529,327 research outputs found
Statistical bounds on the dynamical production of entanglement
We present a random-matrix analysis of the entangling power of a unitary
operator as a function of the number of times it is iterated. We consider
unitaries belonging to the circular ensembles of random matrices (CUE or COE)
applied to random (real or complex) non-entangled states. We verify numerically
that the average entangling power is a monotonic decreasing function of time.
The same behavior is observed for the "operator entanglement" --an alternative
measure of the entangling strength of a unitary. On the analytical side we
calculate the CUE operator entanglement and asymptotic values for the
entangling power. We also provide a theoretical explanation of the time
dependence in the CUE cases.Comment: preprint format, 14 pages, 2 figure
Pythagorean 2-tuple linguistic power aggregation operators in multiple attribute decision making
In this paper, we investigate the multiple attribute decision making
problems with Pythagorean 2-tuple linguistic information.
Then, we utilize power average and power geometric operations
to develop some Pythagorean 2-tuple linguistic power aggregation
operators: Pythagorean 2-tuple linguistic power weighted
average (P2TLPWA) operator, Pythagorean 2-tuple linguistic power
weighted geometric (P2TLPWG) operator, Pythagorean 2-tuple linguistic
power ordered weighted average (P2TLPOWA) operator,
Pythagorean 2-tuple linguistic power ordered weighted geometric
(P2TLPOWG) operator, Pythagorean 2-tuple linguistic power
hybrid average (P2TLPHA) operator and Pythagorean 2-tuple linguistic
power hybrid geometric (P2TLPHG) operator. The prominent
characteristic of these proposed operators are studied. Then,
we have utilized these operators to develop some approaches to
solve the Pythagorean 2-tuple linguistic multiple attribute decision
making problems. Finally, a practical example for enterprise
resource planning (ERP) system selection is given to verify the
developed approach and to demonstrate its practicality and
effectiveness
Minimum Entangling Power is Close to Its Maximum
Given a quantum gate acting on a bipartite quantum system, its maximum
(average, minimum) entangling power is the maximum (average, minimum)
entanglement generation with respect to certain entanglement measure when the
inputs are restricted to be product states. In this paper, we mainly focus on
the 'weakest' one, i.e., the minimum entangling power, among all these
entangling powers. We show that, by choosing von Neumann entropy of reduced
density operator or Schmidt rank as entanglement measure, even the 'weakest'
entangling power is generically very close to its maximal possible entanglement
generation. In other words, maximum, average and minimum entangling powers are
generically close. We then study minimum entangling power with respect to other
Lipschitiz-continuous entanglement measures and generalize our results to
multipartite quantum systems.
As a straightforward application, a random quantum gate will almost surely be
an intrinsically fault-tolerant entangling device that will always transform
every low-entangled state to near-maximally entangled state.Comment: 26 pages, subsection III.A.2 revised, authors list updated, comments
are welcom
Boltzmann Suppression of Interacting Heavy Particles
Matsumoto and Yoshimura have recently argued that the number density of heavy
particles in a thermal bath is not necessarily Boltzmann-suppressed for T << M,
as power law corrections may emerge at higher orders in perturbation theory.
This fact might have important implications on the determination of WIMP relic
densities. On the other hand, the definition of number densities in a
interacting theory is not a straightforward procedure. It usually requires
renormalization of composite operators and operator mixing, which obscure the
physical interpretation of the computed thermal average. We propose a new
definition for the thermal average of a composite operator, which does not
require any new renormalization counterterm and is thus free from such
ambiguities. Applying this definition to the model of Matsumoto and Yoshimura
we find that it gives number densities which are Boltzmann-suppressed at any
order in perturbation theory. We discuss also heavy particles which are
unstable already at T=0, showing that power law corrections do in general
emerge in this case.Comment: 7 pages, 5 figures. New section added, with the discussion of the
case of an unstable heavy particle. Version to appear on Phys. Rev.
Hierarchy of stochastic pure states for open quantum system dynamics
We derive a hierarchy of stochastic evolution equations for pure states
(quantum trajectories) to efficiently solve open quantum system dynamics with
non-Markovian structured environments. From this hierarchy of pure states
(HOPS) the exact reduced density operator is obtained as an ensemble average.
We demonstrate the power of HOPS by applying it to the Spin-Boson model, the
calculation of absorption spectra of molecular aggregates and energy transfer
in a photosynthetic pigment-protein complex
Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making
The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes
Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions
We study XY and dimerized XX spin-1/2 chains with random exchange couplings
by analytical and numerical methods and scaling considerations. We extend
previous investigations to dynamical properties, to surface quantities and
operator profiles, and give a detailed analysis of the Griffiths phase. We
present a phenomenological scaling theory of average quantities based on the
scaling properties of rare regions, in which the distribution of the couplings
follows a surviving random walk character. Using this theory we have obtained
the complete set of critical decay exponents of the random XY and XX models,
both in the volume and at the surface. The scaling results are confronted with
numerical calculations based on a mapping to free fermions, which then lead to
an exact correspondence with directed walks. The numerically calculated
critical operator profiles on large finite systems (L<=512) are found to follow
conformal predictions with the decay exponents of the phenomenological scaling
theory. Dynamical correlations in the critical state are in average
logarithmically slow and their distribution show multi-scaling character. In
the Griffiths phase, which is an extended part of the off-critical region
average autocorrelations have a power-law form with a non-universal decay
exponent, which is analytically calculated. We note on extensions of our work
to the random antiferromagnetic XXZ chain and to higher dimensions.Comment: 19 pages RevTeX, eps-figures include
Oscillation and the mean ergodic theorem for uniformly convex Banach spaces
Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear
operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n
x. We prove the following variational inequality in the case where T is power
bounded from above and below: for any increasing sequence (t_k)_{k in N} of
natural numbers we have sum_k || A_{t_{k+1}} x - A_{t_k} x ||^p <= C || x ||^p,
where the constant C depends only on p and the modulus of uniform convexity.
For T a nonexpansive operator, we obtain a weaker bound on the number of
epsilon-fluctuations in the sequence. We clarify the relationship between
bounds on the number of epsilon-fluctuations in a sequence and bounds on the
rate of metastability, and provide lower bounds on the rate of metastability
that show that our main result is sharp
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