On the Emergent "Quantum" Theory in Complex Adaptive Systems.

We explore the concept of emergent quantum-like theory in complex adaptive systems, and examine in particular the concrete example of such an emergent (or "mock") quantum theory in the Lotka-Volterra system. In general, we investigate the possibility of implementing the mathematical formalism of quantum mechanics on classical systems, and what would be the conditions for using such an approach. We start from a standard description of a classical system via Hamilton-Jacobi (HJ) equation and reduce it to an effective Schr\"odinger-type equation, with a (mock) Planck constant $\mockbar$, which is system-dependent. The condition for this is that the so-called quantum potential VQ, which is state-dependent, is cancelled out by some additional term in the HJ equation. We consider this additional term to provide for the coupling of the classical system under consideration to the "environment." We assume that a classical system could cancel out the VQ term (at least approximately) by fine tuning to the environment. This might provide a mechanism for establishing a stable, stationary states in (complex) adaptive systems, such as biological systems. In this context we emphasize the state dependent nature of the mock quantum dynamics and we also introduce the new concept of the mock quantum, state dependent, statistical field theory. We also discuss some universal features of the quantum-to-classical as well as the mock-quantum-to-classical transition found in the turbulent phase of the hydrodynamic formulation of our proposal. In this way we reframe the concept of decoherence into the concept of "quantum turbulence," i.e. that the transition between quantum and classical could be defined in analogy to the transition from laminar to turbulent flow in hydrodynamics.

Dynamics of genetic code evolution: The emergence of universality.

We study the dynamics of genetic code evolution. The model of Vetsigian et al. [Proc. Natl. Acad. Sci. USA 103, 10696 (2006)PNASA60027-842410.1073/pnas.0603780103] and Vetsigian [Collective evolution of biological and physical systems, Ph.D. thesis, 2005] uses the mechanism of horizontal gene transfer to demonstrate convergence of the genetic code to a near universal solution. We reproduce and analyze the algorithm as a dynamical system. All the parameters used in the model are varied to assess their impact on convergence and optimality score. We show that by allowing specific parameters to vary with time, the solution exhibits attractor dynamics. Finally, we study automorphisms of the genetic code arising due to this model. We use this to examine the scaling of the solutions to re-examine universality and find that there is a direct link to mutation rate.

Electromagnetic Signatures of the Chiral Anomaly in Weyl Semimetals.

Weyl semimetals are predicted to realize the three-dimensional axial anomaly first discussed in particle physics. The anomaly leads to unusual transport phenomena such as the chiral magnetic effect in which an applied magnetic field induces a current parallel to the field. Here we investigate diagnostics of the axial anomaly based on the fundamental equations of axion electrodynamics. We find that materials with Weyl nodes of opposite chirality and finite energy separation immersed in a uniform magnetic field exhibit an anomaly-induced oscillatory magnetic field with a period set by the chemical potential difference of the nodes. In the case where a chemical potential imbalance is created by applying parallel electric and magnetic fields, we find a suppression of the magnetic-field component parallel to the electric field inside the material for rectangular samples, suggesting that the chiral magnetic current opposes this imbalance. For cylindrical geometries, we instead find an enhancement of this magnetic-field component along with an anomaly-induced azimuthal component. We propose experiments to detect such magnetic signatures of the axial anomaly.

Emergent "Quantum" Theory in Complex Adaptive Systems.

Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck constant" associated with such emergent "quantum" theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.

Three-point functions of aging dynamics and the AdS-CFT correspondence.

Aging can be realized as a subalgebra of Schrödinger algebra by discarding the time-translation generator. While the two-point functions of the age algebra have been known for some time, little else was known about the higher n-point correlators. In this Letter, we present novel three-point correlators of scalar primary operators. We find that the aging correlators are distinct from the Schrödinger correlators by more than certain dressings with time-dependent factors, as was the case with two-point functions. In the existing literature, the holographic geometry of aging is obtained by performing certain general coordinate transformations on the holographic dual of the Schrödinger theory. Consequently, the aging two-point functions derived from holography look as the Schrödinger two-point functions dressed by time-dependent factors. However, since the three-point functions obtained in this Letter are not merely dressed Schrödinger correlators and instead, depend on an additional time-translation breaking variable, we conclude that the most general holographic realization of aging is yet to be found. We also comment on various extensions of the Schrödinger and aging algebras.

Gauge fields, membranes, and subdeterminant vector models.

We present a class of classically marginal N-vector models in d=4 and d=3 whose scalar potentials can be written as subdeterminants of symmetric matrices. The d=3 case can be thought of as a generalization of the scalar sector of the Bagger-Lambert-Gustavsson model. Using the Hubbard-Stratonovich transformation we calculate their effective potentials which exhibit intriguing large-N scaling behaviors. We comment on the possible relevance of our models to strings, membranes, and also to a class of novel spin systems that are based on ternary commutation relations.

Robustness of topologically protected surface states in layering of Bi2Te3 thin films.

Bulk Bi2Te3 is known to be a topological insulator. We investigate surface states of Bi2Te3(111) thin films of one to six quintuple layers using density-functional theory including spin-orbit coupling. We construct a method to identify topologically protected surface states of thin film topological insulators. Applying this method to Bi2Te3 thin films, we find that the topological nature of the surface states remains robust with the film thickness and that the films of three or more quintuple layers have topologically nontrivial surface states, which agrees with experiments.

Correspondence between nonrelativistic anti-de Sitter space and conformal field theory, and aging-gravity duality.

We point out that the recent discussion of nonrelativistic anti-de Sitter space and conformal field theory correspondence has a direct application in nonequilibrium statistical physics, a fact which has not been emphasized in the recent literature on the subject. In particular, we propose a duality between aging in systems far from equilibrium characterized by the dynamical exponent z=2 and gravity in a specific background. The key ingredient in our proposal is the recent geometric realization of the Schrödinger group. We also discuss the relevance of the proposed correspondence for the more general aging phenomena in systems where the value of the dynamical exponent is different from 2.

Solving pure yang-mills theory in dimensions.

We analytically compute the spectrum of the spin zero glueballs in the planar limit of pure Yang-Mills theory in 2 + 1 dimensions. The new ingredient is provided by our computation of a new nontrivial form of the ground state wave functional. The mass spectrum of the theory is determined by the zeroes of Bessel functions, and the agreement with large lattice data is excellent.