First and second sound in a two-dimensional harmonically trapped Bose gas across the Berezinskii–Kosterlitz–Thouless transition

We theoretically investigate first and second sound of a two-dimensional (2D) atomic Bose gas in harmonic traps by solving Landau’s two-fluid hydrodynamic equations. For an isotropic trap, we find that first and second sound modes become degenerate at certain temperatures and exhibit typical avoided crossings in mode frequencies. At these temperatures, second sound has significant density fluctuation due to its hybridization with first sound and has a divergent mode frequency towards the Berezinskii–Kosterlitz–Thouless (BKT) transition. For a highly anisotropic trap, we derive the simplified one-dimensional hydrodynamic equations and discuss the sound-wave propagation along the weakly confined direction. Due to the universal jump of the superfluid density inherent to the BKT transition, we show that the first sound velocity exhibits a kink across the transition. These predictions might be readily examined in current experimental setups for 2D dilute Bose gases with a sufficiently large number of atoms, where the finite-size effect due to harmonic traps is relatively weak.     

Hysteresis curves and loops for harmonic and impulse perturbations in some non-equilibrium gases

Evolution of sound in a relaxing gas whose properties vary in the course of wave propagation, is studied. A relaxing medium may reveal normal acoustic properties or be acoustically active. In the first case, losses in acoustic energy lead to an increase in internal energy of a gas similarly as it happens in Newtonian fluids. In the second case, acoustic energy increases in the course of sound propagation, and the internal energy of a medium decreases. Variations in the internal energy of a gas are proportional to some generic parameter, the sign of which is responsible for acoustical activity, and depends on intensity and shape of the sound waveform. Hysteresis curves in the plane of thermodynamic states are plotted. Curves for harmonic and several aperiodic sound impulses are plotted, discussed and compared.     

Exact three-body local correlations for excited states of the 1D Bose gas

We derive an exact analytic expression for the three-body local correlations in the Lieb-Liniger model of 1D Bose gas with contact repulsion. The local three-body correlations control the thermalization and particle loss rates in the presence of terms which break integrability, as is realized in the case of 1D ultracold bosons. Our result is valid not only at finite temperature but also for a large class of nonthermal excited states in the thermodynamic limit. We present finite temperature calculations in the presence of external harmonic confinement within local density approximation, and for a highly excited state that resembles an experimentally realized configuration.     

Gas jets as ultrasonic waveguides

The study of the propagation of ultrasound within a gas jet is extended to obtain waveguide effects, where the jet collimates the ultrasonic beam from a transducer within the flow. Two methods have been investigated to achieve this--cooling the gas within the air jet, and using a different gas whose acoustic velocity is lower than air. Cooling an air jet to a temperature less than that of the surrounding air produced a noticeable waveguide effect. In addition, studies have been carried out using other selected gases, such as carbon dioxide (CO2) with a lower acoustic velocity than air, and helium (He) with a higher value. The former gas enhanced confinement of the ultrasonic beam, whereas the latter caused divergence. An ideal solution was found to be a CO2/air mixture, which produced a well-collimated sound field along the axis, while limiting the excess attenuation of pure CO2 gas jets. The effectiveness of the waveguide using mixed gas jets in producing images in air-coupled testing of solids is demonstrated.     

高频聚焦超声声场和温度场的仿真研究

为探究临床常用的7 MHz高频聚焦超声在多层生物组织中的声传播以及毫秒级时间内的生物传热规律问题,基于Westervelt方程和Pennes传热方程,使用有限元方法建立高频聚焦超声辐照多层组织的非线性热黏性声传播及传热模型。首先分析了线性模型和非线性模型之间的差异,然后在非线性模型下探究换能器的参数对声场和温度场的影响。仿真结果显示：在7 MHz频率下,当换能器输出声功率超过5 W时,声波传播的非线性效应不可忽视(p <0.05);当声功率从5 W增大到15 W时,非线性模型与线性模型预测的温度偏差从20%增加到34.703%;高频聚焦超声波的非线性行为比低频更加显著,基频能量向高次谐波转移的程度增大,声功率为10 W和15 W时4次谐波与基波之比分别达到7.33%和12.12%;高频换能器参数的改变对组织中声场和温度场分布的影响较大,换能器焦距从12 mm减小到11.2 mm,焦点处最高温度增加了77%。结果表明,7 MHz聚焦超声的非线性声传播需要考虑到4次谐波的影响。该文提出的多层组织非线性仿真模型可为高频聚焦超声换能器参数优化及制定安全、有效的术前治疗方案提供理论参考。     

Two-step condensation of lattice bosons

We present a theoretical study of Bose-Einstein condensation in highly anisotropic harmonic traps. The bosons are considered to be moving in an optical lattice in an overall anisotropic harmonic confining potential. We find that two-step condensation occurs for lattice bosons at much reduced harmonic potential anisotropy when compared to the case of an ideal Bose gas in an anisotropic harmonic confinement. We also show that when the bosons are in an isotropic harmonic confinement but with highly anisotropic hopping in the optical lattice, two-step condensation does not occur. We interpret some of our results using single boson density of energy states corresponding to the potentials faced by the bosons.     

