585 research outputs found
Graphene with geometrically induced vorticity
At half filling, the electronic structure of graphene can be modeled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field an everywhere-real Kekulé modulation of the hopping matrix elements can correspond to a nonreal Higgs field with nontrivial vorticity. This provides a natural setting for fractionally charged vortices with localized zero modes. For fullerenelike molecules we employ the index theorem to demonstrate the existence of six low-lying states that do not depend strongly on the Kekulé-induced mass gap
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
Sequential Strong Measurements and Heat Vision
We study scenarios where a finite set of non-demolition von-Neumann
measurements are available. We note that, in some situations, repeated
application of such measurements allows estimating an infinite number of
parameters of the initial quantum state, and illustrate the point with a
physical example. We then move on to study how the system under observation is
perturbed after several rounds of projective measurements. While in the finite
dimensional case the effect of this perturbation always saturates, there are
some instances of infinite dimensional systems where such a perturbation is
accumulative, and the act of retrieving information about the system increases
its energy indefinitely (i.e., we have `Heat Vision'). We analyze this effect
and discuss a specific physical system with two dichotomic von-Neumann
measurements where Heat Vision is expected to show.Comment: See the Appendix for weird examples of heat visio
Power Utility Maximization in Discrete-Time and Continuous-Time Exponential Levy Models
Consider power utility maximization of terminal wealth in a 1-dimensional
continuous-time exponential Levy model with finite time horizon. We discretize
the model by restricting portfolio adjustments to an equidistant discrete time
grid. Under minimal assumptions we prove convergence of the optimal
discrete-time strategies to the continuous-time counterpart. In addition, we
provide and compare qualitative properties of the discrete-time and
continuous-time optimizers.Comment: 18 pages, to appear in Mathematical Methods of Operations Research.
The final publication is available at springerlink.co
Quantum Chi-Squared and Goodness of Fit Testing
The density matrix in quantum mechanics parameterizes the statistical
properties of the system under observation, just like a classical probability
distribution does for classical systems. The expectation value of observables
cannot be measured directly, it can only be approximated by applying classical
statistical methods to the frequencies by which certain measurement outcomes
(clicks) are obtained. In this paper, we make a detailed study of the
statistical fluctuations obtained during an experiment in which a hypothesis is
tested, i.e. the hypothesis that a certain setup produces a given quantum
state. Although the classical and quantum problem are very much related to each
other, the quantum problem is much richer due to the additional optimization
over the measurement basis. Just as in the case of classical hypothesis
testing, the confidence in quantum hypothesis testing scales exponentially in
the number of copies. In this paper, we will argue 1) that the physically
relevant data of quantum experiments is only contained in the frequencies of
the measurement outcomes, and that the statistical fluctuations of the
experiment are essential, so that the correct formulation of the conclusions of
a quantum experiment should be given in terms of hypothesis tests, 2) that the
(classical) test for distinguishing two quantum states gives rise to
the quantum divergence when optimized over the measurement basis, 3)
present a max-min characterization for the optimal measurement basis for
quantum goodness of fit testing, find the quantum measurement which leads both
to the maximal Pitman and Bahadur efficiency, and determine the associated
divergence rates.Comment: 22 Pages, with a new section on parameter estimatio
Crossover between ballistic and diffusive transport: The Quantum Exclusion Process
We study the evolution of a system of free fermions in one dimension under
the simultaneous effects of coherent tunneling and stochastic Markovian noise.
We identify a class of noise terms where a hierarchy of decoupled equations for
the correlation functions emerges. In the special case of incoherent,
nearest-neighbour hopping the equation for the two-point functions is solved
explicitly. The Green's function for the particle density is obtained
analytically and a timescale is identified where a crossover from ballistic to
diffusive behaviour takes place. The result can be interpreted as a competition
between the two types of conduction channels where diffusion dominates on large
timescales.Comment: 20 pages, 5 figure
UCN Upscattering rates in a molecular deuterium crystal
A calculation of ultra-cold neutron (UCN) upscattering rates in molecular
deuterium solids has been carried out, taking into account intra-molecular
exictations and phonons. The different moelcular species ortho-D2 (with even
rotational quantum number J) and para-D2 (with odd J) exhibit significantly
different UCN-phonon annihilation cross-sections. Para- to ortho-D2 conversion,
furthermore, couples UCN to an energy bath of excited rotational states without
mediating phonons. This anomalous upscattering mechanism restricts the UCN
lifetime to 4.6 msec in a normal-D2 solid with 33% para content.Comment: 3 pages, one figur
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