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Oxford, United Kingdom

Sotiriadis S.,International School for Advanced Studies | Cardy J.,Rudolf Peierls Center for Theoretical Physics | Cardy J.,All Souls College
Physical Review B - Condensed Matter and Materials Physics | Year: 2010

We study a composite quantum quench of the energy gap and the interactions in the interacting 4 model using a self-consistent approximation. First we review results for free theories where a quantum quench of the energy gap or mass leads for long times to stationary behavior with thermal characteristics. An exception to this rule is the 2d case with zero mass after the quench. In the composite quench, however, we find that the effect of the interactions in our approximation is simply to effectively change the value of the mass. This means on the one hand that the interacting model also exhibits the same stationary behavior and on the other hand that this is now true even for the massless 2d case. © 2010 The American Physical Society.


Cardy J.,University of Oxford | Cardy J.,All Souls College | Cardy J.,Kavli Institute for Theoretical Physics
Physical Review Letters | Year: 2014

We consider a quantum quench in a finite system of length L described by a 1+1-dimensional conformal field theory (CFT), of central charge c, from a state with finite energy density corresponding to an inverse temperature Îâ‰L. For times t such that â.,"/2


Clarke E.,All Souls College
ISME Journal | Year: 2015

Dense microbial groups such as bacterial biofilms commonly contain a diversity of cell types that define their functioning. However, we have a limited understanding of what maintains, or purges, this diversity. Theory suggests that resource levels are key to understanding diversity and the spatial arrangement of genotypes in microbial groups, but we need empirical tests. Here we use theory and experiments to study the effects of nutrient level on spatio-genetic structuring and diversity in bacterial colonies. Well-fed colonies maintain larger well-mixed areas, but they also expand more rapidly compared with poorly-fed ones. Given enough space to expand, therefore, well-fed colonies lose diversity and separate in space over a similar timescale to poorly fed ones. In sum, as long as there is some degree of nutrient limitation, we observe the emergence of structured communities. We conclude that resource-driven structuring is central to understanding both pattern and process in diverse microbial communities. © 2015 International Society for Microbial Ecology


Cardy J.,University of Oxford | Cardy J.,All Souls College | Herzog C.P.,State University of New York at Stony Brook
Physical Review Letters | Year: 2014

We consider single interval Rényi and entanglement entropies for a two dimensional conformal field theory on a circle at nonzero temperature. Assuming that the finite size of the system introduces a unique ground state with a nonzero mass gap, we calculate the leading corrections to the Rényi and entanglement entropy in a low temperature expansion. These corrections have a universal form for any two dimensional conformal field theory that depends only on the size of the mass gap and its degeneracy. We analyze the limits where the size of the interval becomes small and where it becomes close to the size of the spatial circle. © 2014 American Physical Society.


Calabrese P.,University of Pisa | Cardy J.,University of Oxford | Cardy J.,All Souls College | Tonni E.,International School for Advanced Studies
Physical Review Letters | Year: 2012

We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρAT 2 of the reduced density matrix of a subsystem A=A 1A 2, and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=lnρAT 2. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E∼(c/4)ln[ 12/( 1+ 2)] for the case of two adjacent intervals of lengths 1, 2 in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain. © 2012 American Physical Society.

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