Effective widths of boson gas confined in a harmonic rotating trap

In this Letter, we evaluate the radial and axial square radii (effective widths) of a rapidly rotating boson gas. The corresponding effective area and the expansion energy are calculated from these effective widths. A modified semiclassical approximation is suggested. This approach provides significant corrections to these quantities, such as finite size effect and indirectly interaction effect. We show that the effective widths still follow a non-rotating temperature dependence. Rotation leads to expansion or shrinking the effective widths through the change of the harmonic frequencies of the confinement trap.     

Effect of the bulk viscosity on the sound propagation in nonequilibrium suspensions of microparticles in gas

The sound propagation in a mixture of gas with uniformly dispersed solid particles, whose temperature is maintained above that of the gas by an external source, is considered. The dispersion properties of this kind of suspensions are studied, and expressions for the second viscosity and the sound velocity in such suspensions are derived. It is shown that, in a nonequilibrium suspension, the second viscosity may be negative. The ranges of the suspension parameters, for which the propagation of low-frequency sound is impossible, are determined.     

Evolution of spin-dependent atomic wave packets in a harmonic potential

We have investigated theoretically the evolution of spin-dependent atomic wave packets in a harmonic magnetic trapping potential. For a Bose-condensed gas, which undergoes a Mott insulator transition and a spin-dependent transport, the atomic wavefunction can be described by an entangled single-atom state. Due to the confinement of the harmonic potential, the density distributions exhibit periodic decay and revival, which is different from the case of free expansion after switching off the combined harmonic and optical lattice potential.     

Is there any fast sound in water?

We measured the dynamic structure factor S(Q,omega) of liquid and undercooled water down to 253 K in the Q approximately 0.02-0.1 nm;{-1} momentum transfer region. We observe the neat departure of the apparent speed of sound from the adiabatic regime as a function of decreasing temperature. Our evaluation of the infinite-frequency limit of sound velocity, c_{infinity}, matches with the results obtained in the high momentum transfer limit by inelastic neutron and x-ray scattering. These results strongly support the viscoelastic interpretation of the dynamics of water. Hence, we propose to call c_{infinity} the high-frequency speed of sound and to abandon the term fast sound, which recalls a propagation mechanism through lighter atoms, like in gas mixtures.     

Statistical mechanics of a confinement electron gas in a uniform electromagnetic field

In this paper we study an ideal electron gas in the presence of a uniform electromagnetic field and confinement by a three-dimensional harmonic potential. We find the partition function of this system and in the sequel we examine the Boltzmann statistics and Fermi-Dirac statistics applying the grand canonical ensemble method.     

The stability of a quantized vortex in a dilute Bose gas confined to a toroidal trap

We investigate the stability of a quantized vortex in a weakly interacting Bose gas, trapped in a toroidal container with hard walls. Calculating the excitation spectrum numerically and determining the stability condition by the Landau criterion, we examine the effect of reducing the confinement region of the condensate on the vortex stability. We find that tight confinement of the condensate increases the stabilization of the quantized vortex because an increase in the zero sound velocity due to tight confinement prevents the emergence of the elementary excitation which breaks superfluidity of the Bose system. We also discuss the experimental setup to observe such an effect.     

Second sound in SrTiO3

We study collective phonon excitations in SrTiO3 by low-frequency light scattering. We employ extended thermodynamics for phonon gas to construct a theoretical spectral function that is applicable regardless of local thermal equilibrium. Our analysis reveals the temperature dependence of tauN, the relaxation time for the momentum-conserving phonon collisions (normal processes), in SrTiO3. These results indicate that the previously reported anomalous soundlike spectrum originates from second sound, which is a wavelike propagation of heat.     

Dynamical Properties of the Unitary Fermi Gas: Collective Modes and Shock Waves

We discuss the unitary Fermi gas made of dilute and ultracold atoms with an infinite s-wave inter-atomic scattering length. First we introduce an efficient Thomas–Fermi–von Weizsacker density functional which describes accurately various static properties of the unitary Fermi gas trapped by an external potential. Then, the sound velocity and the collective frequencies of oscillations in a harmonic trap are derived from extended superfluid hydrodynamic equations which are the Euler–Lagrange equations of a Thomas–Fermi–von Weizsacker action functional. Finally, we show that this amazing Fermi gas supports supersonic and subsonic shock waves.     

