151 research outputs found
Scattering and delay time for 1D asymmetric potentials: the step-linear and the step-exponential cases
We analyze the quantum-mechanical behavior of a system described by a
one-dimensional asymmetric potential constituted by a step plus (i) a linear
barrier or (ii) an exponential barrier. We solve the energy eigenvalue equation
by means of the integral representation method, classifying the independent
solutions as equivalence classes of homotopic paths in the complex plane.
We discuss the structure of the bound states as function of the height U_0 of
the step and we study the propagation of a sharp-peaked wave packet reflected
by the barrier. For both the linear and the exponential barrier we provide an
explicit formula for the delay time \tau(E) as a function of the peak energy E.
We display the resonant behavior of \tau(E) at energies close to U_0. By
analyzing the asymptotic behavior for large energies of the eigenfunctions of
the continuous spectrum we also show that, as expected, \tau(E) approaches the
classical value for E -> \infty, thus diverging for the step-linear case and
vanishing for the step-exponential one.Comment: 14 pages, 10 figure
Radiation Damping and Quantum Excitation for Longitudinal Charged Particle Dynamics in the Thermal Wave Model
On the basis of the recently proposed {\it Thermal Wave Model (TWM) for
particle beams}, we give a description of the longitudinal charge particle
dynamics in circular accelerating machines by taking into account both
radiation damping and quantum excitation (stochastic effect), in presence of a
RF potential well. The longitudinal dynamics is governed by a 1-D
Schr\"{o}dinger-like equation for a complex wave function whose squared modulus
gives the longitudinal bunch density profile. In this framework, the
appropriate {\it r.m.s. emittance} scaling law, due to the damping effect, is
naturally recovered, and the asymptotic equilibrium condition for the bunch
length, due to the competition between quantum excitation (QE) and radiation
damping (RD), is found. This result opens the possibility to apply the TWM,
already tested for protons, to electrons, for which QE and RD are very
important.Comment: 10 pages, plain LaTeX; published in Phys. Lett. A194 (1994) 113-11
Approximate entropy of respiratory patterns in panic disorder
OBJECTIVE: Considerable evidence suggests a connection between panic disorder and respiration, but the nature of the respiratory abnormalities in panic disorder remains unclear. The authors investigated the breath-by-breath complexity of respiration dynamics in panic disorder. METHOD: Respiratory physiology was assessed in 40 patients with panic disorder and 31 healthy comparison subjects by using a breath-by-breath stationary system for testing cardiorespiratory function. Irregularity in the breathing pattern was determined by applying the approximate entropy index, which is an indicator of the irregularity and the "disorder" of the measure.
RESULTS: The patients with panic disorder showed significantly higher approximate entropy indexes than the healthy subjects for the measured respiratory parameters. Sighs contributed to the irregularity of breathing patterns but did not account for all the differences in approximate entropy between the patients with panic disorder and the comparison subjects. Anxiety state, severity of illness, and somatic and individual variables such as participation in sports and cigarette smoking did not seem to influence the results.
CONCLUSIONS: Patients with panic disorder showed greater entropy in baseline respiratory patterns, indicating higher levels of irregularity and complexity in their respiratory function. Greater respiratory entropy could be a factor in vulnerability to panic attacks
Unitary relations in time-dependent harmonic oscillators
For a harmonic oscillator with time-dependent (positive) mass and frequency,
an unitary operator is shown to transform the quantum states of the system to
those of a harmonic oscillator system of unit mass and time-dependent
frequency, as well as operators. For a driven harmonic oscillator, it is also
shown that, there are unitary transformations which give the driven system from
the system of same mass and frequency without driving force. The transformation
for a driven oscillator depends on the solution of classical equation of motion
of the driven system. These transformations, thus, give a simple way of finding
exact wave functions of a driven harmonic oscillator system, provided the
quantum states of the corresponding system of unit mass are given.Comment: Submitted to J. Phys.
Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian
We show that the ground state of the well-known pseudo-stationary states for
the Caldirola-Kanai Hamiltonian is a generalized minimum uncertainty state,
which has the minimum allowed uncertainty , where is a constant depending on the damping
factor and natural frequency. The most general symmetric Gaussian states are
obtained as the one-parameter squeezed states of the pseudo-stationary ground
state. It is further shown that the coherent states of the pseudo-stationary
ground state constitute another class of the generalized minimum uncertainty
states.Comment: RevTex4, 9 pages, no fingure; to be published in Journal of Physics
Velocity quantization approach of the one-dimensional dissipative harmonic oscillator
Given a constant of motion for the one-dimensional harmonic oscillator with
linear dissipation in the velocity, the problem to get the Hamiltonian for this
system is pointed out, and the quantization up to second order in the
perturbation approach is used to determine the modification on the eigenvalues
when dissipation is taken into consideration. This quantization is realized
using the constant of motion instead of the Hamiltonian.Comment: 10 pages, 2 figure
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
Time quantization and q-deformations
We extend to quantum mechanics the technique of stochastic subordination, by
means of which one can express any semi-martingale as a time-changed Brownian
motion. As examples, we considered two versions of the q-deformed Harmonic
oscillator in both ordinary and imaginary time and show how these various cases
can be understood as different patterns of time quantization rules.Comment: 4 pages, 2 figure
Towards a quantum universe
In this short review we study the state of the art of the great problems in
cosmology and their interrelationships. The reconciliation of these problems
passes undoubtedly through the idea of a quantum universe.Comment: 7 pages, Accepted for publication in Astrophysics & Space Scienc
Stochastic thermodynamics of holonomic systems
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