12,917 research outputs found
Solving frustration-free spin systems
We identify a large class of quantum many-body systems that can be solved
exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on
arbitrary lattices. We show that the entire ground state manifold of such
models can be found exactly by a tensor network of isometries acting on a space
locally isomorphic to the symmetric subspace. Thus, for this wide class of
models real-space renormalization can be made exact. Our findings also imply
that every such frustration-free spin model satisfies an area law for the
entanglement entropy of the ground state, establishing a novel large class of
models for which an area law is known. Finally, we show that our approach gives
rise to an ansatz class useful for the simulation of almost frustration-free
models in a simple fashion, outperforming mean field theory.Comment: 5 pages, 1 figur
Exact relaxation in a class of non-equilibrium quantum lattice systems
A reasonable physical intuition in the study of interacting quantum systems
says that, independent of the initial state, the system will tend to
equilibrate. In this work we study a setting where relaxation to a steady state
is exact, namely for the Bose-Hubbard model where the system is quenched from a
Mott quantum phase to the strong superfluid regime. We find that the evolving
state locally relaxes to a steady state with maximum entropy constrained by
second moments, maximizing the entanglement, to a state which is different from
the thermal state of the new Hamiltonian. Remarkably, in the infinite system
limit this relaxation is true for all large times, and no time average is
necessary. For large but finite system size we give a time interval for which
the system locally "looks relaxed" up to a prescribed error. Our argument
includes a central limit theorem for harmonic systems and exploits the finite
speed of sound. Additionally, we show that for all periodic initial
configurations, reminiscent of charge density waves, the system relaxes
locally. We sketch experimentally accessible signatures in optical lattices as
well as implications for the foundations of quantum statistical mechanics.Comment: 8 pages, 3 figures, replaced with final versio
On-lattice agent-based simulation of populations of cells within the open-source chaste framework
Over the years, agent-based models have been developed that combine cell division and reinforced random walks of cells on a regular lattice, reaction-diffusion equations for nutrients and growth factors and ordinary differential equations (ODEs) for the subcellular networks regulating the cell cycle. When linked to a vascular layer, this multiple scale model framework has been applied to tumour growth and therapy. Here we report on the creation of an agent-based multiscale environment amalgamating the characteristics of these models within a Virtual Pysiological Human (VPH) Exemplar Project. This project enables re-use, integration, expansion and sharing of the model and relevant data. The agent-based and reactiondiffusion parts of the multiscale model have been implemented and are available for download as part of the latest public release of Chaste (“Cancer, Heart and Soft Tissue Environment”), (http://www.cs.ox.ac.uk/chaste/) version 3.1, part of the VPH Toolkit (http://toolkit.vph-noe.eu/). The environment functionalities are verified against the original models, in addition to extra validation of all aspects of the code. In this work, we present the details of the implementation of the agent-based environment, including the system description, the conceptual model, the development of the simulation model and the processes of verification and validation of the simulation results. We explore the potential use of the environment by presenting exemplar applications of the “what if” scenarios that can easily be studied in the environment. These examples relate to tumour growth, cellular competition for resources and tumour responses to hypoxia. We conclude our work by summarising the future steps for the expansion of the current system
Spectral evolution and the onset of the X-ray GRB afterglow
Based on light curves from the Swift Burst Analyser, we investigate whether a
`dip' feature commonly seen in the early-time hardness ratios of Swift-XRT data
could arise from the juxtaposition of the decaying prompt emission and rising
afterglow. We are able to model the dip as such a feature, assuming the
afterglow rises as predicted by Sari & Piran (1999). Using this model we
measure the initial bulk Lorentz factor of the fireball. For a sample of 23
GRBs we find a median value of Gamma_0=225, assuming a constant-density
circumburst medium; or Gamma_0=93 if we assume a wind-like medium.Comment: 4 pages, 3 figures. To appear in the proceedings of GRB 2010,
Annapolis November 2010. (AIP Conference proceedings
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