Effects of confinement on a magnetized ideal gas: I. The electron gas

Using the framework of the grand canonical ensemble the effects of a two (or three) dimensional confinement (harmonic) potential on the magnetic properties of an ideal electron gas are investigated. The high temperature results for the magnetic moment obtained by Felderhof and Raval are generalized to take into account the spin. At low temperature the confinement potential introduces a new oscillatory phenomena besides a modification or even a destruction of the de Haas-van Alphen effect. The changes in Landau diamagnetism are also analysed.     

Numerical simulation of parametric sound generation and its application to length-limited sound beam

In this study we propose a simulation model for predicting the nonlinear sound propagation of ultrasound beams over a distance of a few hundred wavelengths, and we estimate the beam profile of a parametric array. Using the finite-difference time-domain method based on the Yee algorithm with operator splitting, axisymmetric nonlinear propagation was simulated on the basis of equations for a compressible viscous fluid. The simulation of harmonic generation agreed with the solutions of the Khokhlov–Zabolotskaya–Kuznetsov equation around the sound axis except near the sound source. As an application of the model, we estimated the profiles of length-limited parametric sound beams, which are generated by a pair of parametric sound sources with controlled amplitudes and phases. The simulation indicated a sound beam with a narrow truncated array length and a width of about one-quarter to half that of regular a parametric beam. This result confirms that the control of sound source conditions changes the shape of a parametric beam and can be used to form a torch like low-frequency sound beam.     

Harmonic propagation of finite amplitude sound beams: experimental determination of the nonlinearity parameter B/A

We propose a method to determine the nonlinearity parameter B/A of a liquid from the spatial evolution of harmonic components. We describe an analytical model, in the parabolic and quasi-linear approximations, that predicts the continuous finite amplitude sound beam propagation radiated by a plane piston source. This model takes into consideration attenuation, diffraction and nonlinear effects. The fundamental and second harmonic ultrasonic fields are expressed as the superposition of Gaussian beams. Axial propagation curves are then compared with those obtained by direct numerical solution of the transformed beam equation using the finite difference method, and with experimental results. Accurate measurements of pressure levels for the nonlinearly generated harmonics in water are performed along and across the propagation axis for different pressure values delivered at the piston surface. Experimental results, for water and ethanol, are in agreement with those of our model, which allows us to obtain the expected value of the nonlinearity parameter B/A.     

Effect of laser focus in two-color synthesized waveform on generation of soft x-ray high harmonics

Synthesis of multi-color laser pulses has been developed as a promising way to improve low conversion efficiency of high-order harmonic generation (HHG). Here we systematically study the effect of laser focus in a two-color waveform on generation of macroscopic HHG in soft x-rays. We find that the dependence of HHG yields on laser focus at low or high gas pressure is sensitive to the characteristics of single-atom harmonic response, in which "short"-or "long"-trajectory emissions can be selectively controlled by changing the waveform of two-color synthesized laser pulse. We uncover the phase-matching mechanism of HHG in the gas medium by examining the propagation of the two-color waveform and the evolution of time-frequency emissions of high-harmonic field. We further reveal that the nonlinear effects, such as geometric phase, atomic dispersion, and plasma defocusing, are responsible for modification of two-color waveform upon propagation. This work can be used to find better macroscopic conditions for generating soft x-ray HHG by employing two-color optimized waveforms.     

Quasi-two-dimensional superfluid fermionic gases

We study a quasi-two-dimensional superfluid Fermi gas where the confinement in the third direction is due to a strong harmonic trapping. We investigate the behavior of such a system when the chemical potential is varied and find strong modifications of the superfluid properties due to the discrete harmonic oscillator states. We show that such quasi-two-dimensional behavior can be created and observed with current experimental capabilities.     

Measuring nanopore size from the spin-lattice relaxation of CF4 gas

The NMR 19F spin-lattice relaxation time constant T1 for CF4 gas is dominated by spin-rotation interaction, which is mediated by the molecular collision frequency. When confined to pores of approximately the same size or smaller than the bulk gas mean free path, additional collisions of molecules with the pore walls should substantially change T1. To develop a method for measuring the surface/volume ratio S/V by measuring how T1 changes with confinement, we prepared samples of known S/V from fumed silica of known mass-specific surface area and compressed to varying degrees into cylinders of known volume. We then measured T1 for CF4 in these samples at varying pressures, and developed mathematical models for the change in T1 to fit the data. Even though CF4 has a critical temperature below room temperature, we found that its density in pores was greater than that of the bulk gas and that it was necessary to take this absorption into account. We modeled adsorption in two ways, by assuming that the gas condenses on the pore walls, and by assuming that gas in a region near the wall is denser than the bulk gas because of a simplified attractive potential. Both models suggested the same two-parameter formula, to which we added a third parameter to successfully fit the data and thus achieved a rapid, precise way to measure S/V from the increase in T1 due to confinement in pores.