1,366 research outputs found
Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems
We introduce a one-parameter generalized oscillator algebra A(k) (that covers
the case of the harmonic oscillator algebra) and discuss its finite- and
infinite-dimensional representations according to the sign of the parameter k.
We define an (Hamiltonian) operator associated with A(k) and examine the
degeneracies of its spectrum. For the finite (when k < 0) and the infinite
(when k > 0 or = 0) representations of A(k), we construct the associated phase
operators and build temporally stable phase states as eigenstates of the phase
operators. To overcome the difficulties related to the phase operator in the
infinite-dimensional case and to avoid the degeneracy problem for the
finite-dimensional case, we introduce a truncation procedure which generalizes
the one used by Pegg and Barnett for the harmonic oscillator. This yields a
truncated generalized oscillator algebra A(k,s), where s denotes the truncation
order. We construct two types of temporally stable states for A(k,s) (as
eigenstates of a phase operator and as eigenstates of a polynomial in the
generators of A(k,s)). Two applications are considered in this article. The
first concerns physical realizations of A(k) and A(k,s) in the context of
one-dimensional quantum systems with finite (Morse system) or infinite
(Poeschl-Teller system) discrete spectra. The second deals with mutually
unbiased bases used in quantum information.Comment: Accepted for publication in Journal of Physics A: Mathematical and
Theoretical as a pape
The Moyal Bracket in the Coherent States framework
The star product and Moyal bracket are introduced using the coherent states
corresponding to quantum systems with non-linear spectra. Two kinds of coherent
state are considered. The first kind is the set of Gazeau-Klauder coherent
states and the second kind are constructed following the Perelomov-Klauder
approach. The particular case of the harmonic oscillator is also discussed.Comment: 13 page
Statistical properties of Klauder-Perelomov coherent states for the Morse potential
We present in this paper a realistic construction of the coherent states for
the Morse potential using the Klauder-Perelomov approach . We discuss the
statistical properties of these states, by deducing the Q- and P-distribution
functions. The thermal expectations for the quantum canonical ideal gas of the
Morse oscillators are also calculated
Origin and stability of the dipolar response in a family of tetragonal tungsten bronze relaxors
A new family of relaxor dielectrics with the tetragonal tungsten bronze
structure (nominal composition Ba6M3+Nb9O30, M3+ = Ga, Sc or In) were studied
using dielectric spectroscopy to probe the dynamic dipole response and
correlate this with the crystal structure as determined from powder neutron
diffraction. Independent analyses of real and imaginary parts of the complex
dielectric function were used to determine characteristic temperature
parameters, TVF, and TUDR, respectively. In each composition both these
temperatures correlated with the temperature of maximum crystallographic
strain, Tc/a determined from diffraction data. The overall behaviour is
consistent with dipole freezing and the data indicate that the dipole stability
increases with increasing M3+ cation size as a result of increased
tetragonality of the unit cell. Crystallographic data suggests that these
materials are uniaxial relaxors with the dipole moment predominantly restricted
to the B1 cation site in the structure. Possible origins of the relaxor
behaviour are discussed.Comment: Main article 32 pages, 8 figures; Supplementary data 24 pages, 4
figure
Generalized Intelligent States for an Arbitrary Quantum System
Generalized Intelligent States (coherent and squeezed states) are derived for
an arbitrary quantum system by using the minimization of the so-called
Robertson-Schr\"odinger uncertainty relation. The Fock-Bargmann representation
is also considered. As a direct illustration of our construction, the
P\"oschl-Teller potentials of trigonometric type will be shosen. We will show
the advantage of the Fock-Bargmann representation in obtaining the generalized
intelligent states in an analytical way. Many properties of these states are
studied
Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
We show that the integer quantum Hall effect systems in plane, sphere or
disc, can be formulated in terms of an algebraic unified scheme. This can be
achieved by making use of a generalized Weyl--Heisenberg algebra and
investigating its basic features. We study the electromagnetic excitation and
derive the Hamiltonian for droplets of fermions on a two-dimensional Bargmann
space (phase space). This excitation is introduced through a deformation
(perturbation) of the symplectic structure of the phase space. We show the
major role of Moser's lemma in dressing procedure, which allows us to eliminate
the fluctuations of the symplectic structure. We discuss the emergence of the
Seiberg--Witten map and generation of an abelian noncommutative gauge field in
the theory. As illustration of our model, we give the action describing the
electromagnetic excitation of a quantum Hall droplet in two-dimensional
manifold.Comment: 23 page
Muon spin rotation and neutron scattering study of the non-centrosymmetric tetragonal compound CeAuAl3
We have investigated the non-centrosymmetric tetragonal heavy-fermion
compound CeAuAl3 using muon spin rotation (muSR), neutron diffraction (ND) and
inelastic neutron scattering (INS) measurements. We have also revisited the
magnetic, transport and thermal properties. The magnetic susceptibility reveals
an antiferromagnetic transition at 1.1 K with a possibility of another magnetic
transition near 0.18 K. The heat capacity shows a sharp lambda-type anomaly at
1.1 K in zero-filed, which broadens and moves to higher temperature in applied
magnetic field. Our zero-field muSR and ND measurements confirm the existence
of a long-range magnetic ground state below 1.2 K. Further the ND study reveals
an incommensurate magnetic ordering with a magnetic propagation vector k = (0,
0, 0.52) and a spiral structure of Ce moments coupled ferromagnetically within
the ab-plane. Our INS study reveals the presence of two well-defined crystal
electric field (CEF) excitations at 5.1 meV and 24.6 meV in the paramagnetic
phase of CeAuAl3 which can be explained on the basis of the CEF theory.
