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Register a new userDiamagnetism versus Paramagnetism in charged spin-1 Bose gases
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It has been suggested that either diamagnetism or paramagnetism of Bose gases, due to the charge or spin degrees of freedom respectively, appears solely to be extraordinarily strong. We investigate magnetic properties of charged spin-1 Bose gases in external magnetic field, focusing on the competition between the diamagnetism and paramagnetism, using the Lande-factor $g$ of particles to evaluate the strength of paramagnetic effect. We propose that a gas with $g<{1/sqrt{8}}$ exhibits diamagnetism at all temperatures, while a gas with $g>{1/2}$ always exhibits paramagnetism. Moreover, a gas with the Lande-factor in between shows a shift from paramagnetism to diamagnetism as the temperature decreases. The paramagnetic and diamagnetic contributions to the total magnetization density are also calculated in order to demonstrate some details of the competition.
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The charged Fermi gas with a small Lande-factor $g$ is expected to be diamagnetic, while that with a larger $g$ could be paramagnetic. We calculate the critical value of the $g$-factor which separates the dia- and para-magnetic regions. In the weak-field limit, $g_{c}$ has the same value both at high and low temperatures, $g_{c}=1/sqrt{12}$. Nevertheless, $g_{c}$ increases with the temperature reducing in finite magnetic fields. We also compare the $g_{c}$ value of Fermi gases with those of Boltzmann and Bose gases, supposing the particle has three Zeeman levels $sigma=pm1, 0$, and find that $g_{c}$ of Bose and Fermi gases is larger and smaller than that of Boltzmann gases, respectively.
Within the mean-field theory, we investigate the magnetic properties of a charged spin-1 Bose gas in two dimension. In this system the diamagnetism competes with paramagnetism, where Lande-factor $g$ is introduced to describe the strength of the paramagnetic effect. The system presents a crossover from diamagnetism to paramagnetism with the increasing of Lande-factor. The critical value of the Lande-factor, $g_{c}$, is discussed as a function of the temperature and magnetic field. We get the same value of $g_{c}$ both in the low temperature and strong magnetic field limit. Our results also show that in very weak magnetic field no condensation happens in the two dimensional charged spin-1 Bose gas.
Magnetic properties of a charged spin-1 Bose gas with ferromagnetic interactions is investigated within mean-field theory. It is shown that a competition between paramagnetism, diamagnetism and ferromagnetism exists in this system. It is shown that diamagnetism, being concerned with spontaneous magnetization, cannot exceed ferromagnetism in very weak magnetic field. The critical value of reduced ferromagnetic coupling of paramagnetic phase to ferromagnetic phase transition $bar I_{c}$ increases with increasing temperature. The Lande-factor $g$ is introduced to describe the strength of paramagnetic effect which comes from the spin degree of freedom. The magnetization density $bar M$ increases monotonically with $g$ for fixed reduced ferromagnetic coupling $bar I$ as $bar I>bar I_{c}$. In a weak magnetic field, ferromagnetism makes immense contribution to the magnetization density. While at a high magnetic field, the diamagnetism inclines to saturate. Evidence for condensation can be seen in the magnetization density at weak magnetic field.
The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying nonlinear sound waves emanating from initial density accumulations in the Lieb-Liniger model. We show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-ABACUS algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.
Cold atom developments suggest the prospect of measuring scaling properties and long-range fluctuations of continuous phase transitions at zero-temperature. We discuss the conditions for characterizing the phase separation of Bose-Einstein condensates of boson atoms in two distinct hyperfine spin states. The mean-field description breaks down as the system approaches the transition from the miscible side. An effective spin description clarifies the ferromagnetic nature of the transition. We show that a difference in the scattering lengths for the bosons in the same spin state leads to an effective internal magnetic field. The conditions at which the internal magnetic field vanishes (i.e., equal values of the like-boson scattering lengths) is a special point. We show that the long range density fluctuations are suppressed near that point while the effective spin exhibits the long-range fluctuations that characterize critical points. The zero-temperature system exhibits critical opalescence with respect to long wavelength waves of impurity atoms that interact with the bosons in a spin-dependent manner.
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