1. Spontaneous symmetry breaking and topological excitations in
cold-atomic Bose-Einstein condensates
Recent experimental technique enables us to create and manipulate
quantum degenerate atomic gases. Examples include Bose-Einstein
condensates (BECs) of bosonic atoms and BCS-like superfluid of
fermionic atoms. In the presentation, I will first introduce the
system of cold atomic gases. The main topic of this presentation is a
BEC with spin degrees of freedom, which is called a spinor BEC[1].
When the system has spin internal degrees of freedom, various phases
arise in the ground-state phase diagram, where each phase can be
characterized with the symmetry that the system preserves. I will
explain the symmetry property of the ground-state phases of spinor
BECs and introduce a method to find the ground-state phases from the
symmetry property of the system[2]. Because various phases with
various symmetries arise in spinor BECs, it is regarded as an ideal
testing ground to investigate the static and dynamical properties of
topological excitations, such as vortices, monopoles, and skyrmions.
In the latter part of the presentation, I will explain what kind of
topological excitations can be accommodated in spinor BECs[3].

2. Nonlinear magnetization dynamics in spinor Bose-Einstein condensates
The dynamics of BECs has many similarities with classical fluid and
classical ferromagnets. In the mean field theory, the condensate is
described with a macroscopic wave function, which is the order
parameter of the system, and the equation of motion of the wave
function governed by a nonlinear Schrodinger equation, called the
Gross-Pitaevskii (GP) equation. When we rewrite the GP equation to the
equation of motion for the particle density, it reduces to the Eular's
equation that describes the dynamics of a perfect fluid[4]. On the
other hand, when the condensate has internal degrees of freedom, it
can be described with a multi-component order parameter, which obeys
the multi-component GP equation. In this case, when the condensate is
ferromagnetic, the multi-component GP equation is shown to reduce to
the Landau-Lifshitz (LL) equation that describes the magnetization
dynamics in solid state materials[5]. When we phenomenologically
introduce an energy dissipation, we have the Landau-Lifshitz Gilbaet
(LLG) equation[6]. In the presentation, I first explain the
correspondence between BECs and classical systems. Then, I will
compare the domain growth dynamics in a spinor BEC with that in a
solid-state ferromagnet[7].

References:
[1] YK and M. Ueda, Phys. Rep. 520, 253 (2012);D. M. Stamper-Kurn and
M. Ueda, Rev. Mod. Phys. 85, 1191 (2013).
[2] YK and M. Ueda, Phys. Rev. A 84, 053616 (2011).
[3] YK, M. Nitta, and M. Ueda, Phys. Rev. Lett. 100, 180403 (2008).M;
Kobayashi, YK, M. Nitta, and M. Ueda, Phys. Rev. Lett. 103, 115301
(2009).
[4] C. J. Pethick and H. Smith, "Bose-Einstein Condensation in Dilute
Gases", (Cambridge University Press, 2nd ed. 2008).
[5] A. Lamacraft, Phys. Rev. A 77, 063622 (2008); R. Barnett, D.
Podolsky, and G. Refael, Phys. Rev. B 80, 024420 (2009).
[6] K. Kudo and YK, Phys. Rev. A 84, 043607 (2011).
[7] K. Kudo and YK, Phys. Rev. A 88, 013630 (2013); K. Kudo and YK,
Phys. Rev. A 91, 053609 (2015).