28 research outputs found
Canonical transformations in three-dimensional phase space
Canonical transformation in a three-dimensional phase space endowed with
Nambu bracket is discussed in a general framework. Definition of the canonical
transformations is constructed as based on canonoid transformations. It is
shown that generating functions, transformed Hamilton functions and the
transformation itself for given generating functions can be determined by
solving Pfaffian differential equations corresponding to that quantities. Types
of the generating functions are introduced and all of them is listed.
Infinitesimal canonical transformations are also discussed. Finally, we show
that decomposition of canonical transformations is also possible in
three-dimensional phase space as in the usual two-dimensional one.Comment: 19 pages, 1 table, no figures. Accepted for publication in Int. J.
Mod. Phys.
Local current distribution at large quantum dots (QDs): a self-consistent screening model
We report the implementation of the self-consistent Thomas-Fermi screening
theory, together with the local Ohm's law to a quantum dot system in order to
obtain local current distribution within the dot and at the leads. We consider
a large dot (size
nm) defined by split gates, and coupled to the leads. Numerical
calculations show that the non-dissipative current is confined to the
incompressible strips. Due to the non-linear screening properties of the 2DES
at low temperatures, this distribution is highly sensitive to external magnetic
field. Our findings support the phenomenological models provided by the
experimental studies so far, where the formation of the (direct) edge channels
dominate the transport.Comment: 6 Pages, 2 Figure
The self-consistent calculation of the edge states at quantum Hall effect (QHE) based Mach-Zehnder interferometers (MZI)
The spatial distribution of the incompressible edge states (IES) is obtained
for a geometry which is topologically equivalent to an electronic Mach-Zehnder
interferometer, taking into account the electron-electron interactions within a
Hartree type self-consistent model. The magnetic field dependence of these IES
is investigated and it is found that an interference pattern may be observed if
two IES merge or come very close, near the quantum point contacts. Our
calculations demonstrate that, being in a quantized Hall plateau does not
guarantee observing the interference behavior.Comment: EP2DS-17 Proceedings, 6 Pages, 2 Figure
Unconventional pairings and radial line nodes in inversion symmetry broken superconductors
Noncentrosymmetric superconductors (NCSs) with broken inversion symmetry can have spin-dependent order parameters (OPs) with mixed parity which can also have nodes in the pair potential as well as the energy spectra. These nodes are distinct features that are not present in conventional superconductors. They appear as points or lines in the momentum space where the latter can have angular or radial geometries dictated by the dimensionality, the lattice structure and the pairing interaction. In this work we study the nodes in time reversal symmetry (TRS) preserving NCSs at the OP, the pair potential, and the energy spectrum levels. Nodes are examined by using spin independent pairing interactions respecting the rotational C∞v symmetry in the presence of spin-orbit coupling (SOC). The pairing symmetries and the nodal topology are affected by the relative strength of the pairing channels which is studied for the mixed singlet-triplet, pure singlet, and pure triplet. Complementary to the angular line nodes widely present in the literature, the C∞v symmetry here allows radial line nodes (RLNs) due to the nonlinear momentum dependence in the OPs. The topology of the RLNs in the mixed case shows a distinctly different characterization than the half-spin quantum vortex at the Dirac point. We apply this NCS physics to the inversion symmetry broken exciton condensates (ECs) in double quantum wells where the point and the RLNs can be found. On the other hand, for a pure triplet condensate, two fully gapped and topologically distinct regimes exist, separated by a QSHI-like zero energy superconducting state with even number of Majorana modes. We also remark on how the point and the RLNs can be manipulated, enabling an external control on the topology. © 2016 Elsevier B.V
Nonlocal, noncommutative picture in quantum mechanics and distinguished canonical maps
Classical nonlinear canonical (Poisson) maps have a distinguished role in
quantum mechanics. They act unitarily on the quantum phase space and generate
-independent quantum canonical maps. It is shown that such maps act in
the noncommutative phase space as dictated by the classical covariance. A
crucial observation made is that under the classical covariance the local
quantum mechanical picture can become nonlocal in the Hilbert space. This
nonlocal picture is made equivalent by the Weyl map to a noncommutative picture
in the phase space formulation of the theory. The connection between the
entanglement and nonlocality of the representation is explored and specific
examples of the generation of entanglement are provided by using such concepts
as the generalized Bell states. That the results have direct application in
generating vacuum soliton configurations in the recently popular scalar field
theories of noncommutative coordinates is also demonstrated.Comment: 14 pages, one figur
-independent Universality of the Quantum-Classical Canonical Transformations
A theory of non-unitary-invertible as well as unitary canonical
transformations is formulated in the context of Weyl's phase space
representations. That all quantum canonical transformations without an explicit
dependence are also classical mechanical and vice versa is demonstrated
in the phase space. Contrary to some earlier results, it is also shown that the
quantum generators and their classical counterparts are identical and
-independent. The latter is a powerful result bringing the theory of
classical canonical transformations and the -independent quantum ones on
an equal footing.Comment: 13 pages, no figure
Operational approach in the weak-field measurement of polarization fluctuations
The operational approach to the measurement of phase studied by Noh, Fougeres
and Mandel is applied to the measurement of the state of polarization of fully
polarized light. Operational counterparts of the quantum Stokes parameters are
introduced and their fluctuations are examined. It is shown that if the
polarized field is weak, the measured fluctuations are influenced not only by
the quantum properties of the source field but also that of the measurement.
This character is reflected on the measured probability distributions of the
parameters of polarization, which are also investigated independently for the
fully polarized coherent states and the Fock states as the initial field
strength is varied. Finally, connection between the operational approach to the
measurement of polarization and the su(2) interferometry is examined.Comment: 17 pages, 14 figure