Dalfovo and stringari developed a finitedifference based method for solving the timeindependent gpe both for the ground state, and the vortex states, in anisotropic traps. In this case, from simple dimensional arguments, the groundstate energy. Bcs to bec crossover and the unitarity fermi gas mohit. Associate pdf files to always open in reader or acrobat on. The gpe is a nonlinear schrodingerlike equation, including here a. Since the model produces the correct sound velocity, it correctly describes the long wavelength part of the excitation spectrum.
An introduction to the mathematical theory of quantum fluids paolo antonelli gran sasso science institute paolo. Sandro stringari university of trento 1 introduction to boseeinstein condensation 3. Smith, boseeinstein condensation in dilute gases, cambridge university, 01 complexvalued wave function. Click add files and select the files you want to include in your pdf. This cited by count includes citations to the following articles in scholar. The order parameter or wave function of a boseeinstein condensate bec is obtained, in a mean field approximation, by the grosspitaevskii equation gpe f. In a place where the density is non zero, the velocity. Clarendon press, apr 3, 2003 literary criticism 382 pages. Boseeinstein condensates of dilute gases offer a rich field to study fundamental. It makes special reference to the physics of ultracold atomic gases. Pdf the grosspitaevskii equation and boseeinstein condensates. Pitaevskii, sandro stringari, alessio recati, arxiv. Optimal persistent currents for interacting bosons on a. The collision term references to nonlinear schr odinger equation.
Microsoft edge is the default program for opening pdf files on windows 10. Dodd zerotemperature, meanfield theory of atomic boseeinstein condensates 298 kb. Our approach points out the crucial role played by. Cazenave book, 2003,tao book 2006, papers from ginibrevelo in the 70s, 80s, colliander, j. Hybridization of first and second sound in a weakly interacting bose gas. Optimal persistent currents for interacting bosons on a ring. Particlewave duality in quantum tunneling of a bright soliton. Exact theory for t0 weakly interacting bose gases follows from schrodinger equation, lieb,seiringer, yingvanson, 2000. Landau damping in weakly interacting bose gases is investigated by means of perturbation theory. In exonucelar systems, the gross pitaevskii equation is widely used to model the magnetic vortex behaviour in fermi holes and in superfluids 7,8,12, where some studies provide also exact. When nonmagnetic y31 ions are randomly substitut ed for the ho31 ions, the fact that the anisotro pic dipolar interaction can be antiferromagnetic.
Questo conteggio citato da include citazioni ai seguenti articoli in scholar. Buy stationary and time dependent gross pitaevskii equations. How to merge pdfs and combine pdf files adobe acrobat dc. Numerical simulation of boseeinstein condensates based on. Collective excitations of a trapped bosecondensed gas. Anisotropic dependence of tuneout wavelength near dy 741. Applications to bose superfluids, antiferromagnets and crystals at zero temperature are discussed.
The inequality is employed to derive useful constraints on the behaviour of quantum fluctuations in problems with continuous group symmetries. A basisset based fortran program to solve the gross. Using landaus theory of twofluid hydrodynamics we investigate the sound modes propagating in a uniform weaklyinteracting superfluid bose gas for values. You can change the default program for pdf files to open it in a program thats more suitable and featurerich, such as acrobat reader dc or acrobat dc. This spindependent loss can be described by a potential i z up to a constant energy shift i. 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. Pitaevskii l p and stringari s 1999 theory of boseeinstein condensation in. Stringari, macroscopic dynamics of a trapped boseeinstein condensate in the presence of 1d and 2d optical lattices, phys. By lucas verney, lev pitaevskii and sandro stringari. Efficient and spectrally accurate numerical methods for. Acknowledgments this work was supported in part by a grant ota264 and 21, uzbekistan. Stringari approximate solutions of the nonlinear schrodinger equation for ground and excited states of boseeinstein condensates 165 kb r.
Analytic solution of gross pitaevskii equation tsuzuki, 1971 maximum soliton velocity v fixed by sound velocity c. 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 natural generalization of the heisenberg uncertainty principle inequality holding for non hermitian operators is presented and applied to the fractional. The ones marked may be different from the article in the profile.
Grosspitaevskii dynamics of boseeinstein condensates and. Theory of boseeinstein condensation in trapped gases. Gross pitaevskii equation for the order parameter and beyond. The averaged lagrangian of solitons of the boseeinstein condensation is found, on the basis of which it is possible to study the dynamics of solitons under the action of various perturbations. Discover book depositorys huge selection of l p pitaevskii books online. My researchid profile here at the bottom of the page a pdf file of my. A mathematical framework for optimal bilinear control of nonlinear schr odinger equations of grosspitaevskii type arising in the description of boseeinstein condensates is presented. The book is an introductory text to the physics of boseeinstein condensation. This book is an introductory text to the physics of boseeinstein condensation. Ground state of the timeindependent grosspitaevskii. Rj wild, m antezza, lp pitaevskii, s stringari, ea cornell.
