530 research outputs found
Solving Gapped Hamiltonians Locally
We show that any short-range Hamiltonian with a gap between the ground and
excited states can be written as a sum of local operators, such that the ground
state is an approximate eigenvector of each operator separately. We then show
that the ground state of any such Hamiltonian is close to a generalized matrix
product state. The range of the given operators needed to obtain a good
approximation to the ground state is proportional to the square of the
logarithm of the system size times a characteristic "factorization length".
Applications to many-body quantum simulation are discussed. We also consider
density matrices of systems at non-zero temperature.Comment: 13 pages, 2 figures; minor changes to references, additional
discussion of numerics; additional explanation of nonzero temperature matrix
product for
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
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
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
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
West Nile virus outbreak among horses in New York State, 1999 and 2000.
West Nile (WN) virus was identified in the Western Hemisphere in 1999. Along with human encephalitis cases, 20 equine cases of WN virus were detected in 1999 and 23 equine cases in 2000 in New York. During both years, the equine cases occurred after human cases in New York had been identified
Disturbance spreading in incommensurate and quasiperiodic systems
The propagation of an initially localized excitation in one dimensional
incommensurate, quasiperiodic and random systems is investigated numerically.
It is discovered that the time evolution of variances of atom
displacements depends on the initial condition. For the initial condition with
nonzero momentum, goes as with and 0 for
incommensurate Frenkel-Kontorova (FK) model at below and above
respectively; and for uniform, quasiperiodic and random chains. It
is also found that with the exponent of distribution
function of frequency at zero frequency, i.e., (as ). For the initial condition with zero
momentum, for all systems studied. The underlying physical meaning
of this diffusive behavior is discussed.Comment: 8 Revtex Pages, 5 PS figures included, to appear in Phys. Rev. B
April 200
Phonon Localization in One-Dimensional Quasiperiodic Chains
Quasiperiodic long range order is intermediate between spatial periodicity
and disorder, and the excitations in 1D quasiperiodic systems are believed to
be transitional between extended and localized. These ideas are tested with a
numerical analysis of two incommensurate 1D elastic chains: Frenkel-Kontorova
(FK) and Lennard-Jones (LJ). The ground state configurations and the
eigenfrequencies and eigenfunctions for harmonic excitations are determined.
Aubry's "transition by breaking the analyticity" is observed in the ground
state of each model, but the behavior of the excitations is qualitatively
different. Phonon localization is observed for some modes in the LJ chain on
both sides of the transition. The localization phenomenon apparently is
decoupled from the distribution of eigenfrequencies since the spectrum changes
from continuous to Cantor-set-like when the interaction parameters are varied
to cross the analyticity--breaking transition. The eigenfunctions of the FK
chain satisfy the "quasi-Bloch" theorem below the transition, but not above it,
while only a subset of the eigenfunctions of the LJ chain satisfy the theorem.Comment: This is a revised version to appear in Physical Review B; includes
additional and necessary clarifications and comments. 7 pages; requires
revtex.sty v3.0, epsf.sty; includes 6 EPS figures. Postscript version also
available at
http://lifshitz.physics.wisc.edu/www/koltenbah/koltenbah_homepage.htm
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