We present a theory of spin waves in a noncondensed gas of spin-1 bosons and provide both analytic calculations of the linear theory and full numerical simulations of the nonlinear response. We highlight the role of spin-dependent contact interactions in the dynamics of a thermal gas. Although these interactions are small compared to the thermal energy, they set the scale for low-energy, long-wavelength spin waves. In particular, we find that the polar state of $^{87}\mathrm{Rb}$ is unstable to collisional mixing of magnetic sublevels even in the normal state. We augment our analytic calculations by providing full numerical simulations of a trapped gas, explicitly demonstrating this instability. Further, we show that for strong antiferromagnetic interactions, the polar gas is unstable. Finally, we explore coherent population dynamics in a collisionless transversely polarized gas.We present a theory of spin waves in a noncondensed gas of spin-1 bosons and provide both analytic calculations of the linear theory and full numerical simulations of the nonlinear response. We highlight the role of spin-dependent contact interactions in the dynamics of a thermal gas. Although these interactions are small compared to the thermal energy, they set the scale for low-energy, long-wavelength spin waves. In particular, we find that the polar state of $^{87}\mathrm{Rb}$ is unstable to collisional mixing of magnetic sublevels even in the normal state. We augment our analytic calculations by providing full numerical simulations of a trapped gas, explicitly demonstrating this instability. Further, we show that for strong antiferromagnetic interactions, the polar gas is unstable. Finally, we explore coherent population dynamics in a collisionless transversely polarized gas.

Physical Review AMay 17, 201013 citations

Dynamical properties of quantum antiferromagnets in one and two dimensions

Chiranjeeb Buragohain

Jan 1, 20010 citations

Spin dynamics in quasi-one-dimensional antiferromagnets

Sylvain Capponi, Maxime Dupont, E. Orignac +1 more

Bulletin of the American Physical SocietyMar 4, 20190 citations

Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures

Kedar Damle, Subir Sachdev A

We discuss the theory of the nonzero temperature $(T)$ spin dynamics and transport in one-dimensional Heisenberg antiferromagnets with a gap $\ensuremath{\Delta}$. For $T\ensuremath{\ll}\ensuremath{\Delta}$, we develop a semiclassical picture of thermally excited particles. Multiple inelastic collisions between the particles are crucial, and are described by a two-particle $\mathcal{S}$ matrix which is shown to have a superuniversal form at low momenta. This is established by computations on the $O(3)$ $\ensuremath{\sigma}$ model, and strong- and weak-coupling expansions (the latter using a Majorana fermion representation) for the two-leg $S=1/2$ Heisenberg antiferromagnetic ladder. As an aside, we note that the strong-coupling calculation reveals an $S=1$ , two-particle bound state which leads to the presence of a second peak in the $T=0$ inelastic neutron-scattering (INS) cross section for a range of values of momentum transfer. We obtain exact, or numerically exact, universal expressions for the thermal broadening of the quasiparticle peak in the INS cross section, the spin diffusivity, and for the field dependence of the NMR relaxation rate ${1/T}_{1}$ of the effective semiclassical model; these are expected to be asymptotically exact for the quantum antiferromagnets in the limit $T\ensuremath{\ll}\ensuremath{\Delta}$. The results for ${1/T}_{1}$ are compared with the experimental findings of Takigawa et al. [Phys. Rev. Lett. 76, 2173 (1996)] and the agreement is quite good. In the regime $\ensuremath{\Delta}<T<$(a typical microscopic exchange) and we argue that a complementary description in terms of semiclassical waves applies, and give some exact results for the thermodynamics and dynamics.We discuss the theory of the nonzero temperature $(T)$ spin dynamics and transport in one-dimensional Heisenberg antiferromagnets with a gap $\ensuremath{\Delta}$. For $T\ensuremath{\ll}\ensuremath{\Delta}$, we develop a semiclassical picture of thermally excited particles. Multiple inelastic collisions between the particles are crucial, and are described by a two-particle $\mathcal{S}$ matrix which is shown to have a superuniversal form at low momenta. This is established by computations on the $O(3)$ $\ensuremath{\sigma}$ model, and strong- and weak-coupling expansions (the latter using a Majorana fermion representation) for the two-leg $S=1/2$ Heisenberg antiferromagnetic ladder. As an aside, we note that the strong-coupling calculation reveals an $S=1$, two-particle bound state which leads to the presence of a second peak in the $T=0$ inelastic neutron-scattering (INS) cross section for a range of values of momentum transfer. We obtain exact, or numerically exact, universal expressions for the thermal broadening of the quasiparticle peak in the INS cross section, the spin diffusivity, and for the field dependence of the NMR relaxation rate ${1/T}_{1}$ of the effective semiclassical model; these are expected to be asymptotically exact for the quantum antiferromagnets in the limit $T\ensuremath{\ll}\ensuremath{\Delta}$. The results for ${1/T}_{1}$ are compared with the experimental findings of Takigawa et al. [Phys. Rev. Lett. 76, 2173 (1996)] and the agreement is quite good. In the regime $\ensuremath{\Delta}<T<$(a typical microscopic exchange) and we argue that a complementary description in terms of semiclassical waves applies, and give some exact results for the thermodynamics and dynamics.

