Critical readings and discussions with them in the journal club deepened my understanding of the phenomenon of the boseeinstein condensation and made me con. We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the grosspitaevskii equation. A timesplitting spectral method for coupled grosspitaevskii. We study asymptotically and numerically the fundamental gaps i. Read stationary solutions of the grosspitaevskii equation with linear counterpart, physics letters a on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Buy lev pitaevskii ebooks to read online or download in pdf or epub on your pc, tablet or mobile device. The grosspitaevskii 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. 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. Discover book depositorys huge selection of l p pitaevskii books online. Sandro stringari lecture 4 7 mar 05 fluctuations of the order parameter previous lecture. Quantum fluctuations, bec depletion and kinetic energybeyond mean field effects on collective oscillations thermal. Pdf theory of boseeinstein condensation in trapped gases.
The mean field theory of bec is based on coupled grosspitaevskii equations nonlinear schrodinger equations with cubic nonlinear terms. This system is formed of coupled meanfield equations, which are based on coupled grosspitaevskii equations. Theory of boseeinstein condensation in trapped gases lptms. In preparation for the numerics we scale the 3d gross pitaevskii equation and obtain a fourparameter model. Senior scientist dipartimento di fisica, universita di trento tel. We present a suite of programs to determine the ground state of the timeindependent gross pitaevskii equation, used in the simulation of boseeinstein condensates. Now, polaritons are shown to condense at room temperature using a microcavity within an. Roomtemperature boseeinstein condensation of cavity exciton. Second sound and the superfluid fraction in a fermi gas. In this paper, we discuss the different splitting approaches to numerically solve the grosspitaevskii equation gpe. This book is an introductory text to the physics of boseeinstein condensation. Zambelli, momentum transferred to a trapped boseeinstein.
Sustained turbulence in the threedimensional gross. Using the linearized version of the time dependent grosspitaevskii equation, we calculate the dynamic response of a boseeinstein condensed gas to periodic density and particle perturbations. Grosspitaevskii pitaevskii gp equation macroscopic quantum wavefunction a quantum state with large number of bosons occupying the same oneparticle states can be described by a macroscopic wavefunction 0 r t, 0 r t n r t, remark. Pitaevskii ebooks to read online or download in pdf or epub on your pc, tablet or mobile device. Nonlinear phenomena on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Our approach points out the crucial role played by. Harmonic traps, effect of interactions, and grosspitaevskii equation. Unlike electrons, atoms are electrically neutral, but they can interact when they get very close and collide one with each other. Mca free fulltext comparison of splitting methods for.
Hiroaki enomoto belonging to professors ohba and nakazatos group. Fundamental gaps of the grosspitaevskii equation with. Boseeinstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 nobel prize. A first spectacular demonstration of the possibility of using cold atoms to make quantum simulation of condensedmatter models 4. Jan 23, 2019 using the linearized version of the time dependent grosspitaevskii equation, we calculate the dynamic response of a boseeinstein condensed gas to periodic density and particle perturbations. Uncertainty principle, quantum fluctuations, and broken. Apr 03, 2003 the book is an introductory text to the physics of boseeinstein condensation. The grosspitaevskii equation and the hydrodynamic expansion. Gross pitaevskii gp equation for order parameter plays role analogous to maxwell equations in classical electrodynamics. The basic idea is to make a variational ansatz for the wavefunction with free parameters, plug it into the free energy, and minimize the energy with respect to the free parameters. Pdf on dec 8, 2005, franco dalfovo and others published bose einstein. We present a suite of programs to determine the ground state of the timeindependent grosspitaevskii equation, used in the simulation of boseeinstein condensates. Wave packet dynamics for grosspitaevskii equation in one.
F using a free surface synthetic schlieren technique moisy et al. Downloaded from transformation optics using graphene. Buy stationary and time dependent grosspitaevskii equations. It is predicted analytically and verified numerically that for a free particle with attractive interaction, the dynamics of the width is governed by an effective potential which is sensitive to initial conditions. Stationary solutions of the grosspitaevskii equation with. Boseeinstein condensates of excitonpolaritons have been stabilized in a range of crystalline systems. Quantum fluctuations and grosspitaevskii theory springerlink. About launched in 2000, is a popular ebook retailer hosting over a million unique ebooks. Read sustained turbulence in the threedimensional grosspitaevskii model, physica d. Stationary and time dependent grosspitaevskii equations.
