3,027 research outputs found
Fundamental Approach to the Cosmological Constant Issue
The issue of the cosmological constant is discussed in details and a solution
to the problem is suggested.Comment: 13 pages in LaTeX with 3 figures in eps files, paper presented at the
Fifth Friedmann Seminar; the cls file necessary for successful PostScript
generation is also attache
Clustered Integer 3SUM via Additive Combinatorics
We present a collection of new results on problems related to 3SUM,
including:
1. The first truly subquadratic algorithm for
1a. computing the (min,+) convolution for monotone increasing
sequences with integer values bounded by ,
1b. solving 3SUM for monotone sets in 2D with integer coordinates
bounded by , and
1c. preprocessing a binary string for histogram indexing (also
called jumbled indexing).
The running time is:
with
randomization, or deterministically. This greatly improves the
previous time bound obtained from Williams'
recent result on all-pairs shortest paths [STOC'14], and answers an open
question raised by several researchers studying the histogram indexing problem.
2. The first algorithm for histogram indexing for any constant alphabet size
that achieves truly subquadratic preprocessing time and truly sublinear query
time.
3. A truly subquadratic algorithm for integer 3SUM in the case when the given
set can be partitioned into clusters each covered by an interval
of length , for any constant .
4. An algorithm to preprocess any set of integers so that subsequently
3SUM on any given subset can be solved in
time.
All these results are obtained by a surprising new technique, based on the
Balog--Szemer\'edi--Gowers Theorem from additive combinatorics
Effective Field Theory for Chaotic CFTs
We derive an effective field theory for general chaotic two-dimensional
conformal field theories with a large central charge. The theory is a specific
and calculable instance of a more general framework recently proposed in [1].
We discuss the gauge symmetries of the model and how they relate to the
Lyapunov behaviour of certain correlators. We calculate the out-of-time-ordered
correlators diagnosing quantum chaos, as well as certain more fine-grained
higher-point generalizations, using our Lorentzian effective field theory. We
comment on potential future applications of the effective theory to real-time
thermal physics and conformal field theory.Comment: 33 pages, 4 figures; v2: minor improvements, added paragraph on
higher spin exchanges; v3: minor improvements, added reference, published
versio
Fine-Grained Chaos in Gravity
Quantum chaos can be characterized by an exponential growth of the thermal
out-of-time-order four-point function up to a scrambling time .
We discuss generalizations of this statement for certain higher-point
correlation functions. For concreteness, we study the Schwarzian theory of a
one-dimensional time reparametrization mode, which describes gravity
and the low-energy dynamics of the SYK model. We identify a particular set of
-point functions, characterized as being both "maximally braided" and
"k-OTO", which exhibit exponential growth until progressively longer timescales
. We suggest an interpretation as
scrambling of increasingly fine-grained measures of quantum information, which
correspondingly take progressively longer time to reach their thermal values.Comment: 8 pages; v2: minor clarifications, typos, added ref
Extreme(ly) mean(ingful): Sequential formation of a quality group
The present paper studies the limiting behavior of the average score of a
sequentially selected group of items or individuals, the underlying
distribution of which, , belongs to the Gumbel domain of attraction of
extreme value distributions. This class contains the Normal, Lognormal, Gamma,
Weibull and many other distributions. The selection rules are the "better than
average" () and the "-better than average" rule, defined as
follows. After the first item is selected, another item is admitted into the
group if and only if its score is greater than times the average score
of those already selected. Denote by the average of the first
selected items, and by the time it takes to amass them. Some of the key
results obtained are: under mild conditions, for the better than average rule,
less a suitable chosen function of converges almost surely
to a finite random variable. When ,
and , then
is of approximate order . When , the asymptotic results for
are of a completely different order of magnitude. Interestingly,
for a class of distributions, , suitably normalized, asymptotically
approaches 1, almost surely for relatively small , in probability
for moderate sized and in distribution when is large.Comment: Published in at http://dx.doi.org/10.1214/10-AAP684 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Robust ultrafast currents in molecular wires through Stark shifts
A novel way to induce ultrafast currents in molecular wires using two
incident laser frequencies, and , is demonstrated. The
mechanism relies on Stark shifts, instead of photon absorption, to transfer
population to the excited states and exploits the temporal profile of the field
to generate phase controllable transport. Calculations in a
\emph{trans}-polyacetylene oligomer coupled to metallic leads indicate that the
mechanism is highly efficient and robust to ultrafast electronic dephasing
processes induced by vibronic couplings.Comment: 4 pages, 2 figures, accepted to Physical Review Letter
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