13,494 research outputs found
Bistable Chimera Attractors on a Triangular Network of Oscillator Populations
We study a triangular network of three populations of coupled phase
oscillators with identical frequencies. The populations interact nonlocally, in
the sense that all oscillators are coupled to one another, but more weakly to
those in neighboring populations than to those in their own population. This
triangular network is the simplest discretization of a continuous ring of
oscillators. Yet it displays an unexpectedly different behavior: in contrast to
the lone stable chimera observed in continuous rings of oscillators, we find
that this system exhibits \emph{two coexisting stable chimeras}. Both chimeras
are, as usual, born through a saddle node bifurcation. As the coupling becomes
increasingly local in nature they lose stability through a Hopf bifurcation,
giving rise to breathing chimeras, which in turn get destroyed through a
homoclinic bifurcation. Remarkably, one of the chimeras reemerges by a reversal
of this scenario as we further increase the locality of the coupling, until it
is annihilated through another saddle node bifurcation.Comment: 12 pages, 5 figure
Measurements, errors, and negative kinetic energy
An analysis of errors in measurement yields new insight into the penetration
of quantum particles into classically forbidden regions. In addition to
``physical" values, realistic measurements yield ``unphysical" values which, we
show, can form a consistent pattern. An experiment to isolate a particle in a
classically forbidden region obtains negative values for its kinetic energy.
These values realize the concept of a {\it weak value}, discussed in previous
works.Comment: 22 pp, TAUP 1850-9
No-cloning theorem in thermofield dynamics
We discuss the relation between the no-cloning theorem from quantum
information and the doubling procedure used in the formalism of thermofield
dynamics (TFD). We also discuss how to apply the no-cloning theorem in the
context of thermofield states defined in TFD. Consequences associated to mixed
states, von Neumann entropy and thermofield vacuum are also addressed.Comment: 16 pages, 3 figure
Weak value of Dwell time for Quantum Dissipative spin-1/2 System
The dwell time is calculated within the framework of time dependent weak
measurement considering dissipative interaction between a spin half system and
the environment. Caldirola and Montaldi's method of retarded Schroedinger
equation is used to study the dissipative system. The result shows that
inclusion of dissipative interaction prevents zero time tunneling.Comment: This work is original. arXiv admin note: text overlap with
arXiv:0807.1357, arXiv:quant-ph/9611018, arXiv:quant-ph/9501015 by other
author
The Hartman effect and weak measurements "which are not really weak"
We show that in wavepacket tunnelling localisation of the transmitted
particle amounts to a quantum measurement of the delay it experiences in the
barrier. With no external degree of freedom involved, the envelope of the
wavepacket plays the role of the initial pointer state. Under tunnelling
conditions such 'self measurement' is necessarily weak, and the Hartman effect
just reflects the general tendency of weak values to diverge, as post-selection
in the final state becomes improbable. We also demonstrate that it is a good
precision, or 'not really weak' quantum measurement: no matter how wide the
barrier d, it is possible to transmit a wavepacket with a width {\sigma} small
compared to the observed advancement. As is the case with all weak
measurements, the probability of transmission rapidly decreases with the ratio
{\sigma}/d.Comment: 6 pages, 1 figur
Weak measurement takes a simple form for cumulants
A weak measurement on a system is made by coupling a pointer weakly to the
system and then measuring the position of the pointer. If the initial
wavefunction for the pointer is real, the mean displacement of the pointer is
proportional to the so-called weak value of the observable being measured. This
gives an intuitively direct way of understanding weak measurement. However, if
the initial pointer wavefunction takes complex values, the relationship between
pointer displacement and weak value is not quite so simple, as pointed out
recently by R. Jozsa. This is even more striking in the case of sequential weak
measurements. These are carried out by coupling several pointers at different
stages of evolution of the system, and the relationship between the products of
the measured pointer positions and the sequential weak values can become
extremely complicated for an arbitrary initial pointer wavefunction.
Surprisingly, all this complication vanishes when one calculates the cumulants
of pointer positions. These are directly proportional to the cumulants of
sequential weak values. This suggests that cumulants have a fundamental
physical significance for weak measurement
Comment on ``Protective measurements of the wave function of a single squeezed harmonic-oscillator state''
Alter and Yamamoto [Phys. Rev. A 53, R2911 (1996)] claimed to consider
``protective measurements'' [Phys. Lett. A 178, 38 (1993)] which we have
recently introduced. We show that the measurements discussed by Alter and
Yamamoto ``are not'' the protective measurements we proposed. Therefore, their
results are irrelevant to the nature of protective measurements.Comment: 2 pages LaTe
Lorentz-Invariant "Elements of Reality" and the Question of Joint Measurability of Commuting Observables
It is shown that the joint measurements of some physical variables
corresponding to commuting operators performed on pre- and post-selected
quantum systems invariably disturb each other. The significance of this result
for recent proofs of the impossibility of realistic Lorentz invariant
interpretation of quantum theory (without assumption of locality) is discussed.Comment: 15 page
Weak Value in Wave Function of Detector
A simple formula to read out the weak value from the wave function of the
measuring device after the postselection with the initial Gaussian profile is
proposed. We apply this formula for the weak value to the classical experiment
of the realization of the weak measurement by the optical polarization and
obtain the weak value for any pre- and post-selections. This formula
automatically includes the interference effect which is necessary to yields the
weak value as an outcome of the weak measurement.Comment: 3 pages, no figures, Published in Journal of the Physical Society of
Japa
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