25 research outputs found
The SUSY partners of the QES sextic potential revisited
In this paper, the SUSY partner Hamiltonians of the quasi-exactly solvable
(QES) sextic potential , , are revisited
from a Lie algebraic perspective. It is demonstrated that, in the variable , the underlying hidden algebra of
is inherited by its SUSY partner potential only for
. At fixed , the algebraic polynomial operator
that governs the exact eigenpolynomial solutions of
is derived explicitly. These odd-parity solutions appear in the form of
zero modes. The potential can be represented as the sum of a polynomial
and rational parts. In particular, it is shown that the polynomial component is
given by with a different non-integer (cohomology) parameter
. A confluent second-order SUSY transformation is also
implemented for a modified QES sextic potential possessing the energy
reflection symmetry. By taking as a continuous real constant and using the
Lagrange-mesh method, highly accurate values ( s. d.) of the energy
in the interval are calculated for the three lowest
states of the system. The critical value above which tunneling
effects (instanton-like terms) can occur is obtained as well. At , the
non-algebraic sector of the spectrum of is described by means of
compact physically relevant trial functions. These solutions allow us to
determine the effects in accuracy when the first-order SUSY approach is applied
on the level of approximate eigenfunctions.Comment: 25 pages, 20 figure
Supersymmetric partners of the trigonometric Poschl-Teller potentials
The first and second-order supersymmetry transformations are used to generate
Hamiltonians with known spectra departing from the trigonometric Poschl-Teller
potentials. The several possibilities of manipulating the initial spectrum are
fully explored, and it is shown how to modify one or two levels, or even to
leave the spectrum unaffected. The behavior of the new potentials at the
boundaries of the domain is studied.Comment: 20 pages, 4 figure
Robustness of spatial Penning trap modes against environment-assisted entanglement
The separability of the spatial modes of a charged particle in a Penning trap
in the presence of an environment is studied by means of the positive partial
transpose (PPT) criterion. Assuming a weak Markovian environment, described by
linear Lindblad operators, our results strongly suggest that the environmental
coupling of the axial and cyclotron degrees of freedom does not lead to
entanglement at experimentally realistic temperatures. We therefore argue that,
apart from unavoidable decoherence, the presence of such an environment does
not alter the effectiveness of recently suggested quantum information protocols
in Penning traps, which are based on the combination of a spatial mode with the
spin of the particle.Comment: 11 pages, 2 figure
Infinite square-well, trigonometric P\"oschl-Teller and other potential wells with a moving barrier
Using mainly two techniques, a point transformation and a time dependent
supersymmetry, we construct in sequence several quantum infinite potential
wells with a moving barrier. We depart from the well known system of a
one-dimensional particle in a box. With a point transformation, an infinite
square-well potential with a moving barrier is generated. Using time dependent
supersymmetry, the latter leads to a trigonometric P\"oschl-Teller potential
with a moving barrier. Finally, a confluent time dependent supersymmetry
transformation is implemented to generate new infinite potential wells, all of
them with a moving barrier. For all systems, solutions of the corresponding
time dependent Schr\"odinger equation fulfilling boundary conditions are
presented in a closed form
Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry
We develop a systematic approach to construct novel completely solvable
rational potentials. Second-order supersymmetric quantum mechanics dictates the
latter to be isospectral to some well-studied quantum systems.
symmetry may facilitate reconciling our approach to the requirement that the
rationally-extended potentials be singularity free. Some examples are shown.Comment: 13 pages, no figure, some additions to introduction and conclusion, 4
more references; to be published in Special issue of Pramana - J. Phy
Position Dependent Mass Oscillators and Coherent States
The solving of the Schrodinger equation for a position-dependent mass quantum
system is studied in two ways. First, it is found the interaction which must be
applied on a mass m(x) in order to supply it with a particular spectrum of
energies. Second, given a specific potential V(x) acting on the mass m(x), the
related spectrum is found. The method of solution is applied to a wide class of
position-dependent mass oscillators and the corresponding coherent states are
constructed. The analytical expressions of such position-dependent mass
coherent states preserve the functional structure of the Glauber states.Comment: 24 pages, 2 tables, 8 figure
Magnetic operations: a little fuzzy physics?
We examine the behaviour of charged particles in homogeneous, constant and/or
oscillating magnetic fields in the non-relativistic approximation. A special
role of the geometric center of the particle trajectory is elucidated. In
quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an
element of non-commutative geometry which enters into the traditional control
problems. We show that its application extends beyond the usually considered
time independent magnetic fields of the quantum Hall effect. Some simple cases
of magnetic control by oscillating fields lead to the stability maps differing
from the traditional Strutt diagram.Comment: 28 pages, 8 figure
Global overview of the management of acute cholecystitis during the COVID-19 pandemic (CHOLECOVID study)
Background: This study provides a global overview of the management of patients with acute cholecystitis during the initial phase of the COVID-19 pandemic. Methods: CHOLECOVID is an international, multicentre, observational comparative study of patients admitted to hospital with acute cholecystitis during the COVID-19 pandemic. Data on management were collected for a 2-month study interval coincident with the WHO declaration of the SARS-CoV-2 pandemic and compared with an equivalent pre-pandemic time interval. Mediation analysis examined the influence of SARS-COV-2 infection on 30-day mortality. Results: This study collected data on 9783 patients with acute cholecystitis admitted to 247 hospitals across the world. The pandemic was associated with reduced availability of surgical workforce and operating facilities globally, a significant shift to worse severity of disease, and increased use of conservative management. There was a reduction (both absolute and proportionate) in the number of patients undergoing cholecystectomy from 3095 patients (56.2 per cent) pre-pandemic to 1998 patients (46.2 per cent) during the pandemic but there was no difference in 30-day all-cause mortality after cholecystectomy comparing the pre-pandemic interval with the pandemic (13 patients (0.4 per cent) pre-pandemic to 13 patients (0.6 per cent) pandemic; P = 0.355). In mediation analysis, an admission with acute cholecystitis during the pandemic was associated with a non-significant increased risk of death (OR 1.29, 95 per cent c.i. 0.93 to 1.79, P = 0.121). Conclusion: CHOLECOVID provides a unique overview of the treatment of patients with cholecystitis across the globe during the first months of the SARS-CoV-2 pandemic. The study highlights the need for system resilience in retention of elective surgical activity. Cholecystectomy was associated with a low risk of mortality and deferral of treatment results in an increase in avoidable morbidity that represents the non-COVID cost of this pandemic