Shock waves in a one-dimensional Bose gas: from a Bose-Einstein condensate to a Tonks gas

We derive and analyze shock-wave solutions of hydrodynamic equations describing repulsively interacting one dimensional Bose gas. We also use the number-conserving Bogolubov approach to verify accuracy of the Gross-Pitaevskii equation in shock wave problems. We show that quantum corrections to dynamics of shocks (dark-shock-originated solitons) in a Bose-Einstein condensate are negligible (important) for a realistic set of system parameters. We point out possible signatures of a Bose-Einstein condensate -- Tonks crossover in shock dynamics. Our findings can be directly verified in different experimental setups.Comment: 10 pages, small corrections with respect to the last submission, version accepted in Phys. Rev.

Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind

The proton temperature anisotropy in the solar wind is known to be constrained by the theoretical thresholds for pressure anisotropy-driven instabilities. Here we use approximately 1 million independent measurements of gyroscale magnetic fluctuations in the solar wind to show for the first time that these fluctuations are enhanced along the temperature anisotropy thresholds of the mirror, proton oblique firehose, and ion cyclotron instabilities. In addition, the measured magnetic compressibility is enhanced at high plasma beta ($\beta_\parallel \gtrsim 1$) along the mirror instability threshold but small elsewhere, consistent with expectations of the mirror mode. The power in this frequency (the 'dissipation') range is often considered to be driven by the solar wind turbulent cascade, an interpretation which should be qualified in light of the present results. In particular, we show that the short wavelength magnetic fluctuation power is a strong function of collisionality, which relaxes the temperature anisotropy away from the instability conditions and reduces correspondingly the fluctuation power.Comment: 4 pages, 4 figure

On topological phases of spin chains

Symmetry protected topological phases of one-dimensional spin systems have been classified using group cohomology. In this paper, we revisit this problem for general spin chains which are invariant under a continuous on-site symmetry group G. We evaluate the relevant cohomology groups and find that the topological phases are in one-to-one correspondence with the elements of the fundamental group of G if G is compact, simple and connected and if no additional symmetries are imposed. For spin chains with symmetry PSU(N)=SU(N)/Z_N our analysis implies the existence of N distinct topological phases. For symmetry groups of orthogonal, symplectic or exceptional type we find up to four different phases. Our work suggests a natural generalization of Haldane's conjecture beyond SU(2).Comment: 18 pages, 7 figures, 2 tables. Version v2 corresponds to the published version. It includes minor revisions, additional references and an application to cold atom system