3,996 research outputs found
The generalization of the Regge-Wheeler equation for self-gravitating matter fields
It is shown that the dynamical evolution of perturbations on a static
spacetime is governed by a standard pulsation equation for the extrinsic
curvature tensor. The centerpiece of the pulsation equation is a wave operator
whose spatial part is manifestly self-adjoint. In contrast to metric
formulations, the curvature-based approach to gravitational perturbation theory
generalizes in a natural way to self-gravitating matter fields. For a certain
relevant subspace of perturbations the pulsation operator is symmetric with
respect to a positive inner product and therefore allows spectral theory to be
applied. In particular, this is the case for odd-parity perturbations of
spherically symmetric background configurations. As an example, the pulsation
equations for self-gravitating, non-Abelian gauge fields are explicitly shown
to be symmetric in the gravitational, the Yang Mills, and the off-diagonal
sector.Comment: 4 pages, revtex, no figure
On the exciton binding energy in a quantum well
We consider a model describing the one-dimensional confinement of an exciton
in a symmetrical, rectangular quantum-well structure and derive upper and lower
bounds for the binding energy of the exciton. Based on these bounds, we
study the dependence of on the width of the confining potential with a
higher accuracy than previous reports. For an infinitely deep potential the
binding energy varies as expected from at large widths to at
small widths. For a finite potential, but without consideration of a mass
mismatch or a dielectric mismatch, we substantiate earlier results that the
binding energy approaches the value for both small and large widths,
having a characteristic peak for some intermediate size of the slab. Taking the
mismatch into account, this result will in general no longer be true. For the
specific case of a quantum-well
structure, however, and in contrast to previous findings, the peak structure is
shown to survive.Comment: 32 pages, ReVTeX, including 9 figure
Analyticity of The Ground State Energy For Massless Nelson Models
We show that the ground state energy of the translationally invariant Nelson
model, describing a particle coupled to a relativistic field of massless
bosons, is an analytic function of the coupling constant and the total
momentum. We derive an explicit expression for the ground state energy which is
used to determine the effective mass.Comment: 33 pages, 1 figure, added a section on the calculation of the
effective mas
Quantum Geometrodynamics I: Quantum-Driven Many-Fingered Time
The classical theory of gravity predicts its own demise -- singularities. We
therefore attempt to quantize gravitation, and present here a new approach to
the quantization of gravity wherein the concept of time is derived by imposing
the constraints as expectation-value equations over the true dynamical degrees
of freedom of the gravitational field -- a representation of the underlying
anisotropy of space. This self-consistent approach leads to qualitatively
different predictions than the Dirac and the ADM quantizations, and in
addition, our theory avoids the interpretational conundrums associated with the
problem of time in quantum gravity. We briefly describe the structure of our
functional equations, and apply our quantization technique to two examples so
as to illustrate the basic ideas of our approach.Comment: 11, (No Figures), (Typeset using RevTeX
Square Root Actions, Metric Signature, and the Path-Integral of Quantum Gravity
We consider quantization of the Baierlein-Sharp-Wheeler form of the
gravitational action, in which the lapse function is determined from the
Hamiltonian constraint. This action has a square root form, analogous to the
actions of the relativistic particle and Nambu string. We argue that
path-integral quantization of the gravitational action should be based on a
path integrand rather than the familiar Feynman expression
, and that unitarity requires integration over manifolds of both
Euclidean and Lorentzian signature. We discuss the relation of this path
integral to our previous considerations regarding the problem of time, and
extend our approach to include fermions.Comment: 32 pages, latex. The revision is a more general treatment of the
regulator. Local constraints are now derived from a requirement of regulator
independenc
Self-Trapping of Polarons in the Rashba-Pekar Model
We performed quantum Monte Carlo study of the exciton-polaron model which
features the self-trapping phenomenon when the coupling strength and/or
particle momentum is varied. For the first time accurate data for energy,
effective mass, the structure of the polaronic cloud, dispersion law, and
spectral function are available throughout the crossover region. We observed
that self-trapping can not be reduced to hybridization of two states with
different lattice deformation, and that at least three states are involved in
the crossover from light- to heavy-mass regimes.Comment: 5 pages, 5 figures, Accepted to Phys. Rev. B Rapid Communication
Numerical integration of variational equations
We present and compare different numerical schemes for the integration of the
variational equations of autonomous Hamiltonian systems whose kinetic energy is
quadratic in the generalized momenta and whose potential is a function of the
generalized positions. We apply these techniques to Hamiltonian systems of
various degrees of freedom, and investigate their efficiency in accurately
reproducing well-known properties of chaos indicators like the Lyapunov
Characteristic Exponents (LCEs) and the Generalized Alignment Indices (GALIs).
