Abstract:
We study the effect of energy loss on charm and bottom quarks in high-energy heavy-ion collisions including hadronization, longitudinal expansion and partial thermalization. We consider in detail the detector geometry and single lepton energy cuts of the ALICE and CMS detectors at the Large Hadron Collider (LHC) to show the large suppression of high $p_T$ heavy quarks and the consequences of their semileptonic decays.

Abstract:
After the public release of A Multi-Phase Transport (AMPT) model in 2004 and detailed descriptions of its physics in a 2005 paper, the model has been constantly updated and developed to make it more versatile and to include more physical processes. This an overview of recent developments of the AMPT model. Ongoing work to fix the violation of charge conservation in the code as well as possible directions for future work are also discussed.

Abstract:
Randomly amplified polymorphic DNA (RAPD) technique was applied to assess the genetic variations and phylogenetic relationships in genetic differentiation within 4 Chromium-treatment Leersia hexandra. The fresh leaves of Leersia hexandra cultivated on the condition of chrome pollution and exogenous organic acids were used as experimental material. The genomic DNA of Leersia hexandra was extracted by using CTAB method. The results showed that different samples of Leersia hexandra exhibited DNA polymorphism when using the random primer S43, S51and S55 as the primers in the RAPD reaction. One specific DNA band about 1000 bp was found in the sample which treated with 10 mmol/L concentration EDTA when used the S43 primer to RAPD. The obvious differences between different EDTA-treatment levels suggest that EDTA has certain effects on enrichment to heavy metals of Leersia hexandra, it will be more favored to Leersia hexandra accumulation of chromium when EDTA concentration increased.

Abstract:
We consider a bipartite quantum system H_A x H_B with M=dim H_A and N=dim H_B. We study the set E of extreme points of the compact convex set of all states having positive partial transpose (PPT) and its subsets E_r={rho in E: rank rho=r}. Our main results pertain to the subsets E_r^{M,N} of E_r consisting of states whose reduced density operators have ranks M and N, respectively. The set E_1 is just the set of pure product states. It is known that E_r^{M,N} is empty for 1< r <= min(M,N) and for r=MN. We prove that also E_{MN-1}^{M,N} is empty. Leinaas, Myrheim and Sollid have conjectured that E_{M+N-2}^{M,N} is not empty for all M,N>2 and that E_r^{M,N} is empty for 13. We introduce the notion of "good" states, show that all pure states are good and give a simple description of the good separable states. For a good state rho in E_{M+N-2}^{M,N}, we prove that the range of rho contains no product vectors and that the partial transpose of rho has rank M+N-2 as well. In the special case M=3, we construct good 3 x N extreme states of rank N+1 for all N>3.

Abstract:
It is known that some two qutrit entangled states of rank 4 with positive partial transpose [PPT] can be built from the unextendible product bases [UPB]. We show that this fact is indeed universal, namely all such states can be constructed from UPB. We also classify the 5-dimensional subspaces of two qutrits which contain only finitely many product states (up to scalar multiple), and in particular those spanned by a UPB.

Abstract:
We show that the length of a qubit-qutrit separable state is equal to the max(r,s), where r is the rank of the state and s is the rank of its partial transpose. We refer to the ordered pair (r,s) as the birank of this state. We also construct examples of qubit-qutrit separable states of any feasible birank (r,s). We determine the closure of the set of normalized two-qutrit entangled states of rank four having positive partial transpose (PPT). The boundary of this set consists of all separable states of length at most four. We prove that the length of any qubit-qudit separable state of birank (d+1,d+1) is d+1. We also show that all qubit-qudit PPT entangled states of birank (d+1,d+1) can be built in a simple way from edge states. If V is a subspace of dimension k

Abstract:
Background: The ground state neutron density of a medium mass nucleus contains fundamental nuclear structure information and is at present relatively poorly known. Purpose: We explore if parity violating elastic electron scattering can provide a feasible and model independent way to determine not just the neutron radius but the full radial shape of the neutron density $\rho_n(r)$ and the weak charge density $\rho_W(r)$ of a nucleus. Methods: We expand the weak charge density of $^{48}$Ca in a model independent Fourier Bessel series and calculate the statistical errors in the individual coefficients that might be obtainable in a model parity violating electron scattering experiment. Results: We find that it is feasible to determine roughly six Fourier Bessel coefficients of the weak charge density of 48Ca within a reasonable amount of beam time. However, it would likely be much harder to determine the full weak density of a significantly heavier nucleus such as 208Pb. Conclusions: Parity violating elastic electron scattering can determine the full weak charge density of a medium mass nucleus in a model independent way. This weak density contains fundamental information on the size, surface thickness, shell oscillations, and saturation density of the neutron distribution in a nucleus. The measured $\rho_W(r)$, combined with the previously known charge density $\rho_{ch}(r)$, will literally provide a detailed textbook picture of where the neutrons and protons are located in an atomic nucleus.

Abstract:
It is known that he bipartite quantum states, with rank strictly smaller than the maximum of the ranks of its two reduced states, are distillable by local operations and classical communication. Our first main result is that this is also true for NPT states with rank equal to this maximum. (A state is PPT if the partial transpose of its density matrix is positive semidefinite, and otherwise it is NPT.) This was conjectured first in 1999 in the special case when the two local ranks are equal. Our second main result provides a complete solution of the separability problem for bipartite states of rank 4. Namely, we show that such a state is separable if and only if it is PPT and its range contains at least one product state. We also prove that the so called checkerboard states are distillable if and only if they are NPT.

Abstract:
One of the most important problems in quantum information is the separability problem, which asks whether a given quantum state is separable. We investigate multipartite states of rank at most four which are PPT (i.e., all their partial transposes are positive semidefinite). We show that any PPT state of rank two or three is separable and has length at most four. For separable states of rank four, we show that they have length at most six. It is six only for some qubit-qutrit or multiqubit states. It turns out that any PPT entangled state of rank four is necessarily supported on a 3x3 or a 2x2x2 subsystem. We obtain a very simple criterion for the separability problem of the PPT states of rank at most four: such a state is entangled if and only if its range contains no product vectors. This criterion can be easily applied since a four-dimensional subspace in the 3x3 or 2x2x2 system contains a product vector if and only if its Pluecker coordinates satisfy a homogeneous polynomial equation (the Chow form of the corresponding Segre variety). We have computed an explicit determinantal expression for the Chow form in the former case, while such expression was already known in the latter case.

Abstract:
Let E' denote the set of non-normalized two-qutrit entangled states of rank four having positive partial transpose (PPT). We show that the set of SLOCC equivalence classes of states in E', equipped with the quotient topology, is homeomorphic to the quotient R/A_5 of the open rectangular box R in the Euclidean space R^4 by an action of the alternating group A_5. We construct an explicit map omega: Omega -> E', where Omega is the open positive orthant in R^4, whose image meets every SLOCC equivalence class E containeed in E'. Although the intersection of the image of omega and E is not necessarily a singleton set, it is always a finite set of cardinality at most 60. By abuse of language, we say that any state in this intersection is a canonical form of states rho in E. In particular, we show that all checkerboard PPT entangled states can be parametrized up to SLOCC equivalence by only two real parameters. We also summarize the known results on two-qutrit extreme PPT states and edge states, and examine which other interesting properties they may have. Thus we find the first examples of extreme PPT states whose rank is different from the rank of its partial transpose.