358 research outputs found
Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems
The long-time behavior of the survival probability for unstable multilevel
systems that follows the power-decay law is studied based on the N-level
Friedrichs model, and is shown to depend on the initial population in unstable
states. A special initial state maximizing the asymptote of the survival
probability at long times is found and examined by considering the spontaneous
emission process for the hydrogen atom interacting with the electromagnetic
field.Comment: 5 pages, 1 table. Accepted for publication in Phys. Rev.
Initial wave packets and the various power-law decreases of scattered wave packets at long times
The long time behavior of scattered wave packets from a
finite-range potential is investigated, by assuming to be
initially located outside the potential. It is then shown that can
asymptotically decrease in the various power laws at long time, according to
its initial characteristics at small momentum. As an application, we consider
the square-barrier potential system and demonstrate that exhibits
the asymptotic behavior , while another behavior like can
also appear for another .Comment: 5 pages, 1 figur
Electrostatics in a Schwarzschild black hole pierced by a cosmic string
We explicitly determine the expression of the electrostatic potential
generated by a point charge at rest in the Schwarzschild black hole pierced by
a cosmic string. We can then calculate the electrostatic self-energy. From
this, we find again the upper entropy bound for a charged object by employing
thermodynamics of the black hole.Comment: Latex, 8 pages, 1 figure in late
The Nystrom plus Correction Method for Solving Bound State Equations in Momentum Space
A new method is presented for solving the momentum-space Schrodinger equation
with a linear potential. The Lande-subtracted momentum space integral equation
can be transformed into a matrix equation by the Nystrom method. The method
produces only approximate eigenvalues in the cases of singular potentials such
as the linear potential. The eigenvalues generated by the Nystrom method can be
improved by calculating the numerical errors and adding the appropriate
corrections. The end results are more accurate eigenvalues than those generated
by the basis function method. The method is also shown to work for a
relativistic equation such as the Thompson equation.Comment: Revtex, 21 pages, 4 tables, to be published in Physical Review
Takagi-Taupin Description of X-ray Dynamical Diffraction from Diffractive Optics with Large Numerical Aperture
We present a formalism of x-ray dynamical diffraction from volume diffractive
optics with large numerical aperture and high aspect ratio, in an analogy to
the Takagi-Taupin equations for strained single crystals. We derive a set of
basic equations for dynamical diffraction from volume diffractive optics, which
enable us to study the focusing property of these optics with various grating
profiles. We study volume diffractive optics that satisfy the Bragg condition
to various degrees, namely flat, tilted and wedged geometries, and derive the
curved geometries required for ultimate focusing. We show that the curved
geometries satisfy the Bragg condition everywhere and phase requirement for
point focusing, and effectively focus hard x-rays to a scale close to the
wavelength.Comment: 18 pages, 12 figure
Chaotic Dynamics of N-degree of Freedom Hamiltonian Systems
We investigate the connection between local and global dynamics of two
N-degree of freedom Hamiltonian systems with different origins describing
one-dimensional nonlinear lattices: The Fermi-Pasta-Ulam (FPU) model and a
discretized version of the nonlinear Schrodinger equation related to
Bose-Einstein Condensation (BEC). We study solutions starting in the vicinity
of simple periodic orbits (SPOs) representing in-phase (IPM) and out-of-phase
motion (OPM), which are known in closed form and whose linear stability can be
analyzed exactly. Our results verify that as the energy E increases for fixed
N, beyond the destabilization threshold of these orbits, all positive Lyapunov
exponents exhibit a transition between two power laws, occurring at the same
value of E. The destabilization energy E_c per particle goes to zero as N goes
to infinity following a simple power-law. However, using SALI, a very efficient
indicator we have recently introduced for distinguishing order from chaos, we
find that the two Hamiltonians have very different dynamics near their stable
SPOs: For example, in the case of the FPU system, as the energy increases for
fixed N, the islands of stability around the OPM decrease in size, the orbit
destabilizes through period-doubling bifurcation and its eigenvalues move
steadily away from -1, while for the BEC model the OPM has islands around it
which grow in size before it bifurcates through symmetry breaking, while its
real eigenvalues return to +1 at very high energies. Still, when calculating
Lyapunov spectra, we find for the OPMs of both Hamiltonians that the Lyapunov
exponents decrease following an exponential law and yield extensive
Kolmogorov--Sinai entropies per particle, in the thermodynamic limit of fixed
energy density E/N with E and N arbitrarily large.Comment: 29 pages, 10 figures, published at International Journal of
Bifurcation and Chaos (IJBC
Alcohol use and breast cancer risk:A qualitative study of womenâs perspectives to inform the development of a preventative intervention in breast clinics
OBJECTIVE: This study aimed to explore women's views about breast cancer risk and alcohol use, to inform the design of a prototype for an intervention in breast clinics about alcohol as a modifiable risk factor for breast cancer.
