513 research outputs found
Smooth adiabatic evolutions with leaky power tails
Adiabatic evolutions with a gap condition have, under a range of
circumstances, exponentially small tails that describe the leaking out of the
spectral subspace. Adiabatic evolutions without a gap condition do not seem to
have this feature in general. This is a known fact for eigenvalue crossing. We
show that this is also the case for eigenvalues at the threshold of the
continuous spectrum by considering the Friedrichs model.Comment: Final form, to appear in J. Phys. A; 11 pages, no figure
A new joining-device for manufacturing tubular butt joints with higher curing temperatures of film adhesives
Airy processes and variational problems
We review the Airy processes; their formulation and how they are conjectured
to govern the large time, large distance spatial fluctuations of one
dimensional random growth models. We also describe formulas which express the
probabilities that they lie below a given curve as Fredholm determinants of
certain boundary value operators, and the several applications of these
formulas to variational problems involving Airy processes that arise in
physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI
Proceedings: Topics in percolative and disordered systems
The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class
We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang
equation with sharp wedge initial conditions. Thereby it is confirmed that the
continuum model belongs to the KPZ universality class, not only as regards to
scaling exponents but also as regards to the full probability distribution of
the height in the long time limit.Comment: Proceedings StatPhys 2
Isotope effects in underdoped cuprate superconductors: a quantum phenomenon
We show that the unusual doping dependence of the isotope effects on
transition temperature and zero temperature in - plane penetration depth
naturally follows from the doping driven 3D-2D crossover, the 2D quantum
superconductor to insulator transition (QSI) in the underdoped limit and the
change of the relative doping concentration upon isotope substitution. Close to
the QSI transition both, the isotope coefficient of transition temperature and
penetration depth approach the coefficient of the relative dopant
concentration, and its divergence sets the scale. These predictions are fully
consistent with the experimental data and imply that close to the underdoped
limit the unusual isotope effect on transition temperature and penetration
depth uncovers critical phenomena associated with the quantum superconductor to
insulator transition in two dimensions.Comment: 6 pages, 3 figure
Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals
High-order derivatives of analytic functions are expressible as Cauchy
integrals over circular contours, which can very effectively be approximated,
e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius
of convergence is equal, numerical stability strongly depends on r. We give a
comprehensive study of this effect; in particular we show that there is a
unique radius that minimizes the loss of accuracy caused by round-off errors.
For large classes of functions, though not for all, this radius actually gives
about full accuracy; a remarkable fact that we explain by the theory of Hardy
spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and
by the saddle-point method of asymptotic analysis. Many examples and
non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature
rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat
Endpoint distribution of directed polymers in 1+1 dimensions
We give an explicit formula for the joint density of the max and argmax of
the Airy process minus a parabola. The argmax has a universal distribution
which governs the rescaled endpoint for large time or temperature of directed
polymers in 1+1 dimensions.Comment: Expanded introductio
Fourier Acceleration of Langevin Molecular Dynamics
Fourier acceleration has been successfully applied to the simulation of
lattice field theories for more than a decade. In this paper, we extend the
method to the dynamics of discrete particles moving in continuum. Although our
method is based on a mapping of the particles' dynamics to a regular grid so
that discrete Fourier transforms may be taken, it should be emphasized that the
introduction of the grid is a purely algorithmic device and that no smoothing,
coarse-graining or mean-field approximations are made. The method thus can be
applied to the equations of motion of molecular dynamics (MD), or its Langevin
or Brownian variants. For example, in Langevin MD simulations our acceleration
technique permits a straightforward spectral decomposition of forces so that
the long-wavelength modes are integrated with a longer time step, thereby
reducing the time required to reach equilibrium or to decorrelate the system in
equilibrium. Speedup factors of up to 30 are observed relative to pure
(unaccelerated) Langevin MD. As with acceleration of critical lattice models,
even further gains relative to the unaccelerated method are expected for larger
systems. Preliminary results for Fourier-accelerated molecular dynamics are
presented in order to illustrate the basic concepts. Possible extensions of the
method and further lines of research are discussed.Comment: 11 pages, two illustrations included using graphic
Statistics and Nos\'e formalism for Ehrenfest dynamics
Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics
(i.e., Hamilton equations) can both be formulated in equal geometric terms: a
Poisson bracket defined on a manifold. In this paper we first show that the
hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can
also be formulated within this general framework, what has been used in the
literature to construct propagation schemes for Ehrenfest dynamics. Then, the
existence of a well defined Poisson bracket allows to arrive to a Liouville
equation for a statistical ensemble of Ehrenfest systems. The study of a
generic toy model shows that the evolution produced by Ehrenfest dynamics is
ergodic and therefore the only constants of motion are functions of the
Hamiltonian. The emergence of the canonical ensemble characterized by the
Boltzmann distribution follows after an appropriate application of the
principle of equal a priori probabilities to this case. Once we know the
canonical distribution of a Ehrenfest system, it is straightforward to extend
the formalism of Nos\'e (invented to do constant temperature Molecular Dynamics
by a non-stochastic method) to our Ehrenfest formalism. This work also provides
the basis for extending stochastic methods to Ehrenfest dynamics.Comment: 28 pages, 1 figure. Published version. arXiv admin note: substantial
text overlap with arXiv:1010.149
Eliashberg-type equations for correlated superconductors
The derivation of the Eliashberg -- type equations for a superconductor with
strong correlations and electron--phonon interaction has been presented. The
proper account of short range Coulomb interactions results in a strongly
anisotropic equations. Possible symmetries of the order parameter include s, p
and d wave. We found the carrier concentration dependence of the coupling
constants corresponding to these symmetries. At low hole doping the d-wave
component is the largest one.Comment: RevTeX, 18 pages, 5 ps figures added at the end of source file, to be
published in Phys.Rev. B, contact: [email protected]
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