We obtain a compact analytical solution for the nonlinear equation for the nuclear spin dynamics in the central spin box model in the limit of many nuclear spins. The total nuclear spin component along the external magnetic field is conserved and the two perpendicular components precess or oscillate depending on the electron spin polarization, with the frequency, determined by the nuclear spin polarization. As applications of our solution, we calculate the nuclear spin noise spectrum and describe the effects of nuclear spin squeezing and many body entanglement in the absence of a system excitation.Genuinely non-Hermitian topological phases can be realized in open systems with sufficiently strong gain and loss; in such phases, the Hamiltonian cannot be deformed into a gapped Hermitian Hamiltonian without energy bands touching each other. Comparing Green functions for periodic and open boundary conditions we find that, in general, there is no correspondence between topological invariants computed for periodic boundary conditions, and boundary eigenstates observed for open boundary conditions. Instead, we find that the non-Hermitian winding number in one dimension signals a topological phase transition in the bulk It implies spatial growth of the bulk Green function.We present results on an automaton model of an amorphous solid under cyclic shear. After a transient, the steady state falls into one of three cases in order of increasing strain amplitude (i) pure elastic behavior with no plastic activity, (ii) limit cycles where the state recurs after an integer period of strain cycles, and (iii) irreversible plasticity with longtime diffusion. The number of cycles N required for the system to reach a periodic orbit diverges as the amplitude approaches the yielding transition between regimes (ii) and (iii) from below, while the effective diffusivity D of the plastic strain field vanishes on approach from above. Both of these divergences can be described by a power law. We further show that the average period T of the limit cycles increases on approach to yielding.The description of an open quantum system's decay almost always requires several approximations so as to remain tractable.  https://www.selleckchem.com/products/CHIR-258.html  In this Letter, we first revisit the meaning, domain, and seeming contradictions of a few of the most widely used of such approximations (semigroup) Markovianity, linear response theory, Wigner-Weisskopf approximation, and rotating-wave approximation. Second, we derive an effective time-dependent decay theory and corresponding generalized quantum regression relations for an open quantum system linearly coupled to an environment. This theory covers all timescales and subsumes the Markovian and linear-response results as limiting cases. Finally, we apply our theory to the phenomenon of quantum friction.In this Letter we introduce a novel equation addressing the effect of quantum noise in optical fibers with arbitrary frequency-dependent nonlinear profiles. To the best of our knowledge, such an endeavor has not been undertaken before despite the growing relevance of fiber optics in the design of new quantum devices. We show that the stochastic generalized nonlinear Schrödinger equation, derived from a quantum theory of optical fibers, leads to unphysical results such as a negative photon number and the appearance of a dominant anti-Stokes sideband when applied to this kind of waveguides. Starting from a recently introduced master-equation approach to propagation in fibers, we derive a novel stochastic photon-conserving nonlinear Schrödinger equation suitable for modeling arbitrary nonlinear profiles, thus greatly enhancing the study of fiber-based quantum devices.An analytic formula is given for the total scattering cross section of an electron and a photon at order α^3 in QED. This includes both the double-Compton scattering real-emission contribution as well as the virtual Compton scattering part. When combined with the recent analytic result for the pair-production cross section, the complete α^3 cross section is now known. Both the next-to-leading order calculation as well as the pair-production cross section are computed using modern multiloop calculation techniques, where cut diagrams are decomposed into a set of master integrals that are then computed using differential equations.We provide a closed-form expression for the motivic Kontsevich-Soibelman invariant for M theory in the background of the toric Calabi-Yau threefold K_F_0. This encodes the refined Bogomol'nyi-Prasad-Sommerfield spectrum of SU(2) 5D N=1 Yang-Mills theory on S^1×R^4, corresponding to rank-zero Donaldson-Thomas invariants for K_F_0, anywhere on the Coulomb branch.Ensembles of composite quantum states can exhibit nonlocal behavior in the sense that their optimal discrimination may require global operations. Such an ensemble containing N pairwise orthogonal pure states, however, can always be perfectly distinguished under an adaptive local scheme if (N-1) copies of the state are available. In this Letter, we provide examples of orthonormal bases in two-qubit Hilbert space whose adaptive discrimination require three copies of the state. For this composite system, we analyze multicopy adaptive local distinguishability of orthogonal ensembles in full generality which, in turn, assigns varying nonlocal strength to different such ensembles. We also come up with ensembles whose discrimination under an adaptive separable scheme require less numbers of copies than adaptive local schemes. Our construction finds important application in multipartite secret sharing tasks and indicates toward an intriguing superadditivity phenomenon for locally accessible information.Experiments measuring the Newtonian gravitational constant G can offer uniquely sensitive probes of the test of the gravitational inverse-square law. An analysis of the non-Newtonian effect in two independent experiments measuring G is presented, which permits a test of the 1/r^2 law at the centimeter range. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 5-500 mm and improves the previous bounds by up to a factor of 7 at the length range of 60-100 mm.