355 research outputs found
High order non-unitary split-step decomposition of unitary operators
We propose a high order numerical decomposition of exponentials of hermitean
operators in terms of a product of exponentials of simple terms, following an
idea which has been pioneered by M. Suzuki, however implementing it for complex
coefficients. We outline a convenient fourth order formula which can be written
compactly for arbitrary number of noncommuting terms in the Hamiltonian and
which is superiour to the optimal formula with real coefficients, both in
complexity and accuracy. We show asymptotic stability of our method for
sufficiently small time step and demonstrate its efficiency and accuracy in
different numerical models.Comment: 10 pages, 4 figures (5 eps files) Submitted to J. of Phys. A: Math.
Ge
Diffusive high-temperature transport in the one-dimensional Hubbard model
We consider charge and spin transport in the one-dimensional Hubbard model at
infinite temperature, half-filling and zero magnetization. Implementing
matrix-product-operator simulations of the non-equilibrium steady states of
boundary-driven open Hubbard chains for up to 100 sites we find clear evidence
of diffusive transport for any (non-zero and finite) value of the interaction
U.Comment: 6 pages RevTeX + 8 eps figures; revised and extended versio
Exact dynamics in dual-unitary quantum circuits
We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size l reaches infinite temperature after a time t ∝ l, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs
Anomalous slow fidelity decay for symmetry breaking perturbations
Symmetries as well as other special conditions can cause anomalous slowing
down of fidelity decay. These situations will be characterized, and a family of
random matrix models to emulate them generically presented. An analytic
solution based on exponentiated linear response will be given. For one
representative case the exact solution is obtained from a supersymmetric
calculation. The results agree well with dynamical calculations for a kicked
top.Comment: 4 pages, 2 figure
Uni-directional transport properties of a serpent billiard
We present a dynamical analysis of a classical billiard chain -- a channel
with parallel semi-circular walls, which can serve as a model for a bended
optical fiber. An interesting feature of this model is the fact that the phase
space separates into two disjoint invariant components corresponding to the
left and right uni-directional motions. Dynamics is decomposed into the jump
map -- a Poincare map between the two ends of a basic cell, and the time
function -- traveling time across a basic cell of a point on a surface of
section. The jump map has a mixed phase space where the relative sizes of the
regular and chaotic components depend on the width of the channel. For a
suitable value of this parameter we can have almost fully chaotic phase space.
We have studied numerically the Lyapunov exponents, time auto-correlation
functions and diffusion of particles along the chain. As a result of a
singularity of the time function we obtain marginally-normal diffusion after we
subtract the average drift. The last result is also supported by some
analytical arguments.Comment: 15 pages, 9 figure (19 .(e)ps files
Separating the regular and irregular energy levels and their statistics in Hamiltonian system with mixed classical dynamics
We look at the high-lying eigenstates (from the 10,001st to the 13,000th) in
the Robnik billiard (defined as a quadratic conformal map of the unit disk)
with the shape parameter . All the 3,000 eigenstates have been
numerically calculated and examined in the configuration space and in the phase
space which - in comparison with the classical phase space - enabled a clear
cut classification of energy levels into regular and irregular. This is the
first successful separation of energy levels based on purely dynamical rather
than special geometrical symmetry properties. We calculate the fractional
measure of regular levels as which is in remarkable
agreement with the classical estimate . This finding
confirms the Percival's (1973) classification scheme, the assumption in
Berry-Robnik (1984) theory and the rigorous result by Lazutkin (1981,1991). The
regular levels obey the Poissonian statistics quite well whereas the irregular
sequence exhibits the fractional power law level repulsion and globally
Brody-like statistics with . This is due to the strong
localization of irregular eigenstates in the classically chaotic regions.
Therefore in the entire spectrum we see that the Berry-Robnik regime is not yet
fully established so that the level spacing distribution is correctly captured
by the Berry-Robnik-Brody distribution (Prosen and Robnik 1994).Comment: 20 pages, file in plain LaTeX, 7 figures upon request submitted to J.
Phys. A. Math. Gen. in December 199
A time-motion analysis of turns performed by highly ranked Viennese waltz dancers
Twenty-four dance couples performing at the 2011 IDSF (International DanceSport Federation) International Slovenia Open were divided into two groups: the first twelve placed couples (top ranked) and the last twelve placed couples (lower ranked). Video recordings were processed automatically using computer vision tracking algorithms under operator supervision to calculate movement parameters. Time and speed of movement were analysed during single natural (right) and reverse (left) turns performed during the Viennese waltz. Both top and lower ranked dancers tended to perform similar proportionate frequencies of reverse (≈ 35%) and natural (≈ 65%) turns. Analysis of reverse turns showed that the top ranked dancers performed less turns on a curved trajectory (16%) than the lower ranked dancers (33%). The top ranked couples performed all turns at similar speeds (F = 1.31, df = 3, p = 0.27; mean = 2.09m/s) all of which were significantly quicker than the lower ranked couples (mean = 1.94m/s), the greatest differences found for reverse turns (12.43% faster for curved trajectories, 8.42% for straight trajectories). This suggests that the ability to maintain a high speed in the more difficult turns, particularly the reverse turns on a curved trajectory, results in the overall dance appearing more fluent as the speed of movement does not fluctuate as much. This aspect of performance needs to be improved by lower ranked dancers if they wish to improve rating of their performance. Future research should determine which factors relate to the speed of turns
Fidelity and level correlations in the transition from regularity to chaos
Mean fidelity amplitude and parametric energy--energy correlations are
calculated exactly for a regular system, which is subject to a chaotic random
perturbation. It turns out that in this particular case under the average both
quantities are identical. The result is compared with the susceptibility of
chaotic systems against random perturbations. Regular systems are more
susceptible against random perturbations than chaotic ones.Comment: 7 pages, 1 figur
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