131 research outputs found
Quantum Walks with Non-Orthogonal Position States
Quantum walks have by now been realized in a large variety of different
physical settings. In some of these, particularly with trapped ions, the walk
is implemented in phase space, where the corresponding position states are not
orthogonal. We develop a general description of such a quantum walk and show
how to map it into a standard one with orthogonal states, thereby making
available all the tools developed for the latter. This enables a variety of
experiments, which can be implemented with smaller step sizes and more steps.
Tuning the non-orthogonality allows for an easy preparation of extended states
such as momentum eigenstates, which travel at a well-defined speed with low
dispersion. We introduce a method to adjust their velocity by momentum shifts,
which allows to investigate intriguing effects such as the analog of Bloch
oscillations.Comment: 5 pages, 4 figure
Электрооборудование и электропривод механизма напора экскаватора ЭКГ-15
В работе произведён расчёт и выбор силового оборудования для электропривода механизма напора карьерного экскаватора.Произведен расчет силовой части электропривода. Рассчитаны и построены характеристики электропривода, построены переходные процессы.In operation, calculation and selection of power equipment for electric drive of pressure mechanism of mine excavator was performed. Electric drive power part was calculated. The characteristics of the electric drive have been calculated and built, and transitional processes have been built
Molecular binding in interacting quantum walks
We show that the presence of an interaction in the quantum walk of two atoms leads to the formation of a stable compound, a molecular state. The wave function of the molecule decays exponentially in the relative position of the two atoms; hence it constitutes a true bound state. Furthermore, for a certain class of interactions, we develop an effective theory and find that the dynamics of the molecule is described by a quantum walk in its own right. We propose a setup for the experimental realization as well as sketch the possibility to observe quasi-particle effects in quantum many-body systems.DFG/FOR/635European Commission/CORNEREuropean Commission/COQUITEuropean Commission/AQUTENRW Nachwuchsgruppe ‘Quantenkontrolle auf der Nanoskala’Alexander von Humboldt Foundatio
Recurrence for discrete time unitary evolutions
We consider quantum dynamical systems specified by a unitary operator U and
an initial state vector \phi. In each step the unitary is followed by a
projective measurement checking whether the system has returned to the initial
state. We call the system recurrent if this eventually happens with probability
one. We show that recurrence is equivalent to the absence of an absolutely
continuous part from the spectral measure of U with respect to \phi. We also
show that in the recurrent case the expected first return time is an integer or
infinite, for which we give a topological interpretation. A key role in our
theory is played by the first arrival amplitudes, which turn out to be the
(complex conjugated) Taylor coefficients of the Schur function of the spectral
measure. On the one hand, this provides a direct dynamical interpretation of
these coefficients; on the other hand it links our definition of first return
times to a large body of mathematical literature.Comment: 27 pages, 5 figures, typos correcte
Index theory of one dimensional quantum walks and cellular automata
If a one-dimensional quantum lattice system is subject to one step of a
reversible discrete-time dynamics, it is intuitive that as much "quantum
information" as moves into any given block of cells from the left, has to exit
that block to the right. For two types of such systems - namely quantum walks
and cellular automata - we make this intuition precise by defining an index, a
quantity that measures the "net flow of quantum information" through the
system. The index supplies a complete characterization of two properties of the
discrete dynamics. First, two systems S_1, S_2 can be pieced together, in the
sense that there is a system S which locally acts like S_1 in one region and
like S_2 in some other region, if and only if S_1 and S_2 have the same index.
Second, the index labels connected components of such systems: equality of the
index is necessary and sufficient for the existence of a continuous deformation
of S_1 into S_2. In the case of quantum walks, the index is integer-valued,
whereas for cellular automata, it takes values in the group of positive
rationals. In both cases, the map S -> ind S is a group homomorphism if
composition of the discrete dynamics is taken as the group law of the quantum
systems. Systems with trivial index are precisely those which can be realized
by partitioned unitaries, and the prototypes of systems with non-trivial index
are shifts.Comment: 38 pages. v2: added examples, terminology clarifie
Localization of the Grover walks on spidernets and free Meixner laws
A spidernet is a graph obtained by adding large cycles to an almost regular
tree and considered as an example having intermediate properties of lattices
and trees in the study of discrete-time quantum walks on graphs. We introduce
the Grover walk on a spidernet and its one-dimensional reduction. We derive an
integral representation of the -step transition amplitude in terms of the
free Meixner law which appears as the spectral distribution. As an application
we determine the class of spidernets which exhibit localization. Our method is
based on quantum probabilistic spectral analysis of graphs.Comment: 32 page
Derivatives of 1-phenyl-3-methylpyrazol-2-in-5-thione and their oxygen analogues in the crystalline phase and their tautomeric transformations in solutions and in the gas phase
1-Phenyl-3-methylpyrazol-2-in-5-thione, crystallised from methanol, was shown to exist in the tautomeric NH-form, stabilised by intermolecular NH···S hydrogen bonds. In solutions, however, the molecule is found predominantly as the SH-tautomer, accompanied (in low-polar solvents) by a small amount of the CH-tautomer. 1-Phenyl-3-methyl-4-benzoylpyrazol-2-in-5-thione occurs in the crystal as well as in solution in the SH-tautomeric form, stabilised by an intramolecular SH···O bridge. In dimethylsulfoxide solution indications were found for an additional SH-tautomer in a conformation lacking the intramolecular H-bridge. The structure of 1-phenyl-3-methylpyrazol-2-in-5-one was redetermined by X-ray single crystal diffraction at 120°K in order to obtain more accurate geometry and hydrogen bonding parameters. © 2001 Elsevier Science B.V. All rights reserved
Experimental simulation and limitations of quantum walks with trapped ions
We examine the prospects of discrete quantum walks (QWs) with trapped ions.
In particular, we analyze in detail the limitations of the protocol of
Travaglione and Milburn (PRA 2002) that has been implemented by several
experimental groups in recent years. Based on the first realization in our
group (PRL 2009), we investigate the consequences of leaving the scope of the
approximations originally made, such as the Lamb--Dicke approximation. We
explain the consequential deviations from the idealized QW for different
experimental realizations and an increasing number of steps by taking into
account higher-order terms of the quantum evolution. It turns out that these
become dominant after a few steps already, which is confirmed by experimental
results and is currently limiting the scalability of this approach. Finally, we
propose a new scheme using short laser pulses, derived from a protocol from the
field of quantum computation. We show that the new scheme is not subject to the
above-mentioned restrictions, and analytically and numerically evaluate its
limitations, based on a realistic implementation with our specific setup.
Implementing the protocol with state-of-the-art techniques should allow for
substantially increasing the number of steps to 100 and beyond and should be
extendable to higher-dimensional QWs.Comment: 29 pages, 15 figue
Disordered Quantum Walks in one lattice dimension
We study a spin-1/2-particle moving on a one dimensional lattice subject to
disorder induced by a random, space-dependent quantum coin. The discrete time
evolution is given by a family of random unitary quantum walk operators, where
the shift operation is assumed to be deterministic. Each coin is an independent
identically distributed random variable with values in the group of two
dimensional unitary matrices. We derive sufficient conditions on the
probability distribution of the coins such that the system exhibits dynamical
localization. Put differently, the tunneling probability between two lattice
sites decays rapidly for almost all choices of random coins and after arbitrary
many time steps with increasing distance. Our findings imply that this effect
takes place if the coin is chosen at random from the Haar measure, or some
measure continuous with respect to it, but also for a class of discrete
probability measures which support consists of two coins, one of them being the
Hadamard coin.Comment: minor change
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