The Dyson-Maleev boson formulation is used to investigate the dynamical properties of Heisenberg antiferromagnets at long wavelengths and low temperatures. Various regimes for the decay rate of spin waves are found, depending on the relation between the wave vector k, the temperature T, and the anisotropy energy ℏω A , and in all cases the decay rate is much smaller than the spin-wave frequency. This result implies that spin waves are well-defined elementary excitations, which interact weakly at low temperatures and long wavelengths, in contrast to results obtained by previous authors, but in close analogy with the ferromagnetic case. When the long-wavelength limit is taken at fixed temperature, the decay rate Γ k⃗ is proportional to the square of the frequency ω E ε k⃗ , where ω E is the exchange frequency. In the quantum-mechanical lowtemperature limit (ST≪T N ), we find Γ k⃗ =2ω E S −2 ε 2 k⃗ τ 3 (2π) −3 (a|1nτ|+a′) for ε k⃗ ≪τ 3 ≪1, where τ=2k B T/ℏω E , and S is the spin quantum number. In the classical low-temperature limit (T N /S≪T≪T N ), we find Γ k⃗ =(4η/ 3π)ω E (T/T N ) 2 ε 2 k⃗ for ε k⃗ ≪1. For small uniaxial single-ion anisotropy [ε 0~( 2ω A /ω E ) 1/2 ≪1], we find Γ 0 =3/ 2ω E S −2 ε 2 0 τ 3 (2π) −3 (a|1nτ|+a'') for ε 0 ≪τ 3 ≪1. (In these expressions, a, a′, η, and a'' are all constants of order unity.) Results are also obtained for other regimes, and for the damping of a spin wave driven off resonance. In each case, the nature and self-consistency of the perturbation expansion are examined in detail. For the isotropic system, the full frequency-dependent transverse spin-correlation functions are calculated in the longwavelength limit, and are found to agree with the forms previously obtained by hydrodynamic arguments. By a comparison of the two forms, the transport coefficients are determined at low temperatures. Several of the calculations have been performed using the Holstein-Primakoff as well as the Dyson-Maleev representations. The results for observable quantities agree in the two formalisms, except at the longest wavelengths, where the Holstein-Primakoff expressions are not self-consistent in lowest order. Finally, the possibility of experimental verification of the present calculations is briefly discussed. case. %hen the long-wavelength limit is taken at fixed temperature, the decay rate I'g is proportional to the square of the frequency co@&g, where v@ is the exchange frequency. In the quantum-mechanical low-temperature limit (ST«Tz), we find I'g=2cogS~j~7 (2~) (a(lnr )+a') for &g«7 «1, where 7=2A~T/Schiz, and S is the spin quantum number. In the classical lowtemperature limit (T~/S«T«T&), we find I'g= (4g/3gco~(T/T~) &g for &g«1. Disciplines Physics | Quantum Physics

The static and dynamic response associated with a low concentration, x, of static defects in a Heisenberg antiferromagnet at zero temperature is analyzed within linearized spin-wave theory. We obtain the dispersion relation for long-wavelength spin waves in the form ω(q)= c (x) q + iγ(x) q τ. Our results for c(x) agree with previous work, and in particular give c(x) = c(0)[1 + αx + O(x 2)] where the coefficient α, which can be related to the helicity modulus and the uniform perpendicular susceptibility, diverges in the limit d→2, where d is the spatial dimensionality. One major new result is that τ=d−1 for defects whose spin, S', is different from that (S) of the host lattice and τ=d+1 when S'=S.

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Quantitative evaluation of small molecule permeation and accumulation in Gram-negative bacteria is important for drug development against these bacteria. While these measurements are commonly performed at physiological pH, Escherichia coli and many other Enterobacteriaceae infect human gastrointestinal and urinary tracts, where they encounter different pH conditions. To understand how external pH affects permeation and accumulation of small molecules in E. coli cells, we apply second harmonic generation (SHG) spectroscopy using SHG-active antimicrobial compound malachite green as the probe molecule. Using SHG, we quantify periplasmic and cytoplasmic accumulations separately in live E. coli cells, which was never done before. Compartment-wise measurements reveal accumulation of the probe molecule in cytoplasm at physiological and alkaline pH, while entrapment in periplasm at weakly acidic pH and retention in external solution at highly acidic pH. Behind such disparity in localizations, up to 2 orders of magnitude reduction in permeability across the inner membrane at weakly acidic pH and outer membrane at highly acidic pH are found to play key roles. Our results unequivocally demonstrate the control of external pH over entry and compartment-wise distribution of small molecules in E. coli cells, which is a vital information and should be taken into account in antibiotic screening against E. coli and other Enterobacteriaceae members. In addition, our results demonstrate the ability of malachite green as an excellent SHG-indicator of changes of individual cell membrane and periplasm properties of live E. coli cells in response to external pH change from acidic to alkaline. This finding, too, has great importance, as there is barely any other molecular probe that can provide similar information.

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