6,803 research outputs found
Chaotic systems in complex phase space
This paper examines numerically the complex classical trajectories of the
kicked rotor and the double pendulum. Both of these systems exhibit a
transition to chaos, and this feature is studied in complex phase space.
Additionally, it is shown that the short-time and long-time behaviors of these
two PT-symmetric dynamical models in complex phase space exhibit strong
qualitative similarities.Comment: 22 page, 16 figure
Spectral zeta functions of a 1D Schr\"odinger problem
We study the spectral zeta functions associated to the radial Schr\"odinger
problem with potential V(x)=x^{2M}+alpha x^{M-1}+(lambda^2-1/4)/x^2. Using the
quantum Wronskian equation, we provide results such as closed-form evaluations
for some of the second zeta functions i.e. the sum over the inverse eigenvalues
squared. Also we discuss how our results can be used to derive relationships
and identities involving special functions, using a particular 5F_4
hypergeometric series as an example. Our work is then extended to a class of
related PT-symmetric eigenvalue problems. Using the fused quantum Wronskian we
give a simple method for calculating the related spectral zeta functions. This
method has a number of applications including the use of the ODE/IM
correspondence to compute the (vacuum) nonlocal integrals of motion G_n which
appear in an associated integrable quantum field theory.Comment: 15 pages, version
Universality in Random Walk Models with Birth and Death
Models of random walks are considered in which walkers are born at one
location and die at all other locations with uniform death rate. Steady-state
distributions of random walkers exhibit dimensionally dependent critical
behavior as a function of the birth rate. Exact analytical results for a
hyperspherical lattice yield a second-order phase transition with a nontrivial
critical exponent for all positive dimensions . Numerical studies
of hypercubic and fractal lattices indicate that these exact results are
universal. Implications for the adsorption transition of polymers at curved
interfaces are discussed.Comment: 11 pages, revtex, 2 postscript figure
New Quasi-Exactly Solvable Sextic Polynomial Potentials
A Hamiltonian is said to be quasi-exactly solvable (QES) if some of the
energy levels and the corresponding eigenfunctions can be calculated exactly
and in closed form. An entirely new class of QES Hamiltonians having sextic
polynomial potentials is constructed. These new Hamiltonians are different from
the sextic QES Hamiltonians in the literature because their eigenfunctions obey
PT-symmetric rather than Hermitian boundary conditions. These new Hamiltonians
present a novel problem that is not encountered when the Hamiltonian is
Hermitian: It is necessary to distinguish between the parametric region of
unbroken PT symmetry, in which all of the eigenvalues are real, and the region
of broken PT symmetry, in which some of the eigenvalues are complex. The
precise location of the boundary between these two regions is determined
numerically using extrapolation techniques and analytically using WKB analysis
The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
Particle production due to external fields (electric, chromo-electric or
gravitational) requires evolving an initial state through an interaction with a
time-dependent background, with the rate being computed from a Bogoliubov
transformation between the in and out vacua. When the background fields have
temporal profiles with sub-structure, a semiclassical analysis of this problem
confronts the full subtlety of the Stokes phenomenon: WKB solutions are only
local, while the production rate requires global information. Incorporating the
Stokes phenomenon, we give a simple quantitative explanation of the recently
computed [Phys. Rev. Lett. 102, 150404 (2009)] oscillatory momentum spectrum of
e+e- pairs produced from vacuum subjected to a time-dependent electric field
with sub-cycle laser pulse structure. This approach also explains naturally why
for spinor and scalar QED these oscillations are out of phase.Comment: 5 pages, 4 figs.; v2 sign typo corrected, version to appear in PR
Polymer-Chain Adsorption Transition at a Cylindrical Boundary
In a recent letter, a simple method was proposed to generate solvable models
that predict the critical properties of statistical systems in hyperspherical
geometries. To that end, it was shown how to reduce a random walk in
dimensions to an anisotropic one-dimensional random walk on concentric
hyperspheres. Here, I construct such a random walk to model the
adsorption-desorption transition of polymer chains growing near an attractive
cylindrical boundary such as that of a cell membrane. I find that the fraction
of adsorbed monomers on the boundary vanishes exponentially when the adsorption
energy decreases towards its critical value. When the adsorption energy rises
beyond a certain value above the critical point whose scale is set by the
radius of the cell, the adsorption fraction exhibits a crossover to a linear
increase characteristic to polymers growing near planar boundaries.Comment: latex, 12 pages, 3 ps-figures, uuencode
Asymptotics of Expansion of the Evolution Operator Kernel in Powers of Time Interval
The upper bound for asymptotic behavior of the coefficients of expansion of
the evolution operator kernel in powers of the time interval \Dt was
obtained. It is found that for the nonpolynomial potentials the coefficients
may increase as . But increasing may be more slow if the contributions with
opposite signs cancel each other. Particularly, it is not excluded that for
number of the potentials the expansion is convergent. For the polynomial
potentials \Dt-expansion is certainly asymptotic one. The coefficients
increase in this case as , where is the order of
the polynom. It means that the point \Dt=0 is singular point of the kernel.Comment: 12 pp., LaTe
Minimizing Flow Time in the Wireless Gathering Problem
We address the problem of efficient data gathering in a wireless network
through multi-hop communication. We focus on the objective of minimizing the
maximum flow time of a data packet. We prove that no polynomial time algorithm
for this problem can have approximation ratio less than \Omega(m^{1/3) when
packets have to be transmitted, unless . We then use resource
augmentation to assess the performance of a FIFO-like strategy. We prove that
this strategy is 5-speed optimal, i.e., its cost remains within the optimal
cost if we allow the algorithm to transmit data at a speed 5 times higher than
that of the optimal solution we compare to
Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. III: Role of particle-number projection
Starting from HFB-6, we have constructed a new mass table, referred to as
HFB-8, including all the 9200 nuclei lying between the two drip lines over the
range of Z and N > 6 and Z < 122. It differs from HFB-6 in that the wave
function is projected on the exact particle number. Like HFB-6, the isoscalar
effective mass is constrained to the value 0.80 M and the pairing is density
independent. The rms errors of the mass-data fit is 0.635 MeV, i.e. better than
almost all our previous HFB mass formulas. The extrapolations of this new mass
formula out to the drip lines do not differ significantly from the previous
HFB-6 mass formula.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.
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