800,571 research outputs found
Right eigenvalue equation in quaternionic quantum mechanics
We study the right eigenvalue equation for quaternionic and complex linear
matrix operators defined in n-dimensional quaternionic vector spaces. For
quaternionic linear operators the eigenvalue spectrum consists of n complex
values. For these operators we give a necessary and sufficient condition for
the diagonalization of their quaternionic matrix representations. Our
discussion is also extended to complex linear operators, whose spectrum is
characterized by 2n complex eigenvalues. We show that a consistent analysis of
the eigenvalue problem for complex linear operators requires the choice of a
complex geometry in defining inner products. Finally, we introduce some
examples of the left eigenvalue equations and highlight the main difficulties
in their solution.Comment: 24 pages, AMS-Te
Dymanics of Generalized Coherent States
We show that generalized coherent states follow Schr\"{o}dinger dynamics in
time-dependent potentials. The normalized wave-packets follow a classical
evolution without spreading; in turn, the Schr\"{o}dinger potential depends on
the state through the classical trajectory. This feedback mechanism with
continuous dynamical re-adjustement allows the packets to remain coherent
indefinetely.Comment: 8 pages, plain latex, no figure
Magnetisation reversal mechanism in Co-Cr media for perpendicular magnetic recording
In this study Co---Cr thin films with perpendicular anisotropy are investigated. Three films with values for Hc of 11, 90 and 170 kA/m have been selected for this paper. Besides the coercivily several other parameters such as the Hc/Hk, Cr-segregation, domain structure, column sizes, etc. were studied by VSM, SEM, NMR, MFM, AFM and selective etching. The anomalous Hall effect (AHE) has been used to record the hysteresis curves of submicron Hall crosses. This very sensitive technique in combination with e-beam lithography and ion-beam etching resulted in the recording of AHE hysteresis loops with dimensions of the Hall crosses as small as 0.3 Ă— 0.3 Âżm2. The AHE loops of three samples, with less than 60 columns, show different micromagnetic properties. Only the sample with Hc1 = 90 kA/m shows clear steps in the curves above the noise level. The largest steps correspond with the reversal of one column and the total number of steps was five times the number of columns for this sample. The different reversal mechanisms observed by the AHE are related to the differences in structure, coercivity and domain size
Theory of controlled quantum dynamics
We introduce a general formalism, based on the stochastic formulation of
quantum mechanics, to obtain localized quasi-classical wave packets as
dynamically controlled systems, for arbitrary anharmonic potentials. The
control is in general linear, and it amounts to introduce additional quadratic
and linear time-dependent terms to the given potential. In this way one can
construct for general systems either coherent packets moving with constant
dispersion, or dynamically squeezed packets whose spreading remains bounded for
all times. In the standard operatorial framework our scheme corresponds to a
suitable generalization of the displacement and scaling operators that generate
the coherent and squeezed states of the harmonic oscillator.Comment: LaTeX, A4wide, 28 pages, no figures. To appear in J. Phys. A: Math.
Gen., April 199
Diffusion Processes and Coherent States
It is shown that stochastic processes of diffusion type possess, in all
generality, a structure of uncertainty relations and of coherent and squeezed
states. This fact is used to obtain, via Nelson stochastic formulation of
quantum mechanics, the harmonic-oscillator coherent and squeezed states. The
method allows to derive new minimum uncertainty states in time-dependent
oscillator potentials and for the Caldirola-Kanai model of quantum damped
oscillator.Comment: 11 pages, plain LaTe
Aproximative solutions to the neutrino oscillation problem in matter
We present approximative solutions to the neutrino evolution equation
calculated by different methods. In a two neutrino framework, using the
physical parameters which gives the main effects to neutrino oscillations from
nu{e} to another flavors for L=3000Km and E=1GeV, the results for the
transition probability calculated by using series solutions, by to take the
neutrino evolution operator as a product of ordered partial operators and by
numerical methods, for a linearly and sinusoidally varying matter density are
compared. The extension to an arbitrary density profile is discussed and the
evolution operator as a product of partial operators in the three neutrino case
is obtained.Comment: 12 pages, 5 figure
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