Binary Bose-Einstein condensates in a disordered time-dependent potential

We study the non-equilibrium evolution of binary Bose-Einstein condensates in the presence of weak random potential with a Gaussian correlation function using the time-dependent perturbation theory. We apply this theory to construct a closed set of equations that highlight the role of the spectacular interplay between the disorder and the interspecies interactions in the time evolution of the density induced by disorder in each component. It is found that this latter increases with time favoring localization of both species. The time scale at which the theory remains valid depends on the respective system parameters. We show analytically and numerically that such a system supports a steady state that periodically changing during its time propagation. The obtained dynamical corrections indicate that disorder may transform the system into a stationary out-of-equilibrium states. Understanding this time evolution is pivotal for the realization of Floquet condensates.

Northeast Arctic Cod and Prey Match-Mismatch in a High-Latitude Spring-Bloom System

By combining an ocean model, a nutrient-phytoplankton-zooplankton-detritus-model and an individual-based model for early life stages of Northeast Arctic cod we systematically investigate food limitations and growth performance for individual cod larvae drifting along the Norwegian coast from spawning grounds toward nursery areas in the Barents Sea. We hypothesize that there is food shortage for larvae spawned early and late in the 2-monthlong spawning period, and to a larger degree to the north and south of the main spawning grounds in the Lofoten. Model results for three contrasting years (1995, 2001, and 2002) show that spawning early in the season at spawning grounds in the Lofoten and farther north is favorable for larval growth close to their size- and temperature-dependent potential. Still, both early and late spawned larvae experience slower growth than individuals originating closer to the time of peak spawning late March/early April. The reasons are low temperatures and shortage in suitable prey, respectively, and this occurs more frequent in areas of strong currents about 1–2 months post hatching. In particular, late spawned larvae grow relatively slow despite higher temperatures later in the season because they are outgrown by their preferred prey.

Confinement in bilayer graphene via intra- and inter-layer interactions

We consider confinement of Dirac fermions in AB-stacked bilayer graphene by inhomogeneous on-site interactions, (pseudo-)magnetic field or inter-layer interaction. Working within the framework of four-band approximation, we focus on the systems where the stationary equation is reducible into two stationary equations with 2x2 Dirac-type Hamiltonians and auxiliary interactions. We show that the localized states are given in terms of solutions of an effective Schrodinger equation with energy-dependent potential. We consider several scenarios where bilayer graphene is subject to inhomogneous (pseudo-)magnetic field, on-site interactions or inter-layer coupling. In explicit examples, we provide analytical solutions for the states localized by local fluctuations or periodicity defects of the interactions.

A real expectation value of the time-dependent non-Hermitian Hamiltonians

With the aim to solve the time-dependent Schr ̈odinger equation associated to a time-dependent non-Hermitian Hamiltonian, we introduce a unitary transformation that maps the Hamiltonian to a time-independent PT-symmetric one. Consequently, the solution of time-dependent Schrödinger equation becomes easily deduced and the evolution preserves the C(t)PT -inner product, where C(t) is a obtained from the charge conjugation operator C through a time dependent unitary transformation. Moreover, the expectation value of the non-Hermitian Hamiltonian in the C(t)PT normed states is guaranteed to be real. As an illustration, we present a specific quantum system given by a quantum oscillator with time-dependent mass subjected to a driving linear complex time-dependent potential.

An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation

In this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and nonlocal initial supplemented by over-determination measurement is numerically investigated. Though the inverse problem under consideration is ill-posed by being unstable to noise in the input data, it has a unique solution. The Crank–Nicolson-finite difference method (CN-FDM) along with the Tikhonov regularization (TR) is applied for calculating an accurate and stable numerical solution. The programming language MATLAB built-in lsqnonlin is used to solve the obtained nonlinear minimization problem. The simulated noisy input data can be inverted by both analytical and numerically simulated. The obtained results show that they are accurate and stable. The stability analysis is performed by using Fourier series.

Transcriptomics-Based Repositioning of Natural Compound, Eudesmin, as a PRC2 Modulator

Extensive epigenetic remodeling occurs during the cell fate determination of stem cells. Previously, we discovered that eudesmin regulates lineage commitment of mesenchymal stem cells through the inhibition of signaling molecules. However, the epigenetic modulations upon eudesmin treatment in genomewide level have not been analyzed. Here, we present a transcriptome profiling data showing the enrichment in PRC2 target genes by eudesmin treatment. Furthermore, gene ontology analysis showed that PRC2 target genes downregulated by eudesmin are closely related to Wnt signaling and pluripotency. We selected DKK1 as an eudesmin-dependent potential top hub gene in the Wnt signaling and pluripotency. Through the ChIP-qPCR and RT-qPCR, we found that eudesmin treatment increased the occupancy of PRC2 components, EZH2 and SUZ12, and H3K27me3 level on the promoter region of DKK1, downregulating its transcription level. According to the analysis of GEO profiles, DEGs by depletion of Oct4 showed an opposite pattern to DEGs by eudesmin treatment. Indeed, the expression of pluripotency markers, Oct4, Sox2, and Nanog, was upregulated upon eudesmin treatment. This finding demonstrates that pharmacological modulation of PRC2 dynamics by eudesmin might control Wnt signaling and maintain pluripotency of stem cells.