Ground State Wave Function of the Schr\"odinger Equation in a Time-Periodic Potential

Using a generalized transfer matrix method we exactly solve the Schr\"odinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating soliton-like wave packet and the wave front is wedge shaped. In a statistical mechanics framework our solution represents the partition sum of a directed polymer subjected to a potential layer with alternating (attractive and repulsive) pinning centers.Comment: 11 Pages in LaTeX. A set of 2 PostScript figures available upon request at [email protected] . Physical Review Letter

Gauge and Poincare' Invariant Regularization and Hopf Symmetries

We consider the regularization of a gauge quantum field theory following a modification of the Polchinski proof based on the introduction of a cutoff function. We work with a Poincare' invariant deformation of the ordinary point-wise product of fields introduced by Ardalan, Arfaei, Ghasemkhani and Sadooghi, and show that it yields, through a limiting procedure of the cutoff functions, to a regularized theory, preserving all symmetries at every stage. The new gauge symmetry yields a new Hopf algebra with deformed co-structures, which is inequivalent to the standard one.Comment: Revised version. 14 pages. Incorrect statements eliminate

Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect

A flux line in a Type-II superconductor with a single nonuniform columnar defect is studied by a perturbative diagrammatic expansion around an annealed approximation. The system undergoes a finite temperature depinning transition for the (rather unphysical) on-the-average repulsive columnar defect, provided that the fluctuations along the axis are sufficiently large to cause some portions of the column to become attractive. The perturbative expansion is convergent throughout the weak pinning regime and becomes exact as the depinning transition is approached, providing an exact determination of the depinning temperature and the divergence of the localization length.Comment: RevTeX, 4 pages, 3 EPS figures embedded with epsf.st

The Tangled Nature model as an evolving quasi-species model

We show that the Tangled Nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al. in a frequency dependent fitness landscape. We present a detailed theoretical derivation of the mutation threshold, consistent with the simulation results, that provides a valuable insight into how the microscopic dynamics of the model determine the observed macroscopic phenomena published previously. The dynamics of the Tangled Nature model is defined on the microevolutionary time scale via reproduction, with heredity, variation, and natural selection. Each organism reproduces with a rate that is linked to the individuals' genetic sequence and depends on the composition of the population in genotype space. Thus the microevolutionary dynamics of the fitness landscape is regulated by, and regulates, the evolution of the species by means of the mutual interactions. At low mutation rate, the macro evolutionary pattern mimics the fossil data: periods of stasis, where the population is concentrated in a network of coexisting species, is interrupted by bursts of activity. As the mutation rate increases, the duration and the frequency of bursts increases. Eventually, when the mutation rate reaches a certain threshold, the population is spread evenly throughout the genotype space showing that natural selection only leads to multiple distinct species if adaptation is allowed time to cause fixation.Comment: Paper submitted to Journal of Physics A. 13 pages, 4 figure

Gauge Invariant Cutoff QED

A hidden generalized gauge symmetry of a cutoff QED is used to show the renormalizability of QED. In particular, it is shown that corresponding Ward identities are valid all along the renormalization group flow. The exact Renormalization Group flow equation corresponding to the effective action of a cutoff lambda phi^4 theory is also derived. Generalization to any gauge group is indicated.Comment: V1: 18 pages, 2 figures; V2: Discussions improved. Version accepted for publication in Physica Script

Error threshold in the evolution of diploid organisms

The effects of error propagation in the reproduction of diploid organisms are studied within the populational genetics framework of the quasispecies model. The dependence of the error threshold on the dominance parameter is fully investigated. In particular, it is shown that dominance can protect the wild-type alleles from the error catastrophe. The analysis is restricted to a diploid analogue of the single-peaked landscape.Comment: 9 pages, 4 Postscript figures. Submitted to J. Phy. A: Mat. and Ge

Depinning transition of a directed polymer by a periodic potential: a d-dimensional solution

We study the depinning phase transition of a directed polymer in a $d$-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the polymer. We show that a bounded state can still arise even if, in average, the potential layer is not attractive and for diverging values of the potential on the repulsive sites. The phase transition is of second order.Comment: 11 Pages in LaTeX. Figures available from the authors. [email protected] (e-mail address

On measurement-based quantum computation with the toric code states

We study measurement-based quantum computation (MQC) using as quantum resource the planar code state on a two-dimensional square lattice (planar analogue of the toric code). It is shown that MQC with the planar code state can be efficiently simulated on a classical computer if at each step of MQC the sets of measured and unmeasured qubits correspond to connected subsets of the lattice.Comment: 9 pages, 5 figure

A Prototype Model of Stock Exchange

A prototype model of stock market is introduced and studied numerically. In this self-organized system, we consider only the interaction among traders without external influences. Agents trade according to their own strategy, to accumulate his assets by speculating on the price's fluctuations which are produced by themselves. The model reproduced rather realistic price histories whose statistical properties are also similar to those observed in real markets.Comment: LaTex, 4 pages, 4 Encapsulated Postscript figures, uses psfi

Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution

In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We reexamine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a ``genotype'' space represented by a unitary hypercubic lattice. The exact solution of the model shows that error catastrophe arises as a direct consequence of the equations involved and confirms some previous qualitative results. The physically relevant consequence is that such equations are not adequate to properly describe evolution of complex life on the Earth.Comment: 10 pages in LaTeX. Figures are available from the authors. [email protected] (e-mail address