DNA viewed as an out-of-equilibrium structure

The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a low order Markov chain of order up to $r=6$. Although detailed balance seems to hold at the level of purine-pyrimidine notation it fails when all four basepairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain we study the exit distances from a specific symbol, the distribution of recurrence distances and the Hurst exponent, all of which show power law tails and long range characteristics. These results suggest that human DNA can be viewed as a non-equilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method we construct a model DNA sequence. This method allows to keep all long range and short range statistical characteristics of the original sequence. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture point-to-point details

Information processing with Page-Wootters states

In order to perceive that a physical system evolves in time, two requirements must be met: (a) it must be possible to define a "clock" and (b) it must be possible to make a copy of the state of the system, that can be reliably retrieved to make a comparison. We investigate what constraints quantum mechanics poses on these issues, in light of recent experiments with entangled photons.Comment: 9 pages LaTeX2e, 1 eps figure. Contribution to the special volume "Chaos, Information Processing and Paradoxical Games", World Scientific (2014

Unconstrained Variables and Equivalence Relations for Lattice Gauge Theories

We write the partition function for a lattice gauge theory, with compact gauge group, exactly in terms of unconstrained variables and show that, in the mean field approximation, the dynamics of pure gauge theories, invariant under compact, continuous,groups of rank 1 is the same for all. We explicitly obtain the equivalence for the case of SU(2) and U(1) and show that it obtains, also, if we consider saddle point configurations that are not,necessarily, uniform, but only proportional to the identity for both groups. This implies that the phase diagrams of the (an)isotropic SU(2) theory and the (an)isotropic U(1) theory in any dimension are identical, within this approximation, up to a re-evaluation of the numerical values of the coupling constants at the transitions. Only nonuniform field configurations, that, also, belong to higher dimensional representations for Yang--Mills fields, will be able to p robe the difference between them. We also show under what conditions the global symmetry of an anisotropic term in the lattice action can be promoted to a gauge symmetry of the theory on layers and point out how deconstruction and flux compactification scenaria may thus be studied on the lattice.Comment: 14 pages, LateX2e. Expanded presentation of equivalence relation. Added discussion on how the global symmetry of the anisotropic term can be promoted to a gauge symmetry on a laye

A particle in equilibrium with a bath realizes worldline supersymmetry

We study the relation between the partition function of a non--relativistic particle, in one spatial dimension, that describes the equilibrium fluctuations implicitly, and the partition function of the same system, deduced from the Langevin equation, that describes the fluctuations explicitly, of a bath with additive white--noise properties using Monte Carlo simulations for computing the correlation functions that satisfy the corresponding identities. We show that both can be related to the partition function of the corresponding, maximally supersymmetric, theory with one--dimensional bosonic worldvolume, by appropriate analytic continuation, from Euclidian to real time, and that they can all describe the same physics, since the correlation functions of the observables satisfy the same identities for all systems.The supersymmetric theory provides the consistent closure for describing the fluctuations. Therefore supersymmetry is relevant at the scale in which equilibrium with the bath is meaningful. At scales when the "true" degrees of freedom of the bath can be resolved (e.g. atoms and molecules for the case of thermal fluctuations) the superpartners become "hidden". They can be, always, revealed through the identities satisfied by the correlation functions of the appropriate noise field, however. In fact, the same formalism applies whatever the "microscopic" origin of the fluctuations. Therefore, all consistently closed physical systems are supersymmetric--and any system that is explicitly not invariant under supersymmetric transformations, is, in fact, open and, therefore, incomplete.Comment: 48 pages, many PNG figures, LaTeX2e. Requires utphys.bst for the bibliography. v2: Extensively rewritten; errors corrected regarding the "fermionic'' action and presentation clarified and sharpene

Anomaly cancellation for anisotropic lattice fields with extra dimensions

The current flow from the bulk is due to the anomaly on the brane-but the absence of current flow is not, necessarily, due to anomaly cancellation, but to the absence of the chiral zero modes themselves, due to the existence of the layered phase. This can be understood in terms of the difference between the Chern-Simons terms in three and five dimensions. Thus the anomaly cancellation in four dimensions, which is essential for shielding the boundary from quantum effects within the bulk, makes sense only along the transition line between the layered and the Coulomb phase, which, in turn, requires the presence of a compact U(1) factor for the gauge group.Comment: 6 pages, 4 figures, LaTeX2e, uses PoS. Contribution to The XXVII International Symposium on Lattice Field Theory - LAT2009, July 26-31 2009,Peking University, Beijing, Chin

Layered Phase Investigations

The extra dimensional defects that are introduced to generate the lattice chiral zero modes are not simply a computational trick, but have interesting physical consequences. After reviewing what is known about the layered phase they can generate, I argue how it is possible to simulate Yang-Mills theories with reduced systematic errors and speculate on how it might be possible to study the fluctuations of the layers' topological charge.Comment: 5 pages (LaTeX, PoS class file included); Contribution to the XXV International Symposium on Lattice Field Theory,July 30 - August 4 2007,Regensburg, German

Second Order Phase Transition in Anisotropic Lattice Gauge Theories with Extra Dimensions

Field theories with extra dimensions live in a limbo. While their classical solutions have been the subject of considerable study, their quantum aspects are difficult to control. A special class of such theories are anisotropic gauge theories. The anisotropy was originally introduced to localize chiral fermions. Their continuum limit is of practical interest and it will be shown that the anisotropy of the gauge couplings plays a crucial role in opening the phase diagram of the theory to a new phase, that is separated from the others by a second order phase transition. The mechanism behind this is generic for a certain class of models, that can be studied with lattice techniques. This leads to new perspectives for the study of quantum effects of extra dimensions.Comment: 7 pages, 1 figure. Uses PoS.cls. Contribution to The XXVIII International Symposium on Lattice Filed Theory, June 14-19,2010,Villasimius, Sardinia Ital