67 research outputs found
Defect-induced condensation and central peak at elastic phase transitions
Static and dynamical properties of elastic phase transitions under the
influence of short--range defects, which locally increase the transition
temperature, are investigated. Our approach is based on a Ginzburg--Landau
theory for three--dimensional crystals with one--, two-- or three--dimensional
soft sectors, respectively. Systems with a finite concentration of
quenched, randomly placed defects display a phase transition at a temperature
, which can be considerably above the transition temperature
of the pure system. The phonon correlation function is calculated in
single--site approximation. For a dynamical central peak
appears; upon approaching , its height diverges and its width
vanishes. Using an appropriate self--consistent method, we calculate the
spatially inhomogeneous order parameter, the free energy and the specific heat,
as well as the dynamical correlation function in the ordered phase. The
dynamical central peak disappears again as the temperatur is lowered below
. The inhomogeneous order parameter causes a static central
peak in the scattering cross section, with a finite width depending on the
orientation of the external wave vector relative to the soft sector.
The jump in the specific heat at the transition temperatur of the pure system
is smeared out by the influence of the defects, leading to a distinct maximum
instead. In addition, there emerges a tiny discontinuity of the specific heat
at . We also discuss the range of validity of the mean--field
approach, and provide a more realistic estimate for the transition temperature.Comment: 11 pages, 11 ps-figures, to appear in PR
Bell-state preparation for electron spins in a semiconductor double quantum dot
A robust scheme for state preparation and state trapping for the spins of two
electrons in a semiconductor double quantum dot is presented. The system is
modeled by two spins coupled to two independent bosonic reservoirs. Decoherence
effects due to this environment are minimized by application of optimized
control fields which make the target state to the ground state of the isolated
driven spin system. We show that stable spin entanglement with respect to pure
dephasing is possible. Specifically, we demonstrate state trapping in a
maximally entangled state (Bell state) in the presence of decoherence.Comment: 9 pages, 4 figure
Dimensional crossover in dipolar magnetic layers
We investigate the static critical behaviour of a uniaxial magnetic layer,
with finite thickness L in one direction, yet infinitely extended in the
remaining d dimensions. The magnetic dipole-dipole interaction is taken into
account. We apply a variant of Wilson's momentum shell renormalisation group
approach to describe the crossover between the critical behaviour of the 3-D
Ising, 2-d Ising, 3-D uniaxial dipolar, and the 2-d uniaxial dipolar
universality classes. The corresponding renormalisation group fixed points are
in addition to different effective dimensionalities characterised by distinct
analytic structures of the propagator, and are consequently associated with
varying upper critical dimensions. While the limiting cases can be discussed by
means of dimensional epsilon expansions with respect to the appropriate upper
critical dimensions, respectively, the crossover features must be addressed in
terms of the renormalisation group flow trajectories at fixed dimensionality d.Comment: 25 pages, Latex, 12 figures (.eps files) and IOP style files include
On the quantum description of Einstein's Brownian motion
A fully quantum treatment of Einstein's Brownian motion is given, showing in
particular the role played by the two original requirements of translational
invariance and connection between dynamics of the Brownian particle and atomic
nature of the medium. The former leads to a clearcut relationship with Holevo's
result on translation-covariant quantum-dynamical semigroups, the latter to a
formulation of the fluctuation-dissipation theorem in terms of the dynamic
structure factor, a two-point correlation function introduced in seminal work
by van Hove, directly related to density fluctuations in the medium and
therefore to its atomistic, discrete nature. A microphysical expression for the
generally temperature dependent friction coefficient is given in terms of the
dynamic structure factor and of the interaction potential describing the single
collisions. A comparison with the Caldeira Leggett model is drawn, especially
in view of the requirement of translational invariance, further characterizing
general structures of reduced dynamics arising in the presence of symmetry
under translations.Comment: 14 pages, latex, no figure
Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion revisited
Stochastic Schr{\"o}dinger equations for quantum trajectories offer an
