Nowadays, one of the most spectacular research is devoted to discuss the dynamics of bec and the appearance of solitons.
Providing a useful introduction to one of the most exciting field of physics today, this text will be of interest. Meanfield theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Einstein 192425 extended boses idea to material particles. The oneparticle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by. Stringari, bose einstein condensation clarendon press.
Gross pitaevskii equation in bose einstein condensates. Conclusions i below a critical temperature t c bose einstein condensation takes place. Boseeinstein condensation in this section we discuss the thermodynamic properties of the ideal bose gas. It is used to find the collective modes of a trapped gas. Lev pitaevskii, senior researcher, university of trento,sandro stringari, professor of theoretical physics, university of trento lev p. I a mean eld approach leads to the gross pitaevskii equation. 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. Theory of boseeinstein condensation in trapped gases, rev. The grosspitaevskii equation, also called the nonlinear schrodinger equation nlse, describes the dynamics of lowtemperature superflows and boseeinstein condensates bec. Bose 1924 quantum statistical treatment of photons i a. Roomtemperature boseeinstein condensation of cavity exciton. Boseeinstein condensation and superfluidity international. Ultracold atomic gases is a rapidly developing area of physics that attracts many young researchers around the world.
Pitaevskii is a researcher at the cnr trento research center on boseeinstein condensation and at the kapitza institute for physical problems in moscow. Citation erdos, laszlo, benjamin schlein, and horngtzer yau. We consider the case of spinless bosons so there is no spin factor in the density of states of section 4. We study the numerical solution of the timedependent gross pitaevskii equation gpe describing a bose einstein condensate bec at zero or very low temperature. Ultracold atomic gases is a rapidly developing field of physics that attracts many young researchers around the world. Complete boseeinstein condensation in the grosspitaevskii. We propose a timesplitting spectral method for the coupled grosspitaevskii equations, which describe the dynamics of rotating twocomponent boseeinstein condensates at a very low temperature. 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. This book gives a comprehensive overview of exciting developments in bose einstein condensation and superfluidity from a theoretical perspective and makes sense of key experiments with a special focus on ultracold atomic gases.
Linesoliton dynamics and stability of boseeinstein. We study the numerical solution of the timedependent grosspitaevskii equation gpe describing a boseeinstein condensate bec at zero or very low temperature. Grosspitaevskii dynamics of boseeinstein condensates and. About boseeinstein condensation bec history of bec 4 28 c stefan kienzle. These describe a boseeinstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate. Introduction to boseeinstein condensation 6 andthecriticaltemperature tc. In a related context, dilute boseeinstein condensates bec have been recently produced experimentally 57. In the standard literature the gross pitaevskii equation is usually obtained in the framework of the second quantisation formalism, which in many cases goes beyond the material covered in many advanced undergraduate courses. Nonautonomous solitons in terms of the double wronskian. Boseeinstein condensation and superfluidity international series. We observe that one can increase the density of the condensates or line solitons by suitably tuning the trap frequency even for constant scattering lengths. Explicit solutions to an effective grosspitaevskii equation.
An effective grosspitaevskii equation, which describes the dynamics of quasionedimensional boseeinstein condensates in specific potential traps, is considered, and new families of exact solutio. They can slow light down to the residential speed limit, flow without friction. Derivation of the grosspitaevskii equation for the dynamics of boseeinstein condensate the harvard community has made this article openly available. The book is an introductory text to the physics of boseeinstein condensation. Boseeinstein condensation in a dilute, trapped gas at. Various properties of these systems are discussed, including the density profiles and the energy of the ground state configurations, the. Get your kindle here, or download a free kindle reading app.
A timesplitting spectral method for coupled grosspitaevskii. Some of the assumptions of the gross pitaevskii equation gpe are. Satyendra nath bose first sent a paper to einstein on the quantum statistics of light quanta now called photons, deriving plancks quantum radiation law without any reference to classical physics, and einstein was impressed, translated the paper himself from english to german and submitted it for bose to the zeitschrift fur physik, which published it. This phenomenon, first predicted by einstein in 1925 has been. The grosspitaevskii equation and boseeinstein condensates. Boseeinstein condensates of excitonpolaritons have been stabilized in a range of crystalline systems.
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 condensates of dilute gases offer a rich field to study. A coherent state develops when the particle density is sufficiently high or the temperature is sufficiently low. In the standard literature the gpe is usually obtained in the framework of the second quantization formalism, which in many cases goes beyond the material covered in many advanced undergraduate courses.
Click and collect from your local waterstones or get free uk delivery on orders over. Clarendon press, apr 3, 2003 literary criticism 382 pages. Theory of boseeinstein condensation in trapped gases. Boseeinstein condensation international series of monographs on physics 1st edition. I a mean eld approach leads to the grosspitaevskii equation. Part i introduces the notion of bec and superfluidity in general terms. This book gives a comprehensive overview of exciting developments in boseeinstein condensation and superfluidity from a theoretical perspective and makes sense of key experiments with a special focus on ultracold atomic gases. Grosspitaevskii dynamics for boseeinstein condensates. Variational solutions of the grosspitaevskii equations v. In preparation for the numerics we scale the 3d gross pitaevskii equation and obtain a fourparameter model. Bifurcation solutions of grosspitaevskii equations for spin. Numerical solution of the grosspitaevskii equation for bose. These describe a bose einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate. Properties of vortices in boseeinstein condensates sciencedirect.
Boseeinstein condensation and superfluidity paperback. Stringari this book is an introductory text to the physics of boseeinstein condensation. Boseeinstein condensate is a rare state or phase of matter in which a large percentage of bosons collapse into their lowest quantum state, allowing quantum effects to be observed on a. This book is an introductory text to the physics of boseeinstein condensation. Aug 30, 2018 we also prove boseeinstein condensation in the following sense. They are effectively super atoms, groups of atoms that behave as one. Gross pitaevskii dynamics for bose einstein condensates. The authors also make sense of key experiments from the past twenty years with a. The grosspitaevskii equation gpe is discussed at the level of an advanced course on statistical physics. The main aim of this paper is to study the bifurcation solutions associated with the spinor boseeinstein condensates.
In preparation for the numerics we scale the 3d grosspitaevskii equation and obtain a fourparameter model. Boseeinstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 nobel prize. Boseeinstein condensation and superfluidity international series of monographs on physics 1st edition. The former work considers the case of simple integrator sde dynamics for a particular class of mfgs, which shows strong analogies with the nonlinear schrodinger and explicitly treating the grosspitaevskii equation. Derivation of the grosspitaevskii equation for the dynamics of boseeinstein condensate. Assuming the unscaled potential to be sufficiently weak, we prove complete boseeinstein condensation for the ground state and for manybody states with finite excitation energy in the limit of large n with a. This book is an introductory text to the physics of bose einstein condensation. Some of the assumptions of the grosspitaevskii equation gpe are.
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