Pdf ground state of the timeindependent grosspitaevskii. I a mean eld approach leads to the gross pitaevskii equation. Uncertainty principle and offdiagonal long range order in. Conclusions i below a critical temperature t c boseeinstein condensation takes place. The calculation is based on the optimal damping algorithm, ensuring a fast convergence to the true ground state. Equation for order parameter is properly derived by replacing v with effective potential where is relevant coupling constant of problem. Providing a useful introduction to one of the most exciting field of physics today, this text will be of interest. Together with evgeny lifshitz and vladimir berestetskii. Equation for order parameter becomes grosspitaevskii. Franco dalfovo curriculum vitae first and last name. Dalfovo and others published theory of trapped bose condensed gases find, read and cite all the research. Landau damping in weakly interacting bose gases is investigated by means of perturbation theory. Quelli contrassegnati con possono essere diversi dallarticolo nel profilo. Wolfgang pauli institute 2006 thematic program januarydecember, 2006 vienna, austria contemporary mathematics on free shipping on qualified orders.
We study the numerical solution of the timedependent grosspitaevskii equation gpe describing a boseeinstein condensate bec at zero or very low temperature. Stringari, hartreefock calculations for 3he4he mixtures at zero temperature, phys. Identifying extreme parameter regimes, the model is accessible to analytical perturbation theory, which justifies formal. Applications to bose superfluids, antiferromagnets and crystals at zero temperature are discussed.
Weakly nonlinear analysis of vortex formation in a. Roomtemperature boseeinstein condensation of cavity. 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. A distinct approach pioneered by the work of stringari and collaborators 34, 21 see also ref. Pdf the grosspitaevskii equation and boseeinstein condensates. Stringari, surface state of 3he on liquid 4he, physica scripta 38, 204 1988. Stringari, macroscopic models for sound propagation in normal liquid 3he, il nuovo cimento 6 d, 445 1985 2.
Questo conteggio citato da include citazioni ai seguenti articoli in scholar. In particular scattering length a is the only relevant interaction parameter. A timesplitting spectral method for coupled grosspitaevskii equations with applications to rotating boseeinstein condensates. The grosspitaevskii equation gpe is discussed at the level of an advanced course on statistical physics. Pdf theory of trapped bosecondensed gases researchgate. 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. However, for the estimation of most experimentally relevant properties, knowledge of the reduced onebody density matrix. A natural generalization of the heisenberg uncertainty principle inequality holding for non hermitian operators is presented and applied to the fractional quantum hall effect fqhe. More on lattice bosons, longrange interactions, quantum simulators, and strong coupling theory. We discuss a natural generalization of the uncertainty inequality holding in the case of nonhermitian operators. Stringari this book is an introductory text to the physics of boseeinstein condensation. A finiteelement toolbox for the stationary grosspitaevskii. The zero temperature limit of the fluctuationdissipation theorem is used to evaluate the corresponding quantum fluctuations induced by the elementary excitations in the ground state. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext.
The ones marked may be different from the article in the profile. The grosspitaevskii equation is used to model the evolution of the boseeinstein condensate bec order parameter for weakly interacting bosons, see references 2,3,4. We study the numerical solution of the timedependent gross pitaevskii equation gpe describing a boseeinstein condensate bec at zero or very low temperature. A distinct approach pioneered by the work of stringari and collaborators 34, 21 see also. Stringari, quantum evaporation from the free surface of superfluid 4he, j. Contents 1 introduction 2 derivation of the grosspitaevskii equation the ideal bose gas in a harmonic trap formalism approximations the grosspitaevskii equation 3 applications of the grosspitaevskii equation the thomasfermi approximation perturbations to the ground state. 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. Russian, born in saratov russia january 18, 1933 s.
Boseeinstein condensation international series of monographs on physics 9780198507192. Feb 01, 2012 read sustained turbulence in the threedimensional grosspitaevskii model, physica d. Boseeinstein condensation of atomic gases phys ens. We consider conservative finitedifference schemes and spectral methods for the spatial. A 100, 023607 2019 supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas. 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. Rev a 54 1996 42 and by lundh, pethick and smith phys rev a55 1997 2126 and has the form. This inequality was used in a previous paper to prove the absence of long range order in the ground state of several 1d systems with continuous group symmetries. The models are motivated from spinor boseeinstein condensate bec. Following impact, a transient wave propagates away from the impact site at a speed of. This cited by count includes citations to the following articles in scholar. The instability occurs as a result of a linear instability of a vortex free steady state as the rotation is increased above a critical threshold.
In an ultracold, superfluid fermi gas, measurements of second sound a wave in which the superfluid and normal components of the gas oscillate in. Clarendon press, apr 3, 2003 literary criticism 382 pages. More on grosspitaevskii equation, optical lattices, and mott insulator super. The grosspitaevskii equation is a partial differential equation in space and time variables. The grosspitaevskii equation and boseeinstein condensates. The grosspitaevskii equation is discussed at the level of an advanced course on statistical physics. The propagation of an initially gaussian wave packet of width. Drag force and superfluidity in the supersolid stripe phase of a spin. This phenomenon, first predicted by einstein in 1925, has been realized experimentally in 1995 in a remarkable series of experiments whose. Versions are given for the one, two, and threedimensional equation, using either a spectral method, well suited for.
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