2,959 research outputs found

### Energy Correlations In Random Transverse Field Ising Spin Chains

The end-to-end energy - energy correlations of random transverse-field
quantum Ising spin chains are computed using a generalization of an
asymptotically exact real-space renormalization group introduced previously.
Away from the critical point, the average energy - energy correlations decay
exponentially with a correlation length that is the same as that of the spin -
spin correlations. The typical correlations, however, decay exponentially with
a characteristic length proportional to the square root of the primary
correlation length. At the quantum critical point, the average correlations
decay sub-exponentially as $\bar{C_{L}}\sim e^{-const\cdot L^{1/3}}$, whereas
the typical correlations decay faster, as $\sim e^{-K\sqrt{L}}$, with $K$ a
random variable with a universal distribution. The critical energy-energy
correlations behave very similarly to the smallest gap, computed previously;
this is explained in terms of the RG flow and the excitation structure of the
chain. In order to obtain the energy correlations, an extension of the
previously used methods was needed; here this was carried out via RG
transformations that involve a sequence of unitary transformations.Comment: Submitted to Phys. Rev.

### Rate of Adaptation in Large Sexual Populations

Adaptation often involves the acquisition of a large number of genomic
changes which arise as mutations in single individuals. In asexual populations,
combinations of mutations can fix only when they arise in the same lineage, but
for populations in which genetic information is exchanged, beneficial mutations
can arise in different individuals and be combined later. In large populations,
when the product of the population size N and the total beneficial mutation
rate U_b is large, many new beneficial alleles can be segregating in the
population simultaneously. We calculate the rate of adaptation, v, in several
models of such sexual populations and show that v is linear in NU_b only in
sufficiently small populations. In large populations, v increases much more
slowly as log NU_b. The prefactor of this logarithm, however, increases as the
square of the recombination rate. This acceleration of adaptation by
recombination implies a strong evolutionary advantage of sex

- â€¦