14,985 research outputs found
Conceptual Unification of Gravity and Quanta
We present a model unifying general relativity and quantum mechanics. The
model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid
\Gamma = E \times G where E is the total space of the frame bundle over
spacetime, and G the Lorentz group. The differential geometry, based on
derivations of \mbox{{\cal A}}, is constructed. The eigenvalue equation for the
Einstein operator plays the role of the generalized Einstein's equation. The
algebra \mbox{{\cal A}}, when suitably represented in a bundle of Hilbert
spaces, is a von Neumann algebra \mathcal{M} of random operators representing
the quantum sector of the model. The Tomita-Takesaki theorem allows us to
define the dynamics of random operators which depends on the state \phi . The
same state defines the noncommutative probability measure (in the sense of
Voiculescu's free probability theory). Moreover, the state \phi satisfies the
Kubo-Martin-Schwinger (KMS) condition, and can be interpreted as describing a
generalized equilibrium state. By suitably averaging elements of the algebra
\mbox{{\cal A}}, one recovers the standard geometry of spacetime. We show that
any act of measurement, performed at a given spacetime point, makes the model
to collapse to the standard quantum mechanics (on the group G). As an example
we compute the noncommutative version of the closed Friedman world model.
Generalized eigenvalues of the Einstein operator produce the correct components
of the energy-momentum tensor. Dynamics of random operators does not ``feel''
singularities.Comment: 28 LaTex pages. Substantially enlarged version. Improved definition
of generalized Einstein's field equation
Controllable quantum scars in semiconductor quantum dots
Quantum scars are enhancements of quantum probability density along classical
periodic orbits. We study the recently discovered phenomenon of strong,
perturbation-induced quantum scarring in the two-dimensional harmonic
oscillator exposed to a homogeneous magnetic field. We demonstrate that both
the geometry and the orientation of the scars are fully controllable with a
magnetic field and a focused perturbative potential, respectively. These
properties may open a path into an experimental scheme to manipulate electric
currents in nanostructures fabricated in a two-dimensional electron gas.Comment: 5 pages, 4 figure
Localization of Eigenfunctions in the Stadium Billiard
We present a systematic survey of scarring and symmetry effects in the
stadium billiard. The localization of individual eigenfunctions in Husimi phase
space is studied first, and it is demonstrated that on average there is more
localization than can be accounted for on the basis of random-matrix theory,
even after removal of bouncing-ball states and visible scars. A major point of
the paper is that symmetry considerations, including parity and time-reversal
symmetries, enter to influence the total amount of localization. The properties
of the local density of states spectrum are also investigated, as a function of
phase space location. Aside from the bouncing-ball region of phase space,
excess localization of the spectrum is found on short periodic orbits and along
certain symmetry-related lines; the origin of all these sources of localization
is discussed quantitatively and comparison is made with analytical predictions.
Scarring is observed to be present in all the energy ranges considered. In
light of these results the excess localization in individual eigenstates is
interpreted as being primarily due to symmetry effects; another source of
excess localization, scarring by multiple unstable periodic orbits, is smaller
by a factor of .Comment: 31 pages, including 10 figure
On the existence of exotic and non-exotic multiquark meson states
To obtain an exact solution of a four-body system containing two quarks and
two antiquarks interacting through two-body terms is a cumbersome task that has
been tackled with more or less success during the last decades. We present an
exact method for the study of four-quark systems based on the hyperspherical
harmonics formalism that allows us to solve it without resorting to further
approximations, like for instance the existence of diquark components. We apply
it to systems containing two heavy and two light quarks using different
quark-quark potentials. While states may be stable in nature,
the stability of states would imply the existence of quark
correlations not taken into account by simple quark dynamical models.Comment: 3 pages. Contribution to the 20th European Conference on Few-Body
Problems in Physics, Pisa, Italy. To be published in Few-Body system
Phase-space correlations of chaotic eigenstates
It is shown that the Husimi representations of chaotic eigenstates are
strongly correlated along classical trajectories. These correlations extend
across the whole system size and, unlike the corresponding eigenfunction
correlations in configuration space, they persist in the semiclassical limit. A
quantitative theory is developed on the basis of Gaussian wavepacket dynamics
and random-matrix arguments. The role of symmetries is discussed for the
example of time-reversal invariance.Comment: Published version with minor corrections to version
Observing trajectories with weak measurements in quantum systems in the semiclassical regime
We propose a scheme allowing to observe the evolution of a quantum system in
the semiclassical regime along the paths generated by the propagator. The
scheme relies on performing consecutive weak measurements of the position. We
show how weak trajectories" can be extracted from the pointers of a series of
measurement devices having weakly interacted with the system. The properties of
these "weak trajectories" are investigated and illustrated in the case of a
time-dependent model system.Comment: v2: Several minor corrections were made. Added Appendix (that will
appear as Suppl. Material). To be published in Phys Rev Let
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