METHODS: Women recruited in NHS breast screening and symptomatic clinics in Southampton, UK, were invited to take part in semiâstructured telephone interviews or a focus group to discuss their perspectives of breast cancer risk, alcohol consumption and their information needs about these topics. Data were analysed thematically. Twentyâeight women took part in telephone interviews, and 16 attended one of three focus groups.
RESULTS: While most women reported a personal responsibility for their health and were interested in advice about modifiable risk factors, few without (or prior to) experience of breast symptoms independently sought information. Many considered alcohol advice irrelevant as the association with breast cancer was largely unknown, and participants did not consider their drinking to be problematic. Women reported trusting information from health organisations like the NHS, but advice needs to be sensitive and nonâblaming.
CONCLUSION: NHS breast screening and symptomatic clinics offer a âteachable momentâ to engage women with contextâspecific advice about alcohol and cancer risk that, if targeted correctly, may assist them in making informed lifestyle choices
Electric force lines of the double Reissner-Nordstrom exact solution
Recently, Alekseev and Belinski have presented a new exact solution of the
Einstein-Maxwell equations which describes two Reissner-Nordstrom (RN) sources
in reciprocal equilibrium (no struts nor strings); one source is a naked
singularity, the other is a black hole: this is the only possible configuration
for separable object, apart from the well-known extreme case ().
In the present paper, after a brief summary of this solution, we study in
some detail the coordinate systems used and the main features of the
gravitational and electric fields. In particular we graph the plots of the
electric force lines in three qualitatively different situations: equal-signed
charges, opposite charges and the case of a naked singularity near a neutral
black hole.Comment: 19 pages, 7 figures, accepted by IJMP
Electrostatic boundary value problems in the Schwarzschild background
The electrostatic potential of any test charge distribution in Schwarzschild
space with boundary values is derived. We calculate the Green's function,
generalize the second Green's identity for p-forms and find the general
solution. Boundary value problems are solved. With a multipole expansion the
asymptotic property for the field of any charge distribution is derived. It is
shown that one produces a Reissner--Nordstrom black hole if one lowers a test
charge distribution slowly toward the horizon. The symmetry of the distribution
is not important. All the multipole moments fade away except the monopole. A
calculation of the gravitationally induced electrostatic self-force on a
pointlike test charge distribution held stationary outside the black hole is
presented.Comment: 18 pages, no figures, uses iopart.st
Applications of the Mellin-Barnes integral representation
We apply the Mellin-Barnes integral representation to several situations of
interest in mathematical-physics. At the purely mathematical level, we derive
useful asymptotic expansions of different zeta-functions and partition
functions. These results are then employed in different topics of quantum field
theory, which include the high-temperature expansion of the free energy of a
scalar field in ultrastatic curved spacetime, the asymptotics of the -brane
density of states, and an explicit approach to the asymptotics of the
determinants that appear in string theory.Comment: 20 pages, LaTe
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