734 research outputs found
Self-Similarity and Localization
The localized eigenstates of the Harper equation exhibit universal
self-similar fluctuations once the exponentially decaying part of a wave
function is factorized out. For a fixed quantum state, we show that the whole
localized phase is characterized by a single strong coupling fixed point of the
renormalization equations. This fixed point also describes the generalized
Harper model with next nearest neighbor interaction below a certain threshold.
Above the threshold, the fluctuations in the generalized Harper model are
described by a strange invariant set of the renormalization equations.Comment: 4 pages, RevTeX, 2 figures include
Universal criterion for the breakup of invariant tori in dissipative systems
The transition from quasiperiodicity to chaos is studied in a two-dimensional
dissipative map with the inverse golden mean rotation number. On the basis of a
decimation scheme, it is argued that the (minimal) slope of the critical
iterated circle map is proportional to the effective Jacobian determinant.
Approaching the zero-Jacobian-determinant limit, the factor of proportion
becomes a universal constant. Numerical investigation on the dissipative
standard map suggests that this universal number could become observable in
experiments. The decimation technique introduced in this paper is readily
applicable also to the discrete quasiperiodic Schrodinger equation.Comment: 13 page
Collision and symmetry-breaking in the transition to strange nonchaotic attractors
Strange nonchaotic attractors (SNAs) can be created due to the collision of
an invariant curve with itself. This novel ``homoclinic'' transition to SNAs
occurs in quasiperiodically driven maps which derive from the discrete
Schr\"odinger equation for a particle in a quasiperiodic potential. In the
classical dynamics, there is a transition from torus attractors to SNAs, which,
in the quantum system is manifest as the localization transition. This
equivalence provides new insights into a variety of properties of SNAs,
including its fractal measure. Further, there is a {\it symmetry breaking}
associated with the creation of SNAs which rigorously shows that the Lyapunov
exponent is nonpositive. By considering other related driven iterative
mappings, we show that these characteristics associated with the the appearance
of SNA are robust and occur in a large class of systems.Comment: To be appear in Physical Review Letter
Economic choices can be made using only stimulus values
Decision-making often involves choices between different stimuli, each of which is associated with a different physical action. A growing consensus suggests that the brain makes such decisions by assigning a value to each available option and then comparing them to make a choice. An open question in decision neuroscience is whether the brain computes these choices by comparing the values of stimuli directly in goods space or instead by first assigning values to the associated actions and then making a choice over actions. We used a functional MRI paradigm in which human subjects made choices between different stimuli with and without knowledge of the actions required to obtain the different stimuli. We found neural correlates of the value of the chosen stimulus (a postdecision signal) in ventromedial prefrontal cortex before the actual stimulus–action pairing was revealed. These findings provide support for the hypothesis that the brain is capable of making choices in the space of goods without first transferring values into action space
The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
We study the spectrum of the Fibonacci Hamiltonian and prove upper and lower
bounds for its fractal dimension in the large coupling regime. These bounds
show that as , converges to an explicit constant (). We also discuss
consequences of these results for the rate of propagation of a wavepacket that
evolves according to Schr\"odinger dynamics generated by the Fibonacci
Hamiltonian.Comment: 23 page
Light Induced Melting of Colloidal Crystals in Two Dimensions
We demonstrate that particles confined to two dimensions (2d) and subjected
to a one-dimensional (1d) periodic potential exhibit a rich phase diagram, with
both ``locked floating solids'' and smectic phases. The resulting phases and
phase transitions are studied as a function of temperature and potential
strength. We find reentrant melting as a function of the potential strength.
Our results lead to universal predictions consistent with recent experiments on
2d colloids in the presence of a laser-induced 1d periodic potential.Comment: 4 pages, 3 figures, also available at http://cmtw.harvard.edu/~fre
Glassiness Vs. Order in Densely Frustrated Josephson Arrays
We carry out extensive Monte Carlo simulations on the Coulomb gas dual to the
uniformly frustrated two dimensional XY model, for a sequence of frustrations f
converging to the irraltional (3-sqrt 5)/2. We find in these systems a sharp
first order equilibrium phase transition to an ordered vortex structure at a
T_c which varies only slightly with f. This ordered vortex structure remains in
general phase incoherent until a lower pinning transition T_p(f) that varies
with f. We argue that the glassy behaviors reported for this model in earlier
simulations are dynamic effects.Comment: 4 pages, 4 eps figure
Anything You Can Do, You Can Do Better: Neural Substrates of Incentive-Based Performance Enhancement
Performance-based pay schemes in many organizations share the fundamental assumption that the performance level for a given task will increase as a function of the amount of incentive provided. Consistent with this notion, psychological studies have demonstrated that expectations of reward can improve performance on a plethora of different cognitive and physical tasks, ranging from problem solving to the voluntary regulation of heart rate. However, much less is understood about the neural mechanisms of incentivized performance enhancement. In particular, it is still an open question how brain areas that encode expectations about reward are able to translate incentives into improved performance across fundamentally different cognitive and physical task requirements
Physical nature of critical wave functions in Fibonacci systems
We report on a new class of critical states in the energy spectrum of general
Fibonacci systems. By introducing a transfer matrix renormalization technique,
we prove that the charge distribution of these states spreads over the whole
system, showing transport properties characteristic of electronic extended
states. Our analytical method is a first step to find out the link between the
spatial structure of these critical wave functions and the quasiperiodic order
of the underlying lattice.Comment: REVTEX 3.0, 11 pages, 2 figures available upon request. To appear in
Phys. Rev. Let
Dimer Decimation and Intricately Nested Localized-Ballistic Phases of Kicked Harper
Dimer decimation scheme is introduced in order to study the kicked quantum
systems exhibiting localization transition. The tight-binding representation of
the model is mapped to a vectorized dimer where an asymptotic dissociation of
the dimer is shown to correspond to the vanishing of the transmission
coefficient thru the system. The method unveils an intricate nesting of
extended and localized phases in two-dimensional parameter space. In addition
to computing transport characteristics with extremely high precision, the
renormalization tools also provide a new method to compute quasienergy
spectrum.Comment: There are five postscript figures. Only half of the figure (3) is
shown to reduce file size. However, missing part is the mirror image of the
part show
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