alternative and sometimes superior approach to the study of open quantum system
dynamics. Here we show that recently established convolutionless non-Markovian
stochastic Schr{\"o}dinger equations may serve as a powerful tool for the
derivation of convolutionless master equations for non-Markovian open quantum
systems. The most interesting example is quantum Brownian motion (QBM) of a
harmonic oscillator coupled to a heat bath of oscillators, one of the
most-employed exactly soluble models of open system dynamics. We show
explicitly how to establish the direct connection between the exact
convolutionless master equation of QBM and the corresponding convolutionless
exact stochastic Schr\"odinger equation.Comment: 18 pages, RevTe
Crossover from Isotropic to Directed Percolation
Percolation clusters are probably the simplest example for scale--invariant
structures which either are governed by isotropic scaling--laws
(``self--similarity'') or --- as in the case of directed percolation --- may
display anisotropic scaling behavior (``self--affinity''). Taking advantage of
the fact that both isotropic and directed bond percolation (with one preferred
direction) may be mapped onto corresponding variants of (Reggeon) field theory,
we discuss the crossover between self--similar and self--affine scaling. This
has been a long--standing and yet unsolved problem because it is accompanied by
different upper critical dimensions: for isotropic, and
for directed percolation, respectively. Using a generalized
subtraction scheme we show that this crossover may nevertheless be treated
consistently within the framework of renormalization group theory. We identify
the corresponding crossover exponent, and calculate effective exponents for
different length scales and the pair correlation function to one--loop order.
Thus we are able to predict at which characteristic anisotropy scale the
crossover should occur. The results are subject to direct tests by both
computer simulations and experiment. We emphasize the broad range of
applicability of the proposed method.Comment: 19 pages, written in RevTeX, 12 figures available upon request (from
[email protected] or [email protected]), EF/UCT--94/2, to be
published in Phys. Rev. E (May 1994
Broken unitarity and phase measurements in Aharonov-Bohm interferometers
Aharonov-Bohm mesoscopic solid-state interferometers yield a conductance
which contains a term , where relates to the magnetic
flux. Experiments with a quantum dot on one of the interfering paths aim to
relate to the dot's intrinsic Friedel transmission phase, .
For closed systems, which conserve the electron current (unitarity), the
Onsager relation requires that . For open systems, we show that
depends in general on the details of the broken unitarity. Although it
gives information on the resonances of the dot, is generally not equal
to . A direct relation between and requires
specific ways of opening the system, which are discussed.Comment: 4 pages, 3 figures(eps). Phys. Rev. Letters (in press
Domain wall roughening in dipolar films in the presence of disorder
We derive a low-energy Hamiltonian for the elastic energy of a N\'eel domain
wall in a thin film with in-plane magnetization, where we consider the
contribution of the long-range dipolar interaction beyond the quadratic
approximation. We show that such a Hamiltonian is analogous to the Hamiltonian
of a one-dimensional polaron in an external random potential. We use a replica
variational method to compute the roughening exponent of the domain wall for
the case of two-dimensional dipolar interactions.Comment: REVTEX, 35 pages, 2 figures. The text suffered minor changes and
references 1,2 and 12 were added to conform with the referee's repor
Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation
The properties of the Volume operator in Loop Quantum Gravity, as constructed
by Ashtekar and Lewandowski, are analyzed for the first time at generic
vertices of valence greater than four. The present analysis benefits from the
general simplified formula for matrix elements of the Volume operator derived
in gr-qc/0405060, making it feasible to implement it on a computer as a matrix
which is then diagonalized numerically. The resulting eigenvalues serve as a
database to investigate the spectral properties of the volume operator.
Analytical results on the spectrum at 4-valent vertices are included. This is a
companion paper to arXiv:0706.0469, providing details of the analysis presented
there.Comment: Companion to arXiv:0706.0469. Version as published in CQG in 2008.
More compact presentation. Sign factor combinatorics now much better
understood in context of oriented matroids, see arXiv:1003.2348, where also
important remarks given regarding sigma configurations. Subsequent
computations revealed some minor errors, which do not change qualitative
results but modify some numbers presented her
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