4,335 research outputs found
Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd
In a recent FTC by Tremblay {\sl et al} (2009 {\sl J. Phys. A: Math. Theor.}
{\bf 42} 205206), it has been conjectured that for any integer value of ,
some novel exactly solvable and integrable quantum Hamiltonian on a plane
is superintegrable and that the additional integral of motion is a th-order
differential operator . Here we demonstrate the conjecture for the
infinite family of Hamiltonians with odd , whose first member
corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination
of the centre-of-mass motion. Our approach is based on the construction of some
-extended and invariant Hamiltonian \chh_k, which can be interpreted
as a modified boson oscillator Hamiltonian. The latter is then shown to possess
a -invariant integral of motion \cyy_{2k}, from which can be
obtained by projection in the identity representation space.Comment: 14 pages, no figure; change of title + important addition to sect. 4
+ 2 more references + minor modifications; accepted by JPA as an FT
Mott physics and first-order transition between two metals in the normal state phase diagram of the two-dimensional Hubbard model
For doped two-dimensional Mott insulators in their normal state, the
challenge is to understand the evolution from a conventional metal at high
doping to a strongly correlated metal near the Mott insulator at zero doping.
To this end, we solve the cellular dynamical mean-field equations for the
two-dimensional Hubbard model using a plaquette as the reference quantum
impurity model and continuous-time quantum Monte Carlo method as impurity
solver. The normal-state phase diagram as a function of interaction strength
, temperature , and filling shows that, upon increasing towards
the Mott insulator, there is a surface of first-order transition between two
metals at nonzero doping. That surface ends at a finite temperature critical
line originating at the half-filled Mott critical point. Associated with this
transition, there is a maximum in scattering rate as well as thermodynamic
signatures. These findings suggest a new scenario for the normal-state phase
diagram of the high temperature superconductors. The criticality surmised in
these systems can originate not from a T=0 quantum critical point, nor from the
proximity of a long-range ordered phase, but from a low temperature transition
between two types of metals at finite doping. The influence of Mott physics
therefore extends well beyond half-filling.Comment: 27 pages, 16 figures, LaTeX, published versio
Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces
We formulate the necessary conditions for the maximal super-integrability of
a certain family of classical potentials defined in the constant curvature
two-dimensional spaces. We give examples of homogeneous potentials of degree -2
on as well as their equivalents on and for which these
necessary conditions are also sufficient. We show explicit forms of the
additional first integrals which always can be chosen polynomial with respect
to the momenta and which can be of an arbitrary high degree with respect to the
momenta
First order Mott transition at zero temperature in two dimensions: Variational plaquette study
The nature of the metal-insulator Mott transition at zero temperature has
been discussed for a number of years. Whether it occurs through a quantum
critical point or through a first order transition is expected to profoundly
influence the nature of the finite temperature phase diagram. In this paper, we
study the zero temperature Mott transition in the two-dimensional Hubbard model
on the square lattice with the variational cluster approximation. This takes
into account the influence of antiferromagnetic short-range correlations. By
contrast to single-site dynamical mean-field theory, the transition turns out
to be first order even at zero temperature.Comment: 6 pages, 5 figures, version 2 with additional results for 8 bath
site
A shrinking Compact Symmetric Object: J11584+2450?
We present multi-frequency multi-epoch Very Long Baseline Array (VLBA)
observations of J11584+2450. These observations clearly show this source,
previously classified as a core-jet, to be a compact symmetric object (CSO).
Comparisons between these new data and data taken over the last 9 years shows
the edge brightened hot spots retreating towards the core (and slightly to the
west) at approximately 0.3c. Whether this motion is strictly apparent or
actually physical in nature is discussed, as well as possible explanations, and
what implications a physical contraction of J11584+2450 would have for current
CSO models.Comment: 16 pages, 6 figures, 5 tables. Accepted for publication in Ap
Third order superintegrable systems separating in polar coordinates
A complete classification is presented of quantum and classical
superintegrable systems in that allow the separation of variables in
polar coordinates and admit an additional integral of motion of order three in
the momentum. New quantum superintegrable systems are discovered for which the
potential is expressed in terms of the sixth Painlev\'e transcendent or in
terms of the Weierstrass elliptic function
N=2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane
The family of Tremblay-Turbiner-Winternitz Hamiltonians on a plane,
corresponding to any positive real value of , is shown to admit a supersymmetric extension of the same kind as that introduced by Freedman
and Mende for the Calogero problem and based on an superalgebra. The irreducible representations of the latter
are characterized by the quantum number specifying the eigenvalues of the first
integral of motion of . Bases for them are explicitly constructed.
The ground state of each supersymmetrized Hamiltonian is shown to belong to an
atypical lowest-weight state irreducible representation.Comment: 18 pages, no figur
Particular Integrability and (Quasi)-exact-solvability
A notion of a particular integrability is introduced when two operators
commute on a subspace of the space where they act. Particular integrals for
one-dimensional (quasi)-exactly-solvable Schroedinger operators and
Calogero-Sutherland Hamiltonians for all roots are found. In the classical case
some special trajectories for which the corresponding particular constants of
motion appear are indicated.Comment: 13 pages, typos correcte
Implementing an analog speedometer in STISIM Drive using Parallax BSTAMP microcontroller
In a non-instrumental cab, STISIM Drive software normally projects the speed of the vehicle through a dashboard presented on the simulation screen. The simulated dashboard can be displayed with several graphical options. In all cases, there is a loss of information arising from the road. A solution is to integrate the speedometer into a dashboard and to disable the simulated projection. This solution increases the virtual immersion of the driver and presents speed in a more realistic way. We are proposing a simple solution based on Parallax Inc. Basic Stramp microcontroller. In addition to its low cost and simplicity, this solution allows integration of other technical elements of the driving experience (e.g., activation of turn signals, horn, etc.)
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