Coherent states for polynomial su(1,1) algebra and a conditionally solvable system

In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105], we constructed a class of coherent states for a polynomially deformed $su(2)$ algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed $su(1,1)$ algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1,1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1,1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.Comment: 2 figure

Klein tunneling in carbon nanostructures: a free particle dynamics in disguise

The absence of backscattering in metallic nanotubes as well as perfect Klein tunneling in potential barriers in graphene are the prominent electronic characteristics of carbon nanostructures. We show that the phenomena can be explained by a peculiar supersymmetry generated by a first order Hamiltonian and zero order supercharge operators. Like the supersymmetry associated with second order reflectionless finite-gap systems, it relates here the low-energy behavior of the charge carriers with the free particle dynamics.Comment: 4 pages, 1 fig., typos correcte

Supersymmetry of a Nonstationary Pauli Equation

The supersymmetry of the electron in both the nonstationary magnetic and electric fields in a two-dimensional case is studied. The supercharges which are the integrals of motion and their algebra are established. Using the obtained algebra the solutions of nonstationary Pauli equation are generated.Comment: 12 pages, Late

Supersymmetry of the Nonstationary Schr\"odinger equation and Time-Dependent Exactly Solvable Quantum Models

New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.Comment: Talk at the 8th International Conference "Symmetry Methods in Physics". Dubna, Russia, 28 July - 2 August, 199

How should we treat chronic daily headache when conservative measures fail?

For the purposes of this review, we considered conservative measures to include such therapies as nonsteroidal anti-inflammatory drugs (NSAIDs), physical therapy, and acetaminophen with codeine. Amitriptyline is the best-supported option for the treatment of chronic daily headaches for those patients who have not been treated by conservative measures (strength of recommendation [SOR]: A, based on a metaanalysis of randomized controlled trials [RCTs]). For patients who overuse symptomatic headache medications, medication withdrawal is effective (SOR: B, based on a systematic review of cohort and case-control studies). Additional therapies include other tricyclic antidepressants (TCAs), selective serotonin reuptake inhibitors (SSRIs), and prophylactic treatments for migraine (SOR: B)

Supersymmetry solution for finitely extensible dumbbell model

Exact relaxation times and eigenfunctions for a simple mechanical model of polymer dynamics are obtained using supersymmetry methods of quantum mechanics. The model includes the finite extensibility of the molecule and does not make use of the self-consistently averaging approximation. The finite extensibility reduces the relaxation times when compared to a linear force. The linear viscoelastic behaviour is obtained in the form of the ``generalized Maxwell model''. Using these results, a numerical integration scheme is proposed in the presence of a given flow kinematics.Comment: 5 pages, 2 figure

Supersymmetric Method for Constructing Quasi-Exactly and Conditionally-Exactly Solvable Potentials

Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES). The considered QES potentials at certain values of parameters become exactly solvable and can be treated as CES ones.Comment: 17 pages, latex, no figure

Deformed Clifford algebra and supersymmetric quantum mechanics on a phase space with applications in quantum optics

In order to realize supersymmetric quantum mechanics methods on a four dimensional classical phase-space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star-product in composing the components of Clifford forms. Two isospectral matrix Hamiltonians having a common bosonic part but different fermionic parts depending on four real-valued phase space functions are obtained. The Hamiltonians are doubly intertwined via matrix-valued functions which are divisors of zero in the resulting Moyal-Clifford algebra. Two illustrative examples corresponding to Jaynes-Cummings-type models of quantum optics are presented as special cases of the method. Their spectra, eigen-spinors and Wigner functions as well as their constants of motion are also obtained within the autonomous framework of deformation quantization.Comment: 22 pages. published versio

Constraints on the Formation of PSR J0737-3039: the most probable isotropic kick magnitude

A strongly relativistic binary pulsar has been recently discovered with the 64m Parkes telescope (Burgay et al. 2003). Here we use the measured properties of this binary (masses and orbital characteristics as well as age estimates), and we derive the complete set of constraints imposed on the physical properties of the binary pulsar progenitor right before the second supernova explosion. We find that: (i) according to our current understanding of neutron-star formation, the helium-rich progenitor of the second neutron star is most likely overflowing its Roche lobe; (ii) the neutron-star kick magnitude is constrained in the range 60-1560 km/s, with the most probable value being equal to 150 km/s. While the first conclusion is in agreement with Dewi & van den Heuvel (2003), our upper limit on the kick magnitude is significantly larger than that derived by these authors. We find that the difference arises because Dewi & van den Heuvel (2003) inadvertently neglected to consider kicks directed out of the pre-supernova orbital plane.Comment: accepted by ApJ Letters, revised version taking into account the referee's comment

Motion of a spin 1/2 particle in shape invariant scalar and magnetic fields

We study the motion of a spin 1/2 particle in a scalar as well as a magnetic field within the framework of supersymmetric quantum mechanics(SUSYQM). We also introduce the concept of shape invariant scalar and magnetic fields and it is shown that the problem admits exact analytical solutions when such fields are considered.Comment: 14 page