Lev1,2,3 1department of applied physics, stanford university, stanford, california 94305, usa. Grosspitaevskii gp equation for order parameter plays role analogous to maxwell equations in classical electrodynamics. Esry used a finiteelement approach to solve for the both the timeindependent gpe, as well as, the hartreefock equations for bosons confined in anisotropic traps 10. Bcs to bec crossover and the unitarity fermi gas mohit randeria. The format of the writing is concise, almost journal publication style. They describe many physical phenomena, for instance in the theory of super uidity of in boseeinstein condensation. Smith, boseeinstein condensation in dilute gases, cambridge university, 01. Pdf theory of boseeinstein condensation in trapped gases. Optimal persistent currents for interacting bosons on a ring with gauge field matteo rizzi johannes gutenberguniversitat mainz komet seminar 27. Emphasis is given to the effect of interactions which play a crucial role, bringing the gas into a superfluid phase at low temperature. This phenomenon, first predicted by einstein in 1925, has been realized experimentally in 1995 in a remarkable series of experiments whose.
Wolfgang pauli institute 2006 thematic program januarydecember, 2006 vienna, austria contemporary mathematics on free shipping on qualified orders. We discuss a natural generalization of the uncertainty inequality holding in the case of nonhermitian operators. Stringari and treiner 12 have used a somewhat different scheme to modify the. Numerical simulations for boseeinstein condensation bec. Derivation of the grosspitaevskii hierarchy springerlink. Thermal effects of the casimir forces on ultra cold gases. Buy stationary and time dependent grosspitaevskii equations. Bcsbec crossover and the unitarity limit iv the only length characterizing the uniform unitary fermi gas is the average distance between particles d n. The grosspitaevskii equation, also called the nonlinear schrodinger equation nlse, describes. Width of the soliton fixed by healing length width becomes larger and larger as v approaches the sound velocity energy of moving soliton.
Sandro stringari university of trento 1 introduction to boseeinstein condensation 4. Supersymmetry breaking and nambugoldstone fermions in. Stationary and time dependent grosspitaevskii equations. A mathematical framework for optimal bilinear control of nonlinear schr odinger equations of gross pitaevskii type arising in the description of boseeinstein condensates is presented. Providing a useful introduction to one of the most exciting field of physics today, this text will be of interest. Computing ground states of spin2 boseeinstein condensates. Particlewave duality in quantum tunneling of a bright soliton chinghao wang,1,2 tzayming hong,1 raykuang lee,2,3,4. Stringari, boseeinstein condensation, oxford science. Numerical simulation of boseeinstein condensates based on grosspitaevskii equations author. Landau damping in weakly interacting bose gases is investigated by means of. By using an appropriate randomization of the fourier coefficients in the collision operator, we prove an averaged form of the main estimate which is used in order to contract the duhamel terms that occur in the study of the hierarchy. Anisotropic dependence of tuneout wavelength near dy 741nm. An introduction to the mathematical theory of quantum fluids. Derivation of the grosspitaevskii hierarchy for the dynamics of a boseeinstein condensate.
In exonucelar systems, the grosspitaevskii equation is widely used to model the magnetic vortex behaviour in fermi holes and in superfluids 7,8,12, where some studies provide also exact. This equation neglects interaction effects arising from the atoms out of the. Stringari this book is an introductory text to the physics of boseeinstein condensation. Rearrange individual pages or entire files in the desired order. Together with evgeny lifshitz and vladimir berestetskii. 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. Generalized irrotationality condition suppose everything is smooth and j. Click, drag, and drop to reorder files or press delete to remove any content you dont want. Gross pitaevskii gp equation for order parameter plays role analogous to maxwell equations in classical electrodynamics. Various theoretical approaches to describing the physics of interacting bosons and of interacting fermi gases, giving rise to. In these dilute systems interactions are characterized by a single parameter, the swave scattering length. Universita di trento, dipartimento di fisica, trento, italy.
Analytic solution of grosspitaevskii equation tsuzuki, 1971 maximum soliton velocity v fixed by sound velocity c. A 100, 023607 2019 supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas. Coherent spin oscillations in a disordered magnet s. Classical ground states susy is unbroken at g 0 w1. Quelli contrassegnati con possono essere diversi dallarticolo nel profilo. This volume introduces the basic concepts of boseeinstein condensation and superfluidity. Pure lihof 4 is a ferromagnet because of its crystal structure and the dominant role of the magnetic dipole interaction 2 between the unpaired f electrons of the ho31 ions.
Colorado p2 antonelli, marcati qhd with large data march 29, 2010 8 34. Uncertainty principle, quantum fluctuations, and broken. Erdos, schlein and yau, 2010 easy generalization to the time dependent case. Boseeinstein condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 nobel prize. Pdf the phenomenon of boseeinstein condensation of dilute gases in. This phase r is a global phase which means that all the atoms in the condensate have the same phase phase coherence. Boseeinstein condensation, journal of research of the. Stringari, boseeinstein condensation and superfluidity, oxford university press dlro in id. Dodd zerotemperature, meanfield theory of atomic boseeinstein condensates 298 kb mark edwards, r.
In the averaged estimate, we do not need to integrate in the time variable. Anisotropic dependence of tuneout wavelength near dy 741nm transition wil kao,1,2 yijun tang,2,3, nathaniel q. Apr 03, 2003 the book is an introductory text to the physics of boseeinstein condensation. You can merge pdfs or a mix of pdf documents and other files. Pdf the grosspitaevskii equation is discussed at the level of an advanced.