Metastable state and macroscopic quantum tunneling of binary mixtures

We provide a mixing model to explore the metastable state and the macroscopic quantum tunneling (MQT) of binary mixtures. For , we first observe the two condensates form the symmetry-breaking state (SBS) and then suddenly transfer to the symmetry-preserving state (SPS) through the MQT. The SBS is shown to be the metastable state in our system. We find the MQT does not spontaneously arise. The inducement mechanism is the damping but not the excitations. The damping mechanism can also control the lifetime and the tunneling decay rate of the SBS. Finally, we further present the origin of these phenomena by examining the energy of the system.     

Brownian motion at short time scales

Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time scales. At short time scales, Brownian motion of a suspended particle is not completely random, due to the inertia of the particle and the surrounding fluid. Moreover, the thermal force exerted on a particle suspended in a liquid is not a white noise, but is colored. Recent experimental developments in optical trapping and detection have made this new regime of Brownian motion accessible. This review summarizes related theories and recent experiments on Brownian motion at short time scales, with a focus on the measurement of the instantaneous velocity of a Brownian particle in a gas and the observation of the transition from ballistic to diffusive Brownian motion in a liquid.     

Comments on “quantum theory does not require action at a distance”

Kraus claims that the argument for action at a distance depends upon the classical prejudice that a measurement always measures something that already exists. It is shown that in the example considered by Kraus no assumption about pre-existing results is needed. A criterion proposed by Kraus for a theory to be compatible with locality is shown to be untenable.     

Espaces homogènes d'Einstein non-compacts

In this text, we consider the solvmanifolds obtained by an abelian extension of two-step nilmanifolds and obtain Einstein metrics (with negative scalar curvature) near to the symmetric spaces.     

Generalized effective-potential Landau theory for the two-dimensional extended Bose-Hubbard model

We analytically study the quantum phase diagrams of ultracold dipolar Bose gases in an optical square lattice at zero temperature by using the generalized effective-potential Landau theory (GEPLT). For a weak nearest-neighbor repulsion, our analytical results are better than the third-order strong-coupling expansion theory calculation. In contrast to a previous quantum Monte Carlo (QMC) simulation, we analytically calculate phase transition boundaries up to the third-order hopping, which are in excellent agreement with QMC simulations for second-order phase transition.     

Collective Excitations in Spin-2 Bose-Einstein Condensates

The Green＇s functions and the correlation functions in spin-2 Bose-Einstein condensates at finite temperature are defined and the generalized Dyson-Beliaev equations are introduced. We discuss the spin conservation in z direction and decouple the Green＇s functions and the generalized Dyson-Beliaev equations according to different spin conservations in z direction. The anomalous vertex functions are introduced and the self-energies are separated into the proper self-energies and the improper self-energies. The generalized Dyson-Beliaev equations are decoupled according to separation of the self-energies. We calculate the Green＇s functions step by step in the Bogoliubov approximation and discuss the collective excitations in spin-2 Bose-Einstein condensates in the polar, ferromagnetic, and cyclic cases, respectively.     

On the Validity of Stokes–Einstein and Stokes–Einstein–Debye Relations in Ionic Liquids and Ionic‐Liquid Mixtures

Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations in the neat ionic liquid (IL) [C₂mim][NTf₂] and IL/chloroform mixtures are studied by means of molecular dynamics (MD) simulations. For this purpose, we simulate the translational diffusion coefficients of the cations and anions, the rotational correlation times of the C(2)? H bond in the cation C₂mim⁺, and the viscosities of the whole system. We find that the SE and SED relations are not valid for the pure ionic liquid, nor for IL/chloroform mixtures down to the miscibility gap (at 50 wt % IL). The deviations from both relations could be related to dynamical heterogeneities described by the non‐Gaussian parameter α(t). If α(t) is close to zero, at a concentration of 1 wt % IL in chloroform, both relations become valid. Then, the effective radii and volumes calculated from the SE and SED equations can be related to the structures found in the MD simulations, such as aggregates of ion pairs. Overall, similarities are observed between the dynamical properties of supercooled water and those of ionic liquids.     

Suppression of Liquid-Liquid Phase Separation and Aggregation of Antibodies by Modest Pressure Application

The high colloidal stability of antibody (immunoglobulin) solutions is important for pharmaceutical applications. Inert cosolutes, excipients, are generally used in therapeutic protein formulations to minimize physical instabilities, such as liquid–liquid phase separation (LLPS), aggregation and precipitation, which are often encountered during manufacturing and storage. Despite their widespread use, a detailed understanding of how excipients modulate the specific protein-protein interactions responsible for these instabilities is still lacking. In this work, we demonstrate the high sensitivity to pressure of globulin condensates as a suitable means to suppress LLPS and subsequent aggregation of concentrated antibody solutions. The addition of excipients has only a minor effect. The high pressure sensitivity observed is due to the fact that these flexible Y-shaped molecules create a considerable amount of void volume in the condensed phase, leading to an overall decrease in the volume of the system upon dissociation of the droplet phase by pressure already at a few tens of to hundred bar. Moreover, we show that immunoglobulin molecules themselves are highly resistant to unfolding under pressure, and can even sustain pressures up to about 6 kbar without conformational changes. This implies that immunoglobulins are resistant to the pressure treatment of foods, such as milk, in high-pressure food-processing technologies, thereby preserving their immunological activity.     

Further results on generalized inverses of tensors via the Einstein product

The notion of the Moore–Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate on this theory by producing a few characterizations of different generalized inverses of tensors. A new method to compute the Moore–Penrose inverse of tensors is proposed. Reverse order laws for several generalized inverses of tensors are also presented. In addition to these, we discuss general solutions of multilinear systems of tensors using such theory.