185 research outputs found
Unification of the conditional probability and semiclassical interpretations for the problem of time in quantum theory
We show that the time-dependent Schr\"odinger equation (TDSE) is the
phenomenological dynamical law of evolution unraveled in the classical limit
from a timeless formulation in terms of probability amplitudes conditioned by
the values of suitably chosen internal clock variables, thereby unifying the
conditional probability interpretation (CPI) and the semiclassical approach for
the problem of time in quantum theory. Our formalism stems from an exact
factorization of the Hamiltonian eigenfunction of the clock plus system
composite, where the clock and system factors play the role of marginal and
conditional probability amplitudes, respectively. Application of the Variation
Principle leads to a pair of exact coupled pseudoeigenvalue equations for these
amplitudes, whose solution requires an iterative self-consistent procedure. The
equation for the conditional amplitude constitutes an effective "equation of
motion" for the quantum state of the system with respect to the clock
variables. These coupled equations also provide a convenient framework for
treating the back-reaction of the system on the clock at various levels of
approximation. At the lowest level, when the WKB approximation for the marginal
amplitude is appropriate, in the classical limit of the clock variables the
TDSE for the system emerges as a matter of course from the conditional
equation. In this connection, we provide a discussion of the characteristics
required by physical systems to serve as good clocks. This development is seen
to be advantageous over the original CPI and semiclassical approach since it
maintains the essence of the conventional formalism of quantum mechanics,
admits a transparent interpretation, avoids the use of the Born-Oppenheimer
approximation, and resolves various objections raised about them.Comment: 10 pages. Typographical errors correcte
Diffusive Ionization of Relativistic Hydrogen-Like Atom
Stochastic ionization of highly excited relativistic hydrogenlike atom in the
monochromatic field is investigated. A theoretical analisis of chaotic dynamics
of the relativistic electron based on Chirikov criterion is given for the cases
of one- and three-dimensional atoms. Critical value of the external field is
evaluated analitically. The diffusion coefficient and ionization time are
calculated.Comment: 13 pages, latex, no figures, submitted to PR
Stochastic ionization through noble tori: Renormalization results
We find that chaos in the stochastic ionization problem develops through the
break-up of a sequence of noble tori. In addition to being very accurate, our
method of choice, the renormalization map, is ideally suited for analyzing
properties at criticality. Our computations of chaos thresholds agree closely
with the widely used empirical Chirikov criterion
The Fermi accelerator in atom optics
We study the classical and quantum dynamics of a Fermi accelerator realized
by an atom bouncing off a modulated atomic mirror. We find that in a window of
the modulation amplitude dynamical localization occurs in both position and
momentum. A recent experiment [A. Steane, P. Szriftgiser, P. Desbiolles, and J.
Dalibard, Phys. Rev. Lett. {\bf 74}, 4972 (1995)] shows that this system can be
implemented experimentally.Comment: 5 pages, 5 figure
Adiabatic description of nonspherical quantum dot models
Within the effective mass approximation an adiabatic description of
spheroidal and dumbbell quantum dot models in the regime of strong dimensional
quantization is presented using the expansion of the wave function in
appropriate sets of single-parameter basis functions. The comparison is given
and the peculiarities are considered for spectral and optical characteristics
of the models with axially symmetric confining potentials depending on their
geometric size making use of the total sets of exact and adiabatic quantum
numbers in appropriate analytic approximations
Insights into a viral motor : the structure of the HK97 packaging termination assembly
Double-stranded DNA viruses utilise machinery, made of terminase proteins, to package viral DNA into the capsid. For cos bacteriophage, a defined signal, recognised by small terminase, flanks each genome unit. Here we present the first structural data for a cos virus DNA packaging motor, assembled from the bacteriophage HK97 terminase proteins, procapsids encompassing the portal protein, and DNA containing a cos site. The cryo-EM structure is consistent with the packaging termination state adopted after DNA cleavage, with DNA density within the large terminase assembly ending abruptly at the portal protein entrance. Retention of the large terminase complex after cleavage of the short DNA substrate suggests that motor dissociation from the capsid requires headful pressure, in common with pac viruses. Interestingly, the clip domain of the 12-subunit portal protein does not adhere to C12 symmetry, indicating asymmetry induced by binding of the large terminase/DNA. The motor assembly is also highly asymmetric, showing a ring of 5 large terminase monomers, tilted against the portal. Variable degrees of extension between N- and C-terminal domains of individual subunits suggest a mechanism of DNA translocation driven by inter-domain contraction and relaxation
Experimental study of the quantum driven pendulum and its classical analogue in atoms optics
We present experimental results for the dynamics of cold atoms in a far detuned amplitude-modulated optical standing wave. Phase-space resonances constitute distinct peaks in the atomic momentum distribution containing up to 65% of all atoms resulting from a mixed quantum chaotic phase space. We characterize the atomic behavior in classical and quantum regimes and we present the applicable quantum and classical theory, which we have developed and refined. We show experimental proof that the size and the position of the resonances in phase space can be controlled by varying several parameters, such as the modulation frequency, the scaled well depth, the modulation amplitude, and the scaled Planck's constant of the system. We have found a surprising stability against amplitude noise. We present methods to accurately control the momentum of an ensemble of atoms using these phase-space resonances which could be used for efficient phase-space state preparation
Quantum chaos in the atomic gravitational cavity
We report quantum chaos phenomena in the atomic gravitational cavity. We consider the reflection of cold atoms from a temporally modulated evanescent wave. In the globally chaotic regime, for small modulation, the squared energy distribution as a function of time demonstrates dynamical localization. However, for larger modulation delocalization occurs
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