1,445 research outputs found
Pressure-induced commensurate stacking of graphene on boron nitride
Combining atomically-thin van der Waals materials into heterostructures
provides a powerful path towards the creation of designer electronic devices.
The interaction strength between neighboring layers, most easily controlled
through their interlayer separation, can have significant influence on the
electronic properties of these composite materials. Here, we demonstrate
unprecedented control over interlayer interactions by locally modifying the
interlayer separation between graphene and boron nitride, which we achieve by
applying pressure with a scanning tunneling microscopy tip. For the special
case of aligned or nearly-aligned graphene on boron nitride, the graphene
lattice can stretch and compress locally to compensate for the slight lattice
mismatch between the two materials. We find that modifying the interlayer
separation directly tunes the lattice strain and induces commensurate stacking
underneath the tip. Our results motivate future studies tailoring the
electronic properties of van der Waals heterostructures by controlling the
interlayer separation of the entire device using hydrostatic pressure.Comment: 17 pages, 4 figures and supplementary information. Updated to
published versio
Optimal Control Theory for Continuous Variable Quantum Gates
We apply the methodology of optimal control theory to the problem of
implementing quantum gates in continuous variable systems with quadratic
Hamiltonians. We demonstrate that it is possible to define a fidelity measure
for continuous variable (CV) gate optimization that is devoid of traps, such
that the search for optimal control fields using local algorithms will not be
hindered. The optimal control of several quantum computing gates, as well as
that of algorithms composed of these primitives, is investigated using several
typical physical models and compared for discrete and continuous quantum
systems. Numerical simulations indicate that the optimization of generic CV
quantum gates is inherently more expensive than that of generic discrete
variable quantum gates, and that the exact-time controllability of CV systems
plays an important role in determining the maximum achievable gate fidelity.
The resulting optimal control fields typically display more complicated Fourier
spectra that suggest a richer variety of possible control mechanisms. Moreover,
the ability to control interactions between qunits is important for delimiting
the total control fluence. The comparative ability of current experimental
protocols to implement such time-dependent controls may help determine which
physical incarnations of CV quantum information processing will be the easiest
to implement with optimal fidelity.Comment: 39 pages, 11 figure
Algorithms for finite Projected Entangled Pair States
Projected Entangled Pair States (PEPS) are a promising ansatz for the study
of strongly correlated quantum many-body systems in two dimensions. But due to
their high computational cost, developing and improving PEPS algorithms is
necessary to make the ansatz widely usable in practice. Here we analyze several
algorithmic aspects of the method. On the one hand, we quantify the connection
between the correlation length of the PEPS and the accuracy of its approximate
contraction, and discuss how purifications can be used in the latter. On the
other, we present algorithmic improvements for the update of the tensor that
introduce drastic gains in the numerical conditioning and the efficiency of the
algorithms. Finally, the state-of-the-art general PEPS code is benchmarked with
the Heisenberg and quantum Ising models on lattices of up to
sites.Comment: 18 pages, 20 figures, accepted versio
Ring exchange, the Bose metal, and bosonization in two dimensions
Motivated by the high-T_c cuprates, we consider a model of bosonic Cooper
pairs moving on a square lattice via ring exchange. We show that this model
offers a natural middle ground between a conventional antiferromagnetic Mott
insulator and the fully deconfined fractionalized phase which underlies the
spin-charge separation scenario for high-T_c superconductivity. We show that
such ring models sustain a stable critical phase in two dimensions, the *Bose
metal*. The Bose metal is a compressible state, with gapless but uncondensed
boson and ``vortex'' excitations, power-law superconducting and charge-ordering
correlations, and broad spectral functions. We characterize the Bose metal with
the aid of an exact plaquette duality transformation, which motivates a
universal low energy description of the Bose metal. This description is in
terms of a pair of dual bosonic phase fields, and is a direct analog of the
well-known one-dimensional bosonization approach. We verify the validity of the
low energy description by numerical simulations of the ring model in its exact
dual form. The relevance to the high-T_c superconductors and a variety of
extensions to other systems are discussed, including the bosonization of a two
dimensional fermionic ring model
Spectral-Element and Adjoint Methods in Seismology
We provide an introduction to the use of the spectral-element method (SEM) in seismology. Following a brief review of the basic equations that govern seismic wave propagation, we discuss in some detail how these equations may be solved numerically based upon the SEM to address the forward problem in seismology. Examples of synthetic seismograms calculated based upon the SEM are compared to data recorded by the Global Seismographic Network. Finally, we discuss the challenge of using the remaining differences between the data and the synthetic seismograms to constrain better Earth models and source descriptions. This leads naturally to adjoint methods, which provide a practical approach to this formidable computational challenge and enables seismologists to tackle the inverse problem
A variational method based on weighted graph states
In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a
class of states which is suitable as a variational set to find ground states in
spin systems of arbitrary spatial dimension and with long-range entanglement.
Here, we continue the exposition of our technique, extend from spin 1/2 to
higher spins and use the boson Hubbard model as a non-trivial example to
demonstrate our scheme.Comment: 36 pages, 13 figure
A Structural Model for Fluctuations in Financial Markets
In this paper we provide a comprehensive analysis of a structural model for
the dynamics of prices of assets traded in a market originally proposed in [1].
The model takes the form of an interacting generalization of the geometric
Brownian motion model. It is formally equivalent to a model describing the
stochastic dynamics of a system of analogue neurons, which is expected to
exhibit glassy properties and thus many meta-stable states in a large portion
of its parameter space. We perform a generating functional analysis,
introducing a slow driving of the dynamics to mimic the effect of slowly
varying macro-economic conditions. Distributions of asset returns over various
time separations are evaluated analytically and are found to be fat-tailed in a
manner broadly in line with empirical observations. Our model also allows to
identify collective, interaction mediated properties of pricing distributions
and it predicts pricing distributions which are significantly broader than
their non-interacting counterparts, if interactions between prices in the model
contain a ferro-magnetic bias. Using simulations, we are able to substantiate
one of the main hypotheses underlying the original modelling, viz. that the
phenomenon of volatility clustering can be rationalised in terms of an
interplay between the dynamics within meta-stable states and the dynamics of
occasional transitions between them.Comment: 16 pages, 8 (multi-part) figure
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