We find that the best numerical performance is exhibited by the
\textit{`tangent map (TM) method'}, a scheme based on symplectic integration
techniques which proves to be optimal in speed and accuracy. According to this
method, a symplectic integrator is used to approximate the solution of the
Hamilton's equations of motion by the repeated action of a symplectic map ,
while the corresponding tangent map , is used for the integration of the
variational equations. A simple and systematic technique to construct is
also presented.Comment: 27 pages, 11 figures, to appear in Phys. Rev.
Variational study of the Holstein polaron
The paper deals with the ground and the first excited state of the polaron in
the one dimensional Holstein model. Various variational methods are used to
investigate both the weak coupling and strong coupling case, as well as the
crossover regime between them. Two of the methods, which are presented here for
the first time, introduce interesting elements to the understanding of the
nature of the polaron. Reliable numerical evidence is found that, in the strong
coupling regime, the ground and the first excited state of the self-trapped
polaron are well described within the adiabatic limit. The lattice vibration
modes associated with the self-trapped polarons are analyzed in detail, and the
frequency softening of the vibration mode at the central site of the small
polaron is estimated. It is shown that the first excited state of the system in
the strong coupling regime corresponds to the excitation of the soft phonon
mode within the polaron. In the crossover regime, the ground and the first
excited state of the system can be approximated by the anticrossing of the
self-trapped and the delocalized polaron state. In this way, the connection
between the behavior of the ground and the first excited state is qualitatively
explained.Comment: 11 pages, 4 figures, PRB 65, 14430
Fundamental Constants and the Problem of Time
We point out that for a large class of parametrized theories, there is a
constant in the constrained Hamiltonian which drops out of the classical
equations of motion in configuration space. Examples include the mass of a
relativistic particle in free fall, the tension of the Nambu string, and
Newton's constant for the case of pure gravity uncoupled to matter or other
fields. In the general case, the classically irrelevant constant is
proportional to the ratio of the kinetic and potential terms in the
Hamiltonian. It is shown that this ratio can be reinterpreted as an {\it
unconstrained} Hamiltonian, which generates the usual classical equations of
motion. At the quantum level, this immediately suggests a resolution of the
"problem of time" in quantum gravity. We then make contact with a recently
proposed transfer matrix formulation of quantum gravity and discuss the
semiclassical limit. In this formulation, it is argued that a physical state
can obey a (generalized) Poincar\'e algebra of constraints, and still be an
approximate eigenstate of 3-geometry. Solutions of the quantum evolution
equations for certain minisuperspace examples are presented. An implication of
our proposal is the existence of a small, inherent uncertainty in the
phenomenological value of Planck's constant.Comment: 46 pages + 5 figures, LaTex, NBI-HE-94-3
Mean parameter model for the Pekar-Fr\"{o}hlich polaron in a multilayered heterostructure
The polaron energy and the effective mass are calculated for an electron
confined in a finite quantum well constructed of
layers. To simplify the study we suggest a model in which parameters of a
medium are averaged over the ground-state wave function. The rectangular and
the Rosen-Morse potential are used as examples.
To describe the confined electron properties explicitly to the second order
of perturbations in powers of the electron-phonon coupling constant we use the
exact energy-dependent Green function for the Rosen-Morse confining potential.
In the case of the rectangular potential, the sum over all intermediate virtual
states is calculated. The comparison is made with the often used leading term
approximation when only the ground-state is taken into account as a virtual
state. It is shown that the results are quite different, so the incorporation
of all virtual states and especially those of the continuous spectrum is
essential.
Our model reproduces the correct three-dimensional asymptotics at both small
and large widths. We obtained a rather monotonous behavior of the polaron
energy as a function of the confining potential width and found a peak of the
effective mass. The comparison is made with theoretical results by other
authors. We found that our model gives practically the same (or very close)
results as the explicit calculations for potential widths .Comment: 12 pages, LaTeX, including 5 PS-figures, subm. to Phys. Rev. B, new
data are discusse
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