9,360 research outputs found
Black hole singularities: a new critical phenomenon
The singularitiy inside a spherical charged black hole, coupled to a
spherical, massless scalar field is studied numerically. The profile of the
characteristic scalar field was taken to be a power of advanced time with an
exponent . A critical exponent exists. For
exponents below the critical one () the singularity
is a union of spacelike and null sectors, as is also the case for data with
compact support. For exponents greater than the critical one
() an all-encompassing, spacelike singularity
evolves, which completely blocks the ``tunnel'' inside the black hole,
preventing the use of the black hole as a portal for hyperspace travel.Comment: 4 pages, 5 eps figures; An Erratum is added. The main conclusions of
the original Letter are unchange
OUTLINE OF A GENERALLY COVARIANT QUANTUM FIELD THEORY AND A QUANTUM THEORY OF GRAVITY
We study a tentative generally covariant quantum field theory, denoted the
T-Theory, as a tool to investigate the consistency of quantum general
relativity. The theory describes the gravitational field and a minimally
coupled scalar field; it is based on the loop representation, and on a certain
number of quantization choices. Four-dimensional diffeomorphism-invariant
quantum transition probabilities can be computed from the theory. We present
the explicit calculation of the transition probability between two volume
eigenstates as an example. We discuss the choices on which the T-theory relies,
and the possibilities of modifying them.Comment: Latex file, 33 page
Localization and superconducting proximity effect in sandwiched potassium films
Thin films of alkali metals when sandwiched at both surfaces by thin metal
films loose their conductance. The superconducting proximity effect is used to
investigate the change in the alkali film. On the length scale of the film
thickness the electronic properties of the alkali film do not change noticeably
although its conductance is dramatically reduced, corresponding to localized
electrons.Comment: 13 pages, 5 figure
Oscillations of the magnetic polarization in a Kondo impurity at finite magnetic fields
The electronic properties of a Kondo impurity are investigated in a magnetic
field using linear response theory. The distribution of electrical charge and
magnetic polarization are calculated in real space. The (small) magnetic field
does not change the charge distribution. However, it unmasks the Kondo cloud.
The (equal) weight of the d-electron components with their magnetic moment up
and down is shifted and the compensating s-electron clouds don't cancel any
longer (a requirement for an experimental detection of the Kondo cloud). In
addition to the net magnetic polarization of the conduction electrons an
oscillating magnetic polarization with a period of half the Fermi wave length
is observed. However, this oscillating magnetic polarization does not show the
long range behavior of Rudermann-Kittel-Kasuya-Yosida oscillations because the
oscillations don't extend beyond the Kondo radius. They represent an internal
electronic structure of the Kondo impurity in a magnetic field. PACS: 75.20.Hr,
71.23.An, 71.27.+
The issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity
Diffeomorphism-induced symmetry transformations and time evolution are
distinct operations in generally covariant theories formulated in phase space.
Time is not frozen. Diffeomorphism invariants are consequently not necessarily
constants of the motion. Time-dependent invariants arise through the choice of
an intrinsic time, or equivalently through the imposition of time-dependent
gauge fixation conditions. One example of such a time-dependent gauge fixing is
the Komar-Bergmann use of Weyl curvature scalars in general relativity. An
analogous gauge fixing is also imposed for the relativistic free particle and
the resulting complete set time-dependent invariants for this exactly solvable
model are displayed. In contrast with the free particle case, we show that
gauge invariants that are simultaneously constants of motion cannot exist in
general relativity. They vary with intrinsic time
Complementarity relation for irreversible process derived from stochastic energetics
When the process of a system in contact with a heat bath is described by
classical Langevin equation, the method of stochastic energetics [K. Sekimoto,
J. Phys. Soc. Jpn. vol. 66 (1997) p.1234] enables to derive the form of
Helmholtz free energy and the dissipation function of the system. We prove that
the irreversible heat Q_irr and the time lapse $Delta t} of an isothermal
process obey the complementarity relation, Q_irr {Delta t} >= k_B T S_min,
where S_min depends on the initial and the final values of the control
parameters, but it does not depend on the pathway between these values.Comment: 3 pages. LaTeX with 6 style macro
Numerical Calculation of the Fidelity for the Kondo and the Friedel-Anderson Impurities
The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are
calculated numerically. The ground states of both systems are calculated with
the FAIR (Friedel artificially inserted resonance) theory. The ground state in
the interacting systems is compared with a nullstate in which the interaction
is zero. The different multi-electron states are expressed in terms of Wilson
states. The use of N Wilson states simulates the use of a large effective
number N_{eff} of states. A plot of ln(F) versus N\proptoln(N_{eff}) reveals
whether one has an Anderson orthogonality catastrophe at zero energy. The
results are at first glance surprising. The ln(F)-ln(N_{eff}) plot for the
Kondo impurity diverges for large N_{eff}. On the other hand, the corresponding
plot for the symmetric FA impurity saturates for large N_{eff} when the level
spacing at the Fermi level is of the order of the singlet-triplet excitation
energy. The behavior of the fidelity allows one to determine the phase shift of
the electron states in this regime. PACS: 75.20.Hr, 71.23.An, 71.27.+a,
05.30.-
Lagrangian approach to a symplectic formalism for singular systems
We develop a Lagrangian approach for constructing a symplectic structure for
singular systems. It gives a simple and unified framework for understanding the
origin of the pathologies that appear in the Dirac-Bergmann formalism, and
offers a more general approach for a symplectic formalism, even when there is
no Hamiltonian in a canonical sense. We can thus overcome the usual limitations
of the canonical quantization, and perform an algebraically consistent
quantization for a more general set of Lagrangian systems.Comment: 30 page
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