New, Highly Accurate Propagator for the Linear and Nonlinear Schr\"odinger Equation

A propagation method for the time dependent Schr\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u_t -Gu = s where G is a operator (matrix) and u is a time-dependent solution vector. Highly accurate methods, based on polynomial approximation of a modified exponential evolution operator, had been developed already for this type of problems where G is a linear, time independent matrix and s is a constant vector. In this paper we will describe a new algorithm for the more general case where s is a time-dependent r.h.s vector. An iterative version of the new algorithm can be applied to the general case where G depends on t or u. Numerical results for Schr\"odinger equation with time-dependent potential and to non-linear Schr\"odinger equation will be presented.Comment: 14 page

Quasi-Particles, Conformal Field Theory, and qq-Series

We review recent results concerning the representation of conformal field theory characters in terms of fermionic quasi-particle excitations, and describe in detail their construction in the case of the integrable three-state Potts chain. These fermionic representations are q-series which are generalizations of the sums occurring in the Rogers-Ramanujan identities

An efficient scheme for numerical simulations of the spin-bath decoherence

We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of few coupled spins: (i) determining the pointer states of the system, and (ii) determining the temporal decay of quantum oscillations. As our results demonstrate, for determining the pointer states, the Chebyshev-based scheme is at least a factor of 8 faster than existing algorithms based on the Suzuki-Trotter decomposition. For the problems of second type, the Chebyshev-based approach has been 3--4 times faster than the Suzuki-Trotter-based schemes. This conclusion holds qualitatively for a wide spectrum of systems, with different spin baths and different Hamiltonians.Comment: 8 pages (RevTeX), 3 EPS figure

Towards Comprehensive Observing and Modeling Systems for Monitoring and Predicting Regional to Coastal Sea Level

A major challenge for managing impacts and implementing effective mitigation and adaptation strategies for coastal zones affected by future sea level (SL) rise is our very limited capacity to predict SL change on coastal scales, over various timescales. Predicting coastal SL requires the ability to monitor and simulate a multitude of physical processes affecting SL, from local effects of wind waves and river runoff to remote influences of the large-scale ocean circulation on the coast. Here we assess our current understanding of the causes of coastal SL variability on seasonal to multi-decadal timescales, including geodetic, oceanographic and atmospheric aspects of the problem, and review available observing systems informing on coastal SL. We also review the ability of current models and data assimilation systems to estimate coastal SL variations and of atmosphere-ocean global coupled models and related regional downscaling efforts to project future SL changes. We discuss (1) key observational gaps and uncertainties, and priorities for the development of an optimal and integrated coastal SL observing system, (2) strategies for advancing model capabilities in forecasting short-term processes and projecting long-term changes affecting coastal SL, and (3) possible future developments of sea level services enabling better connection of scientists and user communities and facilitating assessment and decision making for adaptation to future coastal SL change

Evolution of low-mass metal-free stars including effects of diffusion and external pollution

We investigate the evolution of low-mass metal-free Population III stars. Emphasis is laid upon the question of internal and external sources for CNO-elements, which - if present in sufficient amounts in the hydrogen-burning regions - lead to a strong modification of the stars' evolutionary behavior. For the production of carbon due to nuclear processes inside the stars, we use an extended nuclear network, demonstrating that hot pp-chains do not suffice to produce enough carbon or are less effective than the triple3-alpha-process. As an external source of CNO-elements we test the efficiency of pollution by a nearby massive star combined with particle diffusion. For all cases investigated, the additional metals fail to reach nuclear burning regions before deep convection on the Red Giant Branch obliterates the previous evolution. The surface abundance history of the polluted Pop III stars is presented. The possibilities to discriminate between a Pop II and a polluted Pop III field star are also discussed.Comment: Accepted for publication in Ap

The Many Faces of a Character

We prove an identity between three infinite families of polynomials which are defined in terms of `bosonic', `fermionic', and `one-dimensional configuration' sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine $su(2)$ algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-Ansatz solution of the Heisenberg spin chain.Comment: 14/9 pages in harvmac, Tel-Aviv preprint TAUP 2125-9

Quantum Dynamics of Spin Wave Propagation Through Domain Walls

Through numerical solution of the time-dependent Schrodinger equation, we demonstrate that magnetic chains with uniaxial anisotropy support stable structures, separating ferromagnetic domains of opposite magnetization. These structures, domain walls in a quantum system, are shown to remain stable if they interact with a spin wave. We find that a domain wall transmits the longitudinal component of the spin excitations only. Our results suggests that continuous, classical spin models described by LLG equation cannot be used to describe spin wave-domain wall interaction in microscopic magnetic systems

Origin of the Canonical Ensemble: Thermalization with Decoherence

We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal circumstances we show that the environment drives the reduced density matrix to a fully decoherent state, and furthermore the diagonal elements of the reduced density matrix approach those expected for the system in the canonical ensemble. We show one exception to the normal case is if the spin system cannot exchange energy with the spin bath. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the canonical ensemble is a state that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics.Comment: 12 pages, 4 figures, accepted for publication by J. Phys. Soc. Jp

Impacts of basin-scale climate modes on coastal sea level: a review

Global sea level rise (SLR) associated with a warming climate exerts significant stress on coastal societies and low-lying island regions. The rates of coastal SLR observed in the past few decades, however, have large spatial and temporal differences from the global mean, which to a large part have been attributed to basin-scale climate modes. In this paper, we review our current state of knowledge about climate modes’ impacts on coastal sea level variability from interannual-to-multidecadal timescales. Relevant climate modes, their impacts and associated driving mechanisms through both remote and local processes are elaborated separately for the Pacific, Indian and Atlantic Oceans. This paper also identifies major issues and challenges for future research on climate modes’ impacts on coastal sea level. Understanding the effects of climate modes is essential for skillful near-term predictions and reliable uncertainty quantifications for future projections of coastal SLR