132,818 research outputs found
Consequences of nonclassical measurement for the algorithmic description of continuous dynamical systems
Continuous dynamical systems intuitively seem capable of more complex behavior than discrete systems. If analyzed in the framework of the traditional theory of computation, a continuous dynamical system with countably many quasistable states has at least the computational power of a universal Turing machine. Such an analysis assumes, however, the classical notion of measurement. If measurement is viewed nonclassically, a continuous dynamical system cannot, even in principle, exhibit behavior that cannot be simulated by a universal Turing machine
Universal Uhrig dynamical decoupling for bosonic systems
We construct efficient deterministic dynamical decoupling schemes protecting
continuous variable degrees of freedom. Our schemes target decoherence induced
by quadratic system-bath interactions with analytic time-dependence. We show
how to suppress such interactions to -th order using only pulses.
Furthermore, we show to homogenize a -mode bosonic system using only
pulses, yielding - up to -th order - an effective evolution
described by non-interacting harmonic oscillators with identical frequencies.
The decoupled and homogenized system provides natural decoherence-free
subspaces for encoding quantum information. Our schemes only require pulses
which are tensor products of single-mode passive Gaussian unitaries and SWAP
gates between pairs of modes.Comment: 17 pages, 2 figures
Dynamical Universal Behavior in Quantum Chaotic Systems
We discover numerically that a moving wave packet in a quantum chaotic
billiard will always evolve into a quantum state, whose density probability
distribution is exponential. This exponential distribution is found to be
universal for quantum chaotic systems with rigorous proof. In contrast, for the
corresponding classical system, the distribution is Gaussian. We find that the
quantum exponential distribution can smoothly change to the classical Gaussian
distribution with coarse graining.Comment: 4 figure
Universal properties of many-body delocalization transitions
We study the dynamical melting of "hot" one-dimensional many-body localized
systems. As disorder is weakened below a critical value these non-thermal
quantum glasses melt via a continuous dynamical phase transition into classical
thermal liquids. By accounting for collective resonant tunneling processes, we
derive and numerically solve an effective model for such quantum-to-classical
transitions and compute their universal critical properties. Notably, the
classical thermal liquid exhibits a broad regime of anomalously slow
sub-diffusive equilibration dynamics and energy transport. The subdiffusive
regime is characterized by a continuously evolving dynamical critical exponent
that diverges with a universal power at the transition. Our approach elucidates
the universal long-distance, low-energy scaling structure of many-body
delocalization transitions in one dimension, in a way that is transparently
connected to the underlying microscopic physics.Comment: 12 pages, 6 figures; major changes from v1, including a modified
approach and new emphasis on conventional MBL systems rather than their
critical variant
Universality in Three-Frequency Resonances
We investigate the hierarchical structure of three-frequency resonances in
nonlinear dynamical systems with three interacting frequencies. We hypothesize
an ordering of these resonances based on a generalization of the Farey tree
organization from two frequencies to three. In experiments and numerical
simulations we demonstrate that our hypothesis describes the hierarchies of
three-frequency resonances in representative dynamical systems. We conjecture
that this organization may be universal across a large class of three-frequency
systems
Universality in Systems with Power-Law Memory and Fractional Dynamics
There are a few different ways to extend regular nonlinear dynamical systems
by introducing power-law memory or considering fractional
differential/difference equations instead of integer ones. This extension
allows the introduction of families of nonlinear dynamical systems converging
to regular systems in the case of an integer power-law memory or an integer
order of derivatives/differences. The examples considered in this review
include the logistic family of maps (converging in the case of the first order
difference to the regular logistic map), the universal family of maps, and the
standard family of maps (the latter two converging, in the case of the second
difference, to the regular universal and standard maps). Correspondingly, the
phenomenon of transition to chaos through a period doubling cascade of
bifurcations in regular nonlinear systems, known as "universality", can be
extended to fractional maps, which are maps with power-/asymptotically
power-law memory. The new features of universality, including cascades of
bifurcations on single trajectories, which appear in fractional (with memory)
nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201
Universal Dynamical Decoupling: Two-Qubit States and Beyond
Uhrig's dynamical decoupling pulse sequence has emerged as one universal and
highly promising approach to decoherence suppression. So far both the
theoretical and experimental studies have examined single-qubit decoherence
only. This work extends Uhrig's universal dynamical decoupling from one-qubit
to two-qubit systems and even to general multi-level quantum systems. In
particular, we show that by designing appropriate control Hamiltonians for a
two-qubit or a multi-level system, Uhrig's pulse sequence can also preserve a
generalized quantum coherence measure to the order of , with only
pulses. Our results lead to a very useful scheme for efficiently locking
two-qubit entangled states. Future important applications of Uhrig's pulse
sequence in preserving the quantum coherence of multi-level quantum systems can
also be anticipated.Comment: 10 pages, 4 figures, minor changes made, submitted to PR
- …