Big Rip in SO(1,1) phantom universe

For the inverse linear potential, the SO(1,1) field behaves as phantom for late time and the Big Rip will occur. The field approaches zero as time approaches the Big Rip, here. For this potential the phantom equation of state takes the late-time minimum $w_\Phi=-3$. We give some discussions that the Big Rip in the SO(1,1) model may be treated as either the transition point of universe from expansion to extract phase or the final state. In the latter picture of the universe, the field has the $T$ symmetry and the scale factor possesses the $CT$ symmetry, for which the SO(1,1) charge $\bar{Q}$ plays a crucial role.Comment: 10 pages, 1 figur

Critical state of phantom universe

The late-time evolution behavior of the autonomous system in the SO(1,1) dark energy model with power-law potential is studied. Big Rip may be a critical point of the autonomous system. This means that such a Big Rip may be considered as the middle state between the expanding and contracting phases of phantom universe. This result is also valid for some special interactions between matter and dark energy.Comment: 6 pages, revtex

Vertex Operators of Open String States in the Intersecting D-brane World

Starting with a new bosonization scheme for the \beta\gamma CFT of the super-conformal ghosts, vertex operators are constructed for massless open string states in the intersecting D-brane world. These vertex operators satisfy all requirements for a consistent RNS formulation of superstring theories, so GSO projections can be properly taken.Comment: 4 pages, RevTe

Teleparallel Gravity in Five Dimensional Theories

We study teleparallel gravity in five-dimensional spacetime with particular discussions on Kaluza-Klein (KK) and braneworld theories. We directly perform the dimensional reduction by differential forms. In the braneworld theory, the teleparallel gravity formalism in the Friedmann-Lema\^{i}tre-Robertson-Walker cosmology is equivalent to GR due to the same Friedmann equation, whereas in the KK case the reduction of our formulation does not recover the effect as GR of 4-dimensional spacetime.Comment: 12 pages, no figure, revised version accepted for publication in CQ

Fidelity mechanics: analogues of the four thermodynamic laws and Landauer's principle

Fidelity mechanics is formalized as a framework to investigate quantum critical phenomena in quantum many-body systems. This is achieved by introducing fidelity temperature to properly quantify quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer's principle at zero temperature. Fidelity flows are defined and may be interpreted as an alternative form of renormalization group flows. Thus, both stable and unstable fixed points are characterized in terms of fidelity temperature and fidelity entropy: divergent fidelity temperature for unstable fixed points and zero fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, an inherently fundamental role of duality is clarified, resulting in a canonical form of the Hamiltonian in fidelity mechanics. Dualities, together with symmetry groups and factorizing fields, impose the constraints on a fidelity mechanical system, thus shaping fidelity flows from an unstable fixed point to a stable fixed point. A detailed analysis of fidelity mechanical state functions is presented for the quantum XY model, the transverse field quantum Ising chain in a longitudinal field, the spin-$1/2$ XYZ model and the XXZ model in a magnetic field.Comment: 56 pages, 23 figures and 2 table

The power-law expansion universe and dark energy evolution

In order to depict the transition from deceleration to acceleration expansion of the universe we use a power-law expansion scale factor, $a\sim t^{n_0+bt^m}$, with $n_0$, $b$ and $m$ three parameters determined by $H_0$, $q_0$ and $z_T$. For the spatially flat, isotropic and homogeneous universe, such a scale factor leads to the results that the dark energy density is slowly changing currently, and predicts the equation of state $w_X$ changes from $w_X>-1$ to $w_X<-1$.Comment: 10 pages, 2 figure

The power-law expansion universe and the late-time behavior

Using the SNe Ia data we determine the three parameters in the power-law expanding universe model with time-dependent power \cite{W}. Inputting $H_0$ and $t_0$, then we find the $\dot{a}-t$ evolution curve with $m=5.0$ and $q_0=-0.90$ can fit very well to that from SNe observation data. The model predicts the transition redshift $z\simeq0.38$. The dark energy deduced from this model have phantom property but the universe doesn't encounter the Big Rip singularity. Assuming that this model with the three parameters is valid for the future universe, then we predict that the total energy density of the universe is decreasing and will soon reach its minimum.Comment: 10 pages, 5 figure

Extended complex scalar field as quintessence

In this paper, we show the possibility that an extended complex scalar field can be considered as an extended complex quintessence. For this model, we derive the basic equations with a parameter $\eta$ which govern the evolution of the Universe. Our model may contain a complex quintessence model for $\eta =-1$ and a real quitessence model for $\eta =0$.Comment: 8 pages. to appear in Grav. & Cosmolog

Behavior Sequence Transformer for E-commerce Recommendation in Alibaba

Deep learning based methods have been widely used in industrial recommendation systems (RSs). Previous works adopt an Embedding&MLP paradigm: raw features are embedded into low-dimensional vectors, which are then fed on to MLP for final recommendations. However, most of these works just concatenate different features, ignoring the sequential nature of users' behaviors. In this paper, we propose to use the powerful Transformer model to capture the sequential signals underlying users' behavior sequences for recommendation in Alibaba. Experimental results demonstrate the superiority of the proposed model, which is then deployed online at Taobao and obtain significant improvements in online Click-Through-Rate (CTR) comparing to two baselines.Comment: 4 pages, 1 figur

On the integrable inhomogeneous Myrzakulov I equation

By using the prolongation structure theory proposed by Morris, we give a (2+1)-dimensional integrable inhomogeneous Heisenberg Ferromagnet models, namely, the inhomogeneous Myrzakulov I equation. Through the motion of space curves endowed with an additional spatial variable, its geometrical equivalent counterpart is also presented.Comment: 7 page