2,831 research outputs found
Alternative Structures and Bihamiltonian Systems
In the study of bi-Hamiltonian systems (both classical and quantum) one
starts with a given dynamics and looks for all alternative Hamiltonian
descriptions it admits.In this paper we start with two compatible Hermitian
structures (the quantum analog of two compatible classical Poisson brackets)
and look for all the dynamical systems which turn out to be bi-Hamiltonian with
respect to them.Comment: 18 page
Alternative Algebraic Structures from Bi-Hamiltonian Quantum Systems
We discuss the alternative algebraic structures on the manifold of quantum
states arising from alternative Hermitian structures associated with quantum
bi-Hamiltonian systems. We also consider the consequences at the level of the
Heisenberg picture in terms of deformations of the associative product on the
space of observables.Comment: Accepted for publication in Int. J. Geom. Meth. Mod. Phy
Quantum Bi-Hamiltonian systems, alternative Hermitian structures and Bi-Unitary transformations
We discuss the dynamical quantum systems which turn out to be bi-unitary with
respect to the same alternative Hermitian structures in a infinite-dimensional
complex Hilbert space. We give a necessary and sufficient condition so that the
Hermitian structures are in generic position. Finally the transformations of
the bi-unitary group are explicitly obtained.Comment: Note di Matematica vol 23, 173 (2004
The Quantum-Classical Transition: The Fate of the Complex Structure
According to Dirac, fundamental laws of Classical Mechanics should be
recovered by means of an "appropriate limit" of Quantum Mechanics. In the same
spirit it is reasonable to enquire about the fundamental geometric structures
of Classical Mechanics which will survive the appropriate limit of Quantum
Mechanics. This is the case for the symplectic structure. On the contrary, such
geometric structures as the metric tensor and the complex structure, which are
necessary for the formulation of the Quantum theory, may not survive the
Classical limit, being not relevant in the Classical theory. Here we discuss
the Classical limit of those geometric structures mainly in the Ehrenfest and
Heisenberg pictures, i.e. at the level of observables rather than at the level
of states. A brief discussion of the fate of the complex structure in the
Quantum-Classical transition in the Schroedinger picture is also mentioned.Comment: 19 page
A superconducting absolute spin valve
A superconductor with a spin-split excitation spectrum behaves as an ideal
ferromagnetic spin-injector in a tunneling junction. It was theoretical
predicted that the combination of two such spin-split superconductors with
independently tunable magnetizations, may be used as an ideal
spin-valve. Here we report on the first switchable superconducting spin-valve
based on two EuS/Al bilayers coupled through an aluminum oxide tunnel barrier.
The spin-valve shows a relative resistance change between the parallel and
antiparallel configuration of the EuS layers up to 900% that demonstrates a
highly spin-polarized currents through the junction. Our device may be pivotal
for realization of thermoelectric radiation detectors, logical element for a
memory cell in cryogenics superconductor-based computers and superconducting
spintronics in general.Comment: 6 pages, 4 color figures, 1 tabl
A pedagogical presentation of a -algebraic approach to quantum tomography
It is now well established that quantum tomography provides an alternative
picture of quantum mechanics. It is common to introduce tomographic concepts
starting with the Schrodinger-Dirac picture of quantum mechanics on Hilbert
spaces. In this picture states are a primary concept and observables are
derived from them. On the other hand, the Heisenberg picture,which has evolved
in the algebraic approach to quantum mechanics, starts with the
algebra of observables and introduce states as a derived concept. The
equivalence between these two pictures amounts essentially, to the
Gelfand-Naimark-Segal construction. In this construction, the abstract algebra is realized as an algebra of operators acting on a constructed
Hilbert space. The representation one defines may be reducible or irreducible,
but in either case it allows to identify an unitary group associated with the
algebra by means of its invertible elements. In this picture both
states and observables are appropriate functions on the group, it follows that
also quantum tomograms are strictly related with appropriate functions
(positive-type)on the group. In this paper we present, by means of very simple
examples, the tomographic description emerging from the set of ideas connected
with the algebra picture of quantum mechanics. In particular, the
tomographic probability distributions are introduced for finite and compact
groups and an autonomous criterion to recognize a given probability
distribution as a tomogram of quantum state is formulated
Quantum Systems and Alternative Unitary Descriptions
Motivated by the existence of bi-Hamiltonian classical systems and the
correspondence principle, in this paper we analyze the problem of finding
Hermitian scalar products which turn a given flow on a Hilbert space into a
unitary one. We show how different invariant Hermitian scalar products give
rise to different descriptions of a quantum system in the Ehrenfest and
Heisenberg picture.Comment: 18 page
Revealing the magnetic proximity effect in EuS/Al bilayers through superconducting tunneling spectroscopy
A ferromagnetic insulator attached to a superconductor is known to induce an
exchange splitting of the Bardeen-Cooper-Schrieffer (BCS) singularity by a
magnitude proportional to the magnetization, and penetrating into the
superconductor to a depth comparable with the superconducting coherence length.
We study this long-range magnetic proximity effect in EuS/Al bilayers and find
that the exchange splitting of the BCS peaks is present already in the
unpolarized state of the ferromagnetic insulator (EuS), and is being further
enhanced when magnetizing the sample by a magnetic field. The measurement data
taken at the lowest temperatures feature a high contrast which has allowed us
to relate the line shape of the split BCS conductance peaks to the
characteristic magnetic domain structure of the EuS layer in the unpolarized
state. These results pave the way to engineering triplet superconducting
correlations at domain walls in EuS/Al bilayers. Furthermore, the hard gap and
clear splitting observed in our tunneling spectroscopy measurements indicate
that EuS/Al bilayers are excellent candidates for substituting strong magnetic
fields in experiments studying Majorana bound states.Comment: 9 pages, 4 color figure
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