Furthermore, low energy quasi-elastic excitations show a Gaussian line shape
below 30 K compared to a Lorentzian line shape above 30 K, indicating a
slowdown of spin fluctuation below 30 K. We have estimated a Kondo temperature
of TK=3.5 K from the quasi-elastic linewidth, which is in good agreement with
that estimated from the heat capacity. This study also indicates the absence of
any CEF-phonon coupling unlike that observed in isostructural CeCuAl3. The CEF
parameters, energy level scheme and their wave functions obtained from the
analysis of INS data explain satisfactorily the single crystal susceptibility
in the presence of two-ion anisotropic exchange interaction in CeAuAl3.Comment: 28 pages and 17 figure
Magnetic order and the electronic ground state in the pyrochlore iridate Nd2Ir2O7
We report a combined muon spin relaxation/rotation, bulk magnetization,
neutron scattering, and transport study of the electronic properties of the
pyrochlore iridate Nd2Ir2O7. We observe the onset of strongly hysteretic
behavior in the temperature dependent magnetization below 120 K, and an abrupt
increase in the temperature dependent resistivity below 8 K. Zero field muon
spin relaxation measurements show that the hysteretic magnetization is driven
by a transition to a magnetically disordered state, and that below 8 K a
complex magnetically ordered ground state sets in, as evidenced by the onset of
heavily damped spontaneous muon precession. Our measurements point toward the
absence of a true metal-to-insulator phase transition in this material and
suggest that Nd2Ir2O7 lies either within or on the metallic side of the
boundary of the Dirac semimetal regime within its topological phase diagram.Comment: 21 pages, 7 figure
Incommensurate magnetic ordering in Cu2Te2O5X2 (X=Cl, Br) studied by single crystal neutron diffraction
Polarized and unpolarized neutron diffraction studies have been carried out
on single crystals of the coupled spin tetrahedra systems Cu2Te2O5X2 (X=Cl,
Br). A model of the magnetic structure associated with the propagation vectors
k'Cl ~ -0.150,0.422,1/2 and k'Br ~ -0.172,0.356,1/2 and stable below TN=18 K
for X=Cl and TN=11 K for X=Br is proposed. A feature of the model, common to
both the bromide and chloride, is a canted coplanar motif for the 4 Cu2+ spins
on each tetrahedron which rotates on a helix from cell to cell following the
propagation vector. The Cu2+magnetic moment determined for X=Br, 0.395(5)muB,
is significantly less than for X=Cl, 0.88(1)muB at 2K. The magnetic structure
of the chloride associated with the wave-vector k' differs from that determined
previously for the wave vector k~0.150,0.422,1/2 [O. Zaharko et.al. Phys. Rev.
Lett. 93, 217206 (2004)]
Representations and Properties of Generalized Statistics, Coherent States and Robertson Uncertainty Relations
The generalization of statistics, including bosonic and fermionic
sectors, is performed by means of the so-called Jacobson generators. The
corresponding Fock spaces are constructed. The Bargmann representations are
also considered. For the bosonic statistics, two inequivalent Bargmann
realizations are developed. The first (resp. second) realization induces, in a
natural way, coherent states recognized as Gazeau-Klauder (resp.
Klauder-Perelomov) ones. In the fermionic case, the Bargamnn realization leads
to the Klauder-Perelomov coherent states. For each considered realization, the
inner product of two analytic functions is defined in respect to a measure
explicitly computed. The Jacobson generators are realized as differential
operators. It is shown that the obtained coherent states minimize the
Robertson-Schr\"odinger uncertainty relation.Comment: 16 pages, published in JP
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