arXiv:cond-mat/9711014Physical review. B, Condensed matterApr 1, 1998175 citations

Spin waves in a spin-1 normal Bose gas

Stefan S. Natu, Erich J. Mueller

We present a theory of spin waves in a noncondensed gas of spin-1 bosons and provide both analytic calculations of the linear theory and full numerical simulations of the nonlinear response. We highlight the role of spin-dependent contact interactions in the dynamics of a thermal gas. Although these interactions are small compared to the thermal energy, they set the scale for low-energy, long-wavelength spin waves. In particular, we find that the polar state of {sup 87}Rb is unstable to collisional mixing of magnetic sublevels even in the normal state. We augment our analytic calculations by providing full numerical simulations of a trapped gas, explicitly demonstrating this instability. Further, we show that for strong antiferromagnetic interactions, the polar gas is unstable. Finally, we explore coherent population dynamics in a collisionless transversely polarized gas.We present a theory of spin waves in a noncondensed gas of spin-1 bosons and provide both analytic calculations of the linear theory and full numerical simulations of the nonlinear response. We highlight the role of spin-dependent contact interactions in the dynamics of a thermal gas. Although these interactions are small compared to the thermal energy, they set the scale for low-energy, long-wavelength spin waves. In particular, we find that the polar state of {sup 87}Rb is unstable to collisional mixing of magnetic sublevels even in the normal state. We augment our analytic calculations by providing full numerical simulations of a trapped gas, explicitly demonstrating this instability. Further, we show that for strong antiferromagnetic interactions, the polar gas is unstable. Finally, we explore coherent population dynamics in a collisionless transversely polarized gas.

Bulletin of the American Physical SocietyMar 15, 20100 citations

Spin fluctuations in quantum antiferromagnets

Maciej Fidrysiak

Prace Naukowe Uniwersytetu Ekonomicznego we WrocławiuJan 1, 20150 citations

^{87}\mathrm{Rb}

is unstable to collisional mixing of magnetic sublevels even in the normal state. We augment our analytic calculations by providing full numerical simulations of a trapped gas, explicitly demonstrating this instability. Further, we show that for strong antiferromagnetic interactions, the polar gas is unstable. Finally, we explore coherent population dynamics in a collisionless transversely polarized gas.

We discuss the theory of the nonzero temperature

(T)

spin dynamics and transport in one-dimensional Heisenberg antiferromagnets with a gap $\ensuremath{\Delta}$. For $T\ensuremath{\ll}\ensuremath{\Delta}$, we develop a semiclassical picture of thermally excited particles. Multiple inelastic collisions between the particles are crucial, and are described by a two-particle

\mathcal{S}

matrix which is shown to have a superuniversal form at low momenta. This is established by computations on the

O(3)

$\ensuremath{\sigma}$ model, and strong- and weak-coupling expansions (the latter using a Majorana fermion representation) for the two-leg

S=1/2

Heisenberg antiferromagnetic ladder. As an aside, we note that the strong-coupling calculation reveals an

S=1

, two-particle bound state which leads to the presence of a second peak in the

T=0

inelastic neutron-scattering (INS) cross section for a range of values of momentum transfer. We obtain exact, or numerically exact, universal expressions for the thermal broadening of the quasiparticle peak in the INS cross section, the spin diffusivity, and for the field dependence of the NMR relaxation rate

{1/T}_{1}

of the effective semiclassical model; these are expected to be asymptotically exact for the quantum antiferromagnets in the limit $T\ensuremath{\ll}\ensuremath{\Delta}$. The results for

{1/T}_{1}

are compared with the experimental findings of Takigawa et al. [Phys. Rev. Lett. 76, 2173 (1996)] and the agreement is quite good. In the regime $\ensuremath{\Delta}<T<$(a typical microscopic exchange) and we argue that a complementary description in terms of semiclassical waves applies, and give some exact results for the thermodynamics and dynamics.