41,596 research outputs found
Prompt heavy quarkonium production in association with a massive (anti)bottom quark at the LHC
In this work, we investigate the associated production of prompt heavy
quarkonium with a massive (anti)bottom quark to leading order in the NRQCD
factorization formalism at the LHC. We present numerical results for the
processes involving and . From our work,
we find that the production rates of these processes are quite large, and these
processes have the potential to be detected at the LHC. When is smaller
than about 10 GeV, the state give the main
contribution to the distribution of prompt with a (anti)bottom
quark production. For the process of , the
contribution of the CSM is larger than that in the COM at low region. We
also investigate the processes of and , in these processes, the distribution are dominated
by the CO Fock state contribution at the large region. These processes
provide an interesting signature that could be studied at the LHC, and the
measurement of these processes is useful to test the CSM and COM.Comment: 14 pages, 11 figures, accepted by Phys.Rev.
Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT
We investigate a weak version of subsystem eigenstate thermalization
hypothesis (ETH) for a two-dimensional large central charge conformal field
theory by comparing the local equivalence of high energy state and thermal
state of canonical ensemble. We evaluate the single-interval R\'enyi entropy
and entanglement entropy for a heavy primary state in short interval expansion.
We verify the results of R\'enyi entropy by two different replica methods. We
find nontrivial results at the eighth order of short interval expansion, which
include an infinite number of higher order terms in the large central charge
expansion. We then evaluate the relative entropy of the reduced density
matrices to measure the difference between the heavy primary state and thermal
state of canonical ensemble, and find that the aforementioned nontrivial eighth
order results make the relative entropy unsuppressed in the large central
charge limit. By using Pinsker's and Fannes-Audenaert inequalities, we can
exploit the results of relative entropy to yield the lower and upper bounds on
trace distance of the excited-state and thermal-state reduced density matrices.
Our results are consistent with subsystem weak ETH, which requires the above
trace distance is of power-law suppression by the large central charge.
However, we are unable to pin down the exponent of power-law suppression. As a
byproduct we also calculate the relative entropy to measure the difference
between the reduced density matrices of two different heavy primary states.Comment: 28 pages, 4 figures;v2 change author list;v3 related subtleties about
weak ETH clarified; v4 minor correction to match JHEP versio
Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis
We calculate various quantities that characterize the dissimilarity of
reduced density matrices for a short interval of length in a
two-dimensional (2D) large central charge conformal field theory (CFT). These
quantities include the R\'enyi entropy, entanglement entropy, relative entropy,
Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt
the method of operator product expansion of twist operators, and calculate the
short interval expansion of these quantities up to order of for the
contributions from the vacuum conformal family. The formal forms of these
dissimilarity measures and the derived Fisher information metric from
contributions of general operators are also given. As an application of the
results, we use these dissimilarity measures to compare the excited and thermal
states, and examine the eigenstate thermalization hypothesis (ETH) by showing
how they behave in high temperature limit. This would help to understand how
ETH in 2D CFT can be defined more precisely. We discuss the possibility that
all the dissimilarity measures considered here vanish when comparing the
reduced density matrices of an excited state and a generalized Gibbs ensemble
thermal state. We also discuss ETH for a microcanonical ensemble thermal state
in a 2D large central charge CFT, and find that it is approximately satisfied
for a small subsystem and violated for a large subsystem.Comment: V1, 34 pages, 5 figures, see collection of complete results in the
attached Mathematica notebook; V2, 38 pages, 5 figures, published versio
Arbitrary phase rotation of the marked state can not be used for Grover's quantum search algorithm
A misunderstanding that an arbitrary phase rotation of the marked state
together with the inversion about average operation in Grover's search
algorithm can be used to construct a (less efficient) quantum search algorithm
is cleared. The rotation of the phase of the marked state is not only the
choice for efficiency, but also vital in Grover's quantum search algorithm. The
results also show that Grover's quantum search algorithm is robust.Comment: 5 pages, 5 figure
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