189 research outputs found
Exact quantum states of a general time-dependent quadratic system from classical action
A generalization of driven harmonic oscillator with time-dependent mass and
frequency, by adding total time-derivative terms to the Lagrangian, is
considered. The generalization which gives a general quadratic Hamiltonian
system does not change the classical equation of motion. Based on the
observation by Feynman and Hibbs, the propagators (kernels) of the systems are
calculated from the classical action, in terms of solutions of the classical
equation of motion: two homogeneous and one particular solutions. The kernels
are then used to find wave functions which satisfy the Schr\"{o}dinger
equation. One of the wave functions is shown to be that of a Gaussian pure
state. In every case considered, we prove that the kernel does not depend on
the way of choosing the classical solutions, while the wave functions depend on
the choice. The generalization which gives a rather complicated quadratic
Hamiltonian is simply interpreted as acting an unitary transformation to the
driven harmonic oscillator system in the Hamiltonian formulation.Comment: Submitted to Phys. Rev.
Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential
The unitary operator which transforms a harmonic oscillator system of
time-dependent frequency into that of a simple harmonic oscillator of different
time-scale is found, with and without an inverse-square potential. It is shown
that for both cases, this operator can be used in finding complete sets of wave
functions of a generalized harmonic oscillator system from the well-known sets
of the simple harmonic oscillator. Exact invariants of the time-dependent
systems can also be obtained from the constant Hamiltonians of unit mass and
frequency by making use of this unitary transformation. The geometric phases
for the wave functions of a generalized harmonic oscillator with an
inverse-square potential are given.Comment: Phys. Rev. A (Brief Report), in pres
Classes of exact wavefunctions for general time-dependent Dirac Hamiltonians in 1+1 dimensions
In this work we construct two classes of exact solutions for the most general
time-dependent Dirac Hamiltonian in 1+1 dimensions. Some problems regarding to
some formal solutions in the literature are discussed. Finally the existence of
a generalized Lewis-Riesenfeld invariant connected with such solutions is
discussed
Novel approach to the study of quantum effects in the early universe
We develop a theoretical frame for the study of classical and quantum
gravitational waves based on the properties of a nonlinear ordinary
differential equation for a function of the conformal time
, called the auxiliary field equation. At the classical level,
can be expressed by means of two independent solutions of the
''master equation'' to which the perturbed Einstein equations for the
gravitational waves can be reduced. At the quantum level, all the significant
physical quantities can be formulated using Bogolubov transformations and the
operator quadratic Hamiltonian corresponding to the classical version of a
damped parametrically excited oscillator where the varying mass is replaced by
the square cosmological scale factor . A quantum approach to the
generation of gravitational waves is proposed on the grounds of the previous
dependent Hamiltonian. An estimate in terms of and
of the destruction of quantum coherence due to the gravitational
evolution and an exact expression for the phase of a gravitational wave
corresponding to any value of are also obtained. We conclude by
discussing a few applications to quasi-de Sitter and standard de Sitter
scenarios.Comment: 20 pages, to appear on PRD. Already published background material has
been either settled up in a more compact form or eliminate
Particle production and classical condensates in de Sitter space
The cosmological particle production in a expanding de Sitter universe
with a Hubble parameter is considered for various values of mass or
conformal coupling of a free, scalar field. One finds that, for a minimally
coupled field with mass (except for ),
the one-mode occupation number grows to unity soon after the physical
wavelength of the mode becomes larger than the Hubble radius, and afterwards
diverges as , where . However, for a field with ,
the occupation number of a mode outside the Hubble radius is rapidly
oscillating and bounded and does not exceed unity. These results, readily
generalized for cases of a nonminimal coupling, provide a clear argument that
the long-wavelength vacuum fluctuations of low-mass fields in an inflationary
universe do show classical behavior, while those of heavy fields do not. The
interaction or self-interaction does not appear necessary for the emergence of
classical features, which are entirely due to the rapid expansion of the de
Sitter background and the upside-down nature of quantum oscillators for modes
outside the Hubble radius.Comment: Revtex + 5 postscript figures. Accepted for Phys Rev D15. Revision of
Aug 1996 preprint limited to the inclusion and discussion of references
suggested by the referee
Canonical quantization of so-called non-Lagrangian systems
We present an approach to the canonical quantization of systems with
equations of motion that are historically called non-Lagrangian equations. Our
viewpoint of this problem is the following: despite the fact that a set of
differential equations cannot be directly identified with a set of
Euler-Lagrange equations, one can reformulate such a set in an equivalent
first-order form which can always be treated as the Euler-Lagrange equations of
a certain action. We construct such an action explicitly. It turns out that in
the general case the hamiltonization and canonical quantization of such an
action are non-trivial problems, since the theory involves time-dependent
constraints. We adopt the general approach of hamiltonization and canonical
quantization for such theories (Gitman, Tyutin, 1990) to the case under
consideration. There exists an ambiguity (not reduced to a total time
derivative) in associating a Lagrange function with a given set of equations.
We present a complete description of this ambiguity. The proposed scheme is
applied to the quantization of a general quadratic theory. In addition, we
consider the quantization of a damped oscillator and of a radiating point-like
charge.Comment: 13 page
A geometric approach to time evolution operators of Lie quantum systems
Lie systems in Quantum Mechanics are studied from a geometric point of view.
In particular, we develop methods to obtain time evolution operators of
time-dependent Schrodinger equations of Lie type and we show how these methods
explain certain ad hoc methods used in previous papers in order to obtain exact
solutions. Finally, several instances of time-dependent quadratic Hamiltonian
are solved.Comment: Accepted for publication in the International Journal of Theoretical
Physic
Technical recommendations for clinical translation of renal MRI: a consensus project of the Cooperation in Science and Technology Action PARENCHIMA
Purpose The potential of renal MRI biomarkers has been increasingly recognised, but clinical translation requires more
standardisation. The PARENCHIMA consensus project aims to develop and apply a process for generating technical recommendations on renal MRI.
Methods A task force was formed in July 2018 focused on fve methods. A draft process for attaining consensus was distributed publicly for consultation and fnalised at an open meeting (Prague, October 2018). Four expert panels completed
surveys between October 2018 and March 2019, discussed results and refned the surveys at a face-to-face meeting (Aarhus,
March 2019) and completed a second round (May 2019).
Results A seven-stage process was defned: (1) formation of expert panels; (2) defnition of the context of use; (3) literature
review; (4) collection and comparison of MRI protocols; (5) consensus generation by an approximate Delphi method; (6)
reporting of results in vendor-neutral and vendor-specifc terms; (7) ongoing review and updating. Application of the process
resulted in 166 consensus statements.
Conclusion The process generated meaningful technical recommendations across very diferent MRI methods, while allowing for improvement and refnement as open issues are resolved. The results are likely to be widely supported by the renal
MRI community and thereby promote more harmonisation
Search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS
We present the results of a search for new, heavy particles that decay at a
significant distance from their production point into a final state containing
charged hadrons in association with a high-momentum muon. The search is
conducted in a pp-collision data sample with a center-of-mass energy of 7 TeV
and an integrated luminosity of 33 pb^-1 collected in 2010 by the ATLAS
detector operating at the Large Hadron Collider. Production of such particles
is expected in various scenarios of physics beyond the standard model. We
observe no signal and place limits on the production cross-section of
supersymmetric particles in an R-parity-violating scenario as a function of the
neutralino lifetime. Limits are presented for different squark and neutralino
masses, enabling extension of the limits to a variety of other models.Comment: 8 pages plus author list (20 pages total), 8 figures, 1 table, final
version to appear in Physics Letters
- …