11,270 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
Gamma-Ray Bursts observed by XMM-Newton
Analysis of observations with XMM-Newton have made a significant contribution
to the study of Gamma-ray Burst (GRB) X-ray afterglows. The effective area,
bandpass and resolution of the EPIC instrument permit the study of a wide
variety of spectral features. In particular, strong, time-dependent, soft X-ray
emission lines have been discovered in some bursts. The emission mechanism and
energy source for these lines pose major problems for the current generation of
GRB models. Other GRBs have intrinsic absorption, possibly related to the
environment around the progenitor, or possible iron emission lines similar to
those seen in GRBs observed with BeppoSAX. Further XMM-Newton observations of
GRBs discovered by the Swift satellite should help unlock the origin of the GRB
phenomenon over the next few years.Comment: To appear in proceedings of the "XMM-Newton EPIC Consortium meeting,
Palermo, 2003 October 14-16", published in Memorie della Societa Astronomica
Italian
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
Exploring Interacting Quantum Many-Body Systems by Experimentally Creating Continuous Matrix Product States in Superconducting Circuits
Improving the understanding of strongly correlated quantum many body systems
such as gases of interacting atoms or electrons is one of the most important
challenges in modern condensed matter physics, materials research and
chemistry. Enormous progress has been made in the past decades in developing
both classical and quantum approaches to calculate, simulate and experimentally
probe the properties of such systems. In this work we use a combination of
classical and quantum methods to experimentally explore the properties of an
interacting quantum gas by creating experimental realizations of continuous
matrix product states - a class of states which has proven extremely powerful
as a variational ansatz for numerical simulations. By systematically preparing
and probing these states using a circuit quantum electrodynamics (cQED) system
we experimentally determine a good approximation to the ground-state wave
function of the Lieb-Liniger Hamiltonian, which describes an interacting Bose
gas in one dimension. Since the simulated Hamiltonian is encoded in the
measurement observable rather than the controlled quantum system, this approach
has the potential to apply to exotic models involving multicomponent
interacting fields. Our findings also hint at the possibility of experimentally
exploring general properties of matrix product states and entanglement theory.
The scheme presented here is applicable to a broad range of systems exploiting
strong and tunable light-matter interactions.Comment: 11 pages, 9 figure
Quantum Metropolis Sampling
The original motivation to build a quantum computer came from Feynman who
envisaged a machine capable of simulating generic quantum mechanical systems, a
task that is believed to be intractable for classical computers. Such a machine
would have a wide range of applications in the simulation of many-body quantum
physics, including condensed matter physics, chemistry, and high energy
physics. Part of Feynman's challenge was met by Lloyd who showed how to
approximately decompose the time-evolution operator of interacting quantum
particles into a short sequence of elementary gates, suitable for operation on
a quantum computer. However, this left open the problem of how to simulate the
equilibrium and static properties of quantum systems. This requires the
preparation of ground and Gibbs states on a quantum computer. For classical
systems, this problem is solved by the ubiquitous Metropolis algorithm, a
method that basically acquired a monopoly for the simulation of interacting
particles. Here, we demonstrate how to implement a quantum version of the
Metropolis algorithm on a quantum computer. This algorithm permits to sample
directly from the eigenstates of the Hamiltonian and thus evades the sign
problem present in classical simulations. A small scale implementation of this
algorithm can already be achieved with today's technologyComment: revised versio
The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently
We study families H_n of 1D quantum spin systems, where n is the number of
spins, which have a spectral gap \Delta E between the ground-state and
first-excited state energy that scales, asymptotically, as a constant in n. We
show that if the ground state |\Omega_m> of the hamiltonian H_m on m spins,
where m is an O(1) constant, is locally the same as the ground state
|\Omega_n>, for arbitrarily large n, then an arbitrarily good approximation to
the ground state of H_n can be stored efficiently for all n. We formulate a
conjecture that, if true, would imply our result applies to all noncritical 1D
spin systems. We also include an appendix on quasi-adiabatic evolutions.Comment: 9 pages, 1 eps figure, minor change
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