The effect of temperature evolution on the interior structure of H2{}_{2}O-rich planets

For most planets in the range of radii from 1 to 4 R$_{\oplus}$, water is a major component of the interior composition. At high pressure H${}_{2}$O can be solid, but for larger planets, like Neptune, the temperature can be too high for this. Mass and age play a role in determining the transition between solid and fluid (and mixed) water-rich super-Earth. We use the latest high-pressure and ultra-high-pressure phase diagrams of H${}_{2}$O, and by comparing them with the interior adiabats of various planet models, the temperature evolution of the planet interior is shown, especially for the state of H${}_{2}$O. It turns out that the bulk of H${}_{2}$O in a planet's interior may exist in various states such as plasma, superionic, ionic, Ice VII, Ice X, etc., depending on the size, age and cooling rate of the planet. Different regions of the mass-radius phase space are also identified to correspond to different planet structures. In general, super-Earth-size planets (isolated or without significant parent star irradiation effects) older than about 3 Gyr would be mostly solid.Comment: Accepted by ApJ, in print for March 2014 (14 pages, 3 colored figures, 1 table

On the performance of two protocols: SARG04 and BB84

We compare the performance of BB84 and SARG04, the later of which was proposed by V. Scarani et al., in Phys. Rev. Lett. 92, 057901 (2004). Specifically, in this paper, we investigate SARG04 with two-way classical communications and SARG04 with decoy states. In the first part of the paper, we show that SARG04 with two-way communications can tolerate a higher bit error rate (19.4% for a one-photon source and 6.56% for a two-photon source) than SARG04 with one-way communications (10.95% for a one-photon source and 2.71% for a two-photon source). Also, the upper bounds on the bit error rate for SARG04 with two-way communications are computed in a closed form by considering an individual attack based on a general measurement. In the second part of the paper, we propose employing the idea of decoy states in SARG04 to obtain unconditional security even when realistic devices are used. We compare the performance of SARG04 with decoy states and BB84 with decoy states. We find that the optimal mean-photon number for SARG04 is higher than that of BB84 when the bit error rate is small. Also, we observe that SARG04 does not achieve a longer secure distance and a higher key generation rate than BB84, assuming a typical experimental parameter set.Comment: 48 pages, 10 figures, 1 column, changed Figs. 7 and

Understanding Constraint-Based Processes: A Precursor to Conceptual Change in Physics

Chi (1992; Chi and Slotu, 1993; Slotta, Chi and Joram, 1995) suggests that students experience difficulty in learning certain physics concepts because they inappropriately attribute these concepts with the ontology of material substances(MS). According to accepted physics theory, these concepts (e.g., light, heat, electric current) are actually a special type of process that Chi (1992) calls "Constraint-Based Interactions" (CBI). Students cannot understand the process-like nature of these concepts because of their bias towards substance-like conceptions, and also because they are unfamiliar with the CBI ontology. Thus, conceptual change can be facilitated by providing students with some knowledge of the CBI ontology before they receive the relevant physics instruction. This CBI training was provided by means of a computer-based instructional module in which students manipulated simulations as they read an accompanying text concerning four attributes of the CBI ontology. A control group simply read a (topically similar) text from the computer screen. The two groups then studied a physics textbook concerning concepts of electricity, and performed a post-test which was assessed for evidence of conceptual change. As a result of their training in the CBI ontology, the experimental group showed significant evidence of conceptual change with regards to the CBI concept of electric current

Higher rank numerical ranges of normal matrices

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_n$ has eigenvalues $a_1, \..., a_n$, then its higher rank numerical range $\Lambda_k(A)$ is the intersection of convex polygons with vertices $a_{j_1}, \..., a_{j_{n-k+1}}$, where $1 \le j_1 < \... < j_{n-k+1} \le n$. In this paper, it is shown that the higher rank numerical range of a normal matrix with $m$ distinct eigenvalues can be written as the intersection of no more than $\max\{m,4\}$ closed half planes. In addition, given a convex polygon ${\mathcal P}$ a construction is given for a normal matrix $A \in M_n$ with minimum $n$ such that $\Lambda_k(A) = {\mathcal P}$. In particular, if ${\mathcal P}$ has $p$ vertices, with $p \ge 3$, there is a normal matrix $A \in M_n$ with $n \le \max\left\{p+k-1, 2k+2 \right\}$ such that $\Lambda_k(A) = {\mathcal P}$.Comment: 12 pages, 9 figures, to appear in SIAM Journal on Matrix Analysis and Application

Field-dependent diamagnetic transition in magnetic superconductor Sm1.85Ce0.15CuO4−ySm_{1.85} Ce_{0.15} Cu O_{4-y}

The magnetic penetration depth of single crystal $\rm{Sm_{1.85}Ce_{0.15}CuO_{4-y}}$ was measured down to 0.4 K in dc fields up to 7 kOe. For insulating $\rm{Sm_2CuO_4}$, Sm$^{3+}$ spins order at the N\'{e}el temperature, $T_N = 6$ K, independent of the applied field. Superconducting $\rm{Sm_{1.85}Ce_{0.15}CuO_{4-y}}$ ($T_c \approx 23$ K) shows a sharp increase in diamagnetic screening below $T^{\ast}(H)$ which varied from 4.0 K ($H = 0$) to 0.5 K ($H =$ 7 kOe) for a field along the c-axis. If the field was aligned parallel to the conducting planes, $T^{\ast}$ remained unchanged. The unusual field dependence of $T^{\ast}$ indicates a spin freezing transition that dramatically increases the superfluid density.Comment: 4 pages, RevTex

Security proof of a three-state quantum key distribution protocol without rotational symmetry

Standard security proofs of quantum key distribution (QKD) protocols often rely on symmetry arguments. In this paper, we prove the security of a three-state protocol that does not possess rotational symmetry. The three-state QKD protocol we consider involves three qubit states, where the first two states, |0_z> and |1_z>, can contribute to key generation and the third state, |+>=(|0_z>+|1_z>)/\sqrt{2}, is for channel estimation. This protocol has been proposed and implemented experimentally in some frequency-based QKD systems where the three states can be prepared easily. Thus, by founding on the security of this three-state protocol, we prove that these QKD schemes are, in fact, unconditionally secure against any attacks allowed by quantum mechanics. The main task in our proof is to upper bound the phase error rate of the qubits given the bit error rates observed. Unconditional security can then be proved not only for the ideal case of a single-photon source and perfect detectors, but also for the realistic case of a phase-randomized weak coherent light source and imperfect threshold detectors. Our result on the phase error rate upper bound is independent of the loss in the channel. Also, we compare the three-state protocol with the BB84 protocol. For the single-photon source case, our result proves that the BB84 protocol strictly tolerates a higher quantum bit error rate than the three-state protocol; while for the coherent-source case, the BB84 protocol achieves a higher key generation rate and secure distance than the three-state protocol when a decoy-state method is used.Comment: 10 pages, 3 figures, 2 column