Microscopic explanation for black hole phase transitions via Ruppeiner geometry: two competing factors-the temperature and repulsive interaction among BH molecules

Charged dilatonic black hole (BH) has rather rich phase diagrams which may contain zeroth-order, first-order as well as reentrant phase transitions (RPTs) depending on the value of the coupling constant $\alpha$ between the electromagnetic field and the dilaton. We try to give a microscopic explanation for these phase transitions by adopting Ruppeiner's approach. By studying the behaviors of the Ruppeiner invariant $R$ along the co-existing lines, we find that the various phase transitions may be qualitatively well explained as a result of two competing factors: the first one is the low-temperature effect which tends to shrink the BH and the second one is the repulsive interaction between the BH molecules which, on the contrary, tends to expand the BH. In the standard phase transition without RPT, as temperature is lowered, the first kind of factor dominates over the second one, so that large black hole (LBH) tends to shrink and thus transits to small black hole (SBH); While in the RPT, after the LBH-SBH transition, as temperature is further decreased, the strength of the second factor increases quickly and finally becomes strong enough to dominate over the first factor, so that SBH tends to expand to release the high repulsion and thus transits back to LBH. Moreover, by comparing the behavior of $R$ versus the temperature $T$ with fixed pressure to that of ordinary two-dimensional thermodynamical systems but with fixed specific volume, it is interesting to see that SBH behaves like a Fermionic gas system in cases with RPT, while it behaves oppositely to an anyon system in cases without RPT. And in all cases, LBH behaves like a nearly ideal gas system.Comment: 16 pages, 7 figures;v2:minor modifications, refs added;v3:minor modifications, more refs added; v4:minor modifications to match published versio

2-Modules and the Representation of 2-Rings

In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring \cR, we prove that its modules form a 2-Abelian category.Comment: 78 pages, 99 figure

Higher Dimensional Homology Algebra III:Projective Resolutions and Derived 2-Functors in (2-SGp)

In this paper, we will define the derived 2-functor by projective resolution of any symmetric 2-group, and give some related properties of the derived 2-functor.Comment: 30 pages, 50 figures. This is the third paper of the series of our works on higher dimensional homological algebra. In the coming papers, we define the right derived 2-functor in the 2-categories (2-SGp) and (\cR-2-Mod). In this version, we correct some errors in last version, add more results, such as 2-chain homotopy, its related results, et

Higher Dimensional Homology Algebra II:Projectivity

In this paper, we will prove that the 2-category (2-SGp) of symmetric 2-groups and 2-category (\cR-2-Mod) of \cR-2-modules(\cite{5}) have enough projective objects, respectively.Comment: 10 pages, 4 figures. This is the second paper of the series works on higher dimensional homology algebra. The first paper is "2-Modules and the Representation of 2-Rings\cite{4}". In the coming papers, we shall give the definition of injective object in the 2-category (\cR-2-Mod), prove that this 2-category has enough injective objects and develop the (co)homology theory of i

Higher Dimensional Homology Algebra IV:Projective Resolutions and Derived 2-Functors in (\cR-2-Mod)

In this paper, we will construct the projective resolution of any \cR-2-module, define the derived 2-functor and give some related properties of the derived 2-functor.Comment: 17pages, 32 figures, This is the fourth paper of the series of our works on higher dimensional homological algebra. In the coming papers, we shall define the right derived 2-functor in the 2-categories (2-SGp) and (\cR-2-Mod), and give some relations of left derived 2-functors and right derived 2-functor

Higher Dimensional Homology Algebra V:Injective Resolutions and Derived 2-Functors in (\cR-2-Mod)

In this paper, we will construct the injective resolution of any \cR-2-module, define the right derived 2-functor, and give some related properties of the derived 2-functor in (\cR-2-Mod).Comment: 29 pages, 57 figures. This paper is the fifth paper of the series of our works on higher dimensional homology algebra. In our coming papers, we shall define \cExt 2-functor and spectral sequence in an abelian 2-category, try to give the relation between \cExt 2-functor and the extension of 2-module

Lower bound on concurrence for arbitrary-dimensional tripartite quantum systems

In this paper, we study the concurrence of arbitrary dimensional tripartite quantum systems. An explicit operational lower bound of concurrence is obtained in terms of the concurrence of sub-states. A given example show that our lower bound may improve the well known existing lower bounds of concurrence. The significance of our result is to get a lower bound when we study the concurrence of arbitrary dimensional multipartite quantum systems.Comment: 1 figures, Quantum Information Processing 201

Inversion-symmetry-breaking-activated shear Raman bands in T′T'-MoTe2_2

Type-II Weyl fermion nodes, located at the touching points between electron and hole pockets, have been recently predicted to occur in distorted octahedral ($T'$) transition metal dichalcogenide semimetals, contingent upon the condition that the layered crystal has the noncentrosymmetric orthorhombic ($T'_{or}$) stacking. Here, we report on the emergence of two shear Raman bands activated by inversion symmetry breaking in $T'$-MoTe$_2$ due to sample cooling. Polarization and crystal orientation resolved measurements further point to a phase transition from the monoclinic ($T'_{mo}$) structure to the desired $T'_{or}$ lattice. These results provide spectroscopic evidence that low-temperature $T'$-MoTe$_2$ is suitable for probing type-II Weyl physics

Lower bound of multipartite concurrence based on sub-multipartite quantum systems

We study the concurrence of arbitrary dimensional multipartite quantum systems. An explicit analytical lower bound of concurrence for four-partite mixed states is obtained in terms of the concurrences of tripartite mixed states. Detailed examples are given to show that our lower bounds improve the existing lower bounds of concurrence. The approach is generalized to five-partite quantum systems.Comment: 9 pages,2 figures, correct some error

Estimation on geometric measure of quantum coherence

We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115, 020403 (2015)]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states -- maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.Comment: 13 pages, 1 figur