Dynamical Electron Mass in a Strong Magnetic Field

Motivated by recent interest in understanding properties of strongly magnetized matter, we study the dynamical electron mass generated through approximate chiral symmetry breaking in QED in a strong magnetic field. We reliably calculate the dynamical electron mass by numerically solving the nonperturbative Schwinger-Dyson equations in a consistent truncation within the lowest Landau level approximation. It is shown that the generation of dynamical electron mass in a strong magnetic field is significantly enhanced by the perturbative electron mass that explicitly breaks chiral symmetry in the absence of a magnetic field.Comment: 5 pages, 1 figure, published versio

From Intramolecular (Circular) in an Isolated Molecule to Intermolecular Hole Delocalization in a Two‐Dimensional Solid‐State Assembly: The Case of Pillarene

To achieve long‐range charge transport/separation and, in turn, bolster the efficiency of modern photovoltaic devices, new molecular scaffolds are needed that can self‐assemble in two‐dimensional (2D) arrays while maintaining both intra‐ and intermolecular electronic coupling. In an isolated molecule of pillarene, a single hole delocalizes intramolecularly via hopping amongst the circularly arrayed hydroquinone ether rings. The crystallization of pillarene cation radical produces a 2D self‐assembly with three intermolecular dimeric (sandwich‐like) contacts. Surprisingly, each pillarene in the crystal lattice bears a fractional formal charge of +1.5. This unusual stoichiometry of oxidized pillarene in crystals arises from effective charge distribution within the 2D array via an interplay of intra‐ and intermolecular electronic couplings. This important finding is expected to help advance the rational design of efficient solid‐state materials for long‐range charge transfer

Challenges to smartphone applications for melanoma detection

This commentary addresses the emerging market for health-related smartphone applications. Specific to dermatology, there has been a significant increase not only in applications that promote skin cancer awareness and education but also in those meant for detection. With evidence showing that 365 dermatology-related applications were available in 2014--up from 230 in 2012--and that 1 in 5 patients under the age of 50 have used a smartphone to help diagnose a skin problem, there is clearly a large subset of patients participating in this growing trend. Therefore, we are obligated to take a closer look into this phenomenon. Studies have shown that applications are inferior to in-person consultations with one study showing that 3 out of 4 applications incorrectly classified 30% or more melanomas as low-risk lesions. Although the FDA gained regulatory oversight over mobile health applications in 2012 and recently released their statement in 2015, their reach only extends to cover a selected portion of these applications, leaving many unregulated as they continue to be marketed toward our patients. Dermatologists should be updated on our current situation in order to properly counsel patients on the risks and benefits of these applications and whether they are acceptable for use. © 2016 by the article author(s)

Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer

We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number $m$ of electrons occupying a given number $n$ of spin orbitals. Each spin orbital is mapped to a qubit: the states $| 1 >$ and $| 0>$ of the qubit represent, respectively, whether the spin orbital is occupied by an electron or not. To prepare a general state in the full Hilbert space of $n$ qubits, which is of dimension $2^{n}$%, $O(2^{n})$ controlled-NOT gates are needed, i.e., the number of gates scales \emph{exponentially} with the number of qubits. We make use of the fact that the state to be prepared lies in a smaller Hilbert space, and we find an algorithm that requires at most $O(2^{m+1} n^{m}/{m!})$ gates, i.e., scales \emph{polynomially} with the number of qubits $n$, provided $n\gg m$. The algorithm is simulated numerically for the cases of the hydrogen molecule and the water molecule. The numerical simulations show that when additional symmetries of the system are considered, the number of gates to prepare the state can be drastically reduced, in the examples considered in this paper, by several orders of magnitude, from the above estimate.Comment: 11 pages, 8 figures, errors are corrected, Journal information adde

Density Evolution for Asymmetric Memoryless Channels

Density evolution is one of the most powerful analytical tools for low-density parity-check (LDPC) codes and graph codes with message passing decoding algorithms. With channel symmetry as one of its fundamental assumptions, density evolution (DE) has been widely and successfully applied to different channels, including binary erasure channels, binary symmetric channels, binary additive white Gaussian noise channels, etc. This paper generalizes density evolution for non-symmetric memoryless channels, which in turn broadens the applications to general memoryless channels, e.g. z-channels, composite white Gaussian noise channels, etc. The central theorem underpinning this generalization is the convergence to perfect projection for any fixed size supporting tree. A new iterative formula of the same complexity is then presented and the necessary theorems for the performance concentration theorems are developed. Several properties of the new density evolution method are explored, including stability results for general asymmetric memoryless channels. Simulations, code optimizations, and possible new applications suggested by this new density evolution method are also provided. This result is also used to prove the typicality of linear LDPC codes among the coset code ensemble when the minimum check node degree is sufficiently large. It is shown that the convergence to perfect projection is essential to the belief propagation algorithm even when only symmetric channels are considered. Hence the proof of the convergence to perfect projection serves also as a completion of the theory of classical density evolution for symmetric memoryless channels.Comment: To appear in the IEEE Transactions on Information Theor