121 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
Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes
This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedIn quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand either from the viewpoint of the other. Here we show that all general time-dependent solutions of the free-particle Schrodinger equation can be mapped to solutions of the Schrodinger equation for harmonic potentials, both the trapping oscillator and the inverted `oscillator'. This map is fully invertible and therefore induces an isomorphism between both types of system, they are equivalent. A composition of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant and different center position. The map is independent of the state of the system, consisting only of a coordinate transformation and multiplication by a form factor, and can be chosen such that the state is identical in both systems at one point in time. This transition point in time can be chosen freely, the wave function of the particle evolving in time in one system before the transition point can therefore be linked up smoothly with the wave function for the other system and its future evolution after the transition point. Such a cut-and-paste procedure allows us to describe the instantaneous changes of the environment a particle finds itself in. Transitions from free to trapped systems, between harmonic traps of different spring constants or center positions, or, from harmonic binding to repulsive harmonic potentials are straightforwardly modelled. This includes some time dependent harmonic potentials. The mappings introduced here are computationally more efficient than either state-projection or harmonic oscillator propagator techniques conventionally employed when describing instantaneous (non-adiabatic) changes of a quantum particle's environmentPeer reviewe
Penrose Limits and RG Flows
The Penrose-Gueven limit simplifies a given supergravity solution into a
pp-wave background. Aiming at clarifying its relation to renormalization group
flow we study the Penrose-Guven limit of supergravity backgrounds that are dual
to non-conformal gauge theories. The resulting backgrounds fall in a class
simple enough that the quantum particle is exactly solvable. We propose a map
between the effective time-dependent quantum mechanical problem and the RG flow
in the gauge theory. As a testing ground we consider explicitly two Penrose
limits of the infrared fixed point of the Pilch-Warner solution. We analyze the
corresponding gauge theory picture and write down the operators which are the
duals of the low lying string states. We also address RG flows of a different
nature by considering the Penrose-Gueven limit of a stack of N D_p branes. We
note that in the far IR (for p<3)the limit generically has negative
mass-squared. This phenomenon signals, in the world sheet picture, the
necessity to transform to another description. In this regard, we consider
explicitly the cases of M2 from D2 and F1 from D1 .Comment: 35 pp, 6 figure
Fresh inflation and decoherence of super Hubble fluctuations
I study a stochastic approach to the recently introduced fresh inflation
model for super Hubble scales. I find that the state loses its coherence at the
end of the fresh inflationary period as a consequence of the damping of the
interference function in the reduced density matrix. This fact should be a
consequence of a) the relative evolutions of both the scale factor and the
horizon and b) the additional thermal and dissipative effects. This implies a
relevant difference with respect to supercooled inflationary scenarios which
require a very rapid expansion of the scale factor to give the decoherence of
super Hubble fluctuations.Comment: version with minor changes. To appear in Phys. Rev.
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
Production of Medical Radioisotopes with High Specific Activity in Photonuclear Reactions with Beams of High Intensity and Large Brilliance
We study the production of radioisotopes for nuclear medicine in
photonuclear reactions or ()
photoexcitation reactions with high flux [()/s], small
diameter m and small band width () beams produced by Compton back-scattering of laser
light from relativistic brilliant electron beams. We compare them to (ion,np) reactions with (ion=p,d,) from particle accelerators like
cyclotrons and (n,) or (n,f) reactions from nuclear reactors. For
photonuclear reactions with a narrow beam the energy deposition in the
target can be managed by using a stack of thin target foils or wires, hence
avoiding direct stopping of the Compton and pair electrons (positrons).
isomer production via specially selected cascades
allows to produce high specific activity in multiple excitations, where no
back-pumping of the isomer to the ground state occurs. We discuss in detail
many specific radioisotopes for diagnostics and therapy applications.
Photonuclear reactions with beams allow to produce certain
radioisotopes, e.g. Sc, Ti, Cu, Pd, Sn,
Er, Pt or Ac, with higher specific activity and/or
more economically than with classical methods. This will open the way for
completely new clinical applications of radioisotopes. For example Pt
could be used to verify the patient's response to chemotherapy with platinum
compounds before a complete treatment is performed. Also innovative isotopes
like Sc, Cu and Ac could be produced for the first time
in sufficient quantities for large-scale application in targeted radionuclide
therapy.Comment: submitted to Appl. Phys.
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
Energy-Momentum Tensor of Cosmological Fluctuations during Inflation
We study the renormalized energy-momentum tensor (EMT) of cosmological scalar
fluctuations during the slow-rollover regime for chaotic inflation with a
quadratic potential and find that it is characterized by a negative energy
density which grows during slow-rollover. We also approach the back-reaction
problem as a second-order calculation in perturbation theory finding no
evidence that the back-reaction of cosmological fluctuations is a gauge
artifact. In agreement with the results on the EMT, the average expansion rate
is decreased by the back-reaction of cosmological fluctuations.Comment: 19 pages, no figures.An appendix and references added, conclusions
unchanged, version accepted for publication in PR
A Grand Canonical Ensemble Approach to the Thermodynamic Properties of the Nucleon in the Quark-Gluon Coupling Model
In this paper, we put forward a way to study the nucleon's thermodynamic
properties such as its temperature, entropy and so on, without inputting any
free parameters by human hand, even the nucleon's mass and radius. First we use
the Lagrangian density of the quark gluon coupling fields to deduce the Dirac
Equation of the quarks confined in the gluon fields. By boundary conditions we
solve the wave functions and energy eigenvalues of the quarks, and thus get
energy-momentum tensor, nucleon mass, and density of states. Then we utilize a
hybrid grand canonical ensemble, to generate the temperature and chemical
potentials of quarks, antiquarks of three flovars by the four conservation laws
of the energy and the valence quark numbers, after which, all other
thermodynamic properties are known. The only seemed free paremeter, the nucleon
radius is finally determined by the grand potential minimal principle.Comment: 5 pages, LaTe
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