60,357 research outputs found
Fast quantum noise in Landau-Zener transition
We show by direct calculation starting from a microscopic model that the
two-state system with time-dependent energy levels in the presence of fast
quantum noise obeys the master equation. The solution of master equation is
found analytically and analyzed in a broad range of parameters. The fast
transverse noise affects the transition probability during much longer time
(the accumulation time) than the longitudinal one. The action of the fast
longitudinal noise is restricted by the shorter Landau-Zener time, the same as
in the regular Landau-Zener process. The large ratio of time scales allows
solving the Landau-Zener problem with longitudinal noise only, then solving the
same problem with the transverse noise only and matching the two solutions. The
correlation of the longitudinal and transverse noise renormalizes the
Landau-Zener transition matrix element and can strongly enhance the survival
probability, whereas the transverse noise always reduces it. Both longitudinal
and transverse noise reduce the coherence. The decoherence time is inverse
proportional to the noise intensity. If the noise is fast, its intensity at
which the multi-quantum processes become essential corresponds to a deeply
adiabatic regime. We briefly discuss possible applications of the general
theory to the problem of the qubit decoherence and to the spin relaxation of
molecular magnets.Comment: 12 pages, 8 figure
On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
We study the relationship between the momentum twistor MHV vertex expansion
of planar amplitudes in N=4 super-Yang-Mills and the all-loop generalization of
the BCFW recursion relations. We demonstrate explicitly in several examples
that the MHV vertex expressions for tree-level amplitudes and loop integrands
satisfy the recursion relations. Furthermore, we introduce a rewriting of the
MHV expansion in terms of sums over non-crossing partitions and show that this
cyclically invariant formula satisfies the recursion relations for all numbers
of legs and all loop orders.Comment: 34 pages, 17 figures; v2: Minor improvements to exposition and
discussion, updated references, typos fixe
On the Coloring of Pseudoknots
Pseudodiagrams are diagrams of knots where some information about which
strand goes over/under at certain crossings may be missing. Pseudoknots are
equivalence classes of pseudodiagrams, with equivalence defined by a class of
Reidemeister-type moves. In this paper, we introduce two natural extensions of
classical knot colorability to this broader class of knot-like objects. We use
these definitions to define the determinant of a pseudoknot (i.e. the
pseudodeterminant) that agrees with the classical determinant for classical
knots. Moreover, we extend Conway notation to pseudoknots to facilitate the
investigation of families of pseudoknots and links. The general formulae for
pseudodeterminants of pseudoknot families may then be used as a criterion for
p-colorability of pseudoknots.Comment: 22 pages, 24 figure
On embeddings of CAT(0) cube complexes into products of trees
We prove that the contact graph of a 2-dimensional CAT(0) cube complex of maximum degree can be coloured with at most
colours, for a fixed constant . This implies
that (and the associated median graph) isometrically embeds in the
Cartesian product of at most trees, and that the event
structure whose domain is admits a nice labeling with
labels. On the other hand, we present an example of a
5-dimensional CAT(0) cube complex with uniformly bounded degrees of 0-cubes
which cannot be embedded into a Cartesian product of a finite number of trees.
This answers in the negative a question raised independently by F. Haglund, G.
Niblo, M. Sageev, and the first author of this paper.Comment: Some small corrections; main change is a correction of the
computation of the bounds in Theorem 1. Some figures repaire
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