1,673 research outputs found
Boltzmann Collision Term
We derive the Boltzmann equation for scalar fields using the
Schwinger-Keldysh formalism. The focus lies on the derivation of the collision
term. We show that the relevant self-energy diagrams have a factorization
property. The collision term assumes the Boltzmann-like form of scattering
probability times statistical factors for those self-energy diagrams which
correspond to tree level scattering processes. Our proof covers scattering
processes with any number of external particles, which come from self-energy
diagrams with any number of loops.Comment: 17 pages, 4 figure
Efficient grid-based method in nonequilibrium Green's function calculations. Application to model atoms and molecules
We propose and apply the finite-element discrete variable representation to
express the nonequilibrium Green's function for strongly inhomogeneous quantum
systems. This method is highly favorable against a general basis approach with
regard to numerical complexity, memory resources, and computation time. Its
flexibility also allows for an accurate representation of spatially extended
hamiltonians, and thus opens the way towards a direct solution of the two-time
Schwinger/Keldysh/Kadanoff-Baym equations on spatial grids, including e.g. the
description of highly excited states in atoms. As first benchmarks, we compute
and characterize, in Hartree-Fock and second Born approximation, the ground
states of the He atom, the H molecule and the LiH molecule in one spatial
dimension. Thereby, the ground-state/binding energies, densities and
bond-lengths are compared with the direct solution of the time-dependent
Schr\"odinger equation.Comment: 11 pages, 5 figures, submitted to Physical Review
Schwinger-Keldysh approach to out of equilibrium dynamics of the Bose Hubbard model with time varying hopping
We study the real time dynamics of the Bose Hubbard model in the presence of
time-dependent hopping allowing for a finite temperature initial state. We use
the Schwinger-Keldysh technique to find the real-time strong coupling action
for the problem at both zero and finite temperature. This action allows for the
description of both the superfluid and Mott insulating phases. We use this
action to obtain dynamical equations for the superfluid order parameter as
hopping is tuned in real time so that the system crosses the superfluid phase
boundary. We find that under a quench in the hopping, the system generically
enters a metastable state in which the superfluid order parameter has an
oscillatory time dependence with a finite magnitude, but disappears when
averaged over a period. We relate our results to recent cold atom experiments.Comment: 22 pages, 7 figure
Competing order and nature of the pairing state in the iron pnictides
We show that the competition between magnetism and superconductivity can be
used to determine the pairing state in the iron arsenides. To this end we
demonstrate that the itinerant antiferromagnetic phase (AFM) and the
unconventional sign-changing superconducting state (SC) are near the
borderline of microscopic coexistence and macroscopic phase separation,
explaining the experimentally observed competition of both ordered states. In
contrast, conventional pairing is not able to coexist with magnetism.
Expanding the microscopic free energy of the system with competing orders
around the multicritical point, we find that static magnetism plays the role of
an intrinsic interband Josephson coupling, making the phase diagram sensitive
to the symmetry of the Cooper pair wavefunction. We relate this result to the
quasiparticle excitation spectrum and to the emergent SO symmetry of
systems with particle-hole symmetry. Our results rely on the assumption that
the same electrons that form the ordered moment contribute to the
superconducting condensate and that the system is close to particle-hole
symmetry. We also compare the suppression of SC in different regions of the
FeAs phase diagram, showing that while in the underdoped side it is due to the
competition with AFM, in the overdoped side it is related to the disappearance
of pockets from the Fermi surface.Comment: 24 pages, 13 figures; revised versio
Steady-state nonequilibrium dynamical mean-field theory and the quantum Boltzman
We derive the formalism for steady state nonequilibrium dynamical mean-field
theory in a real-time formalism along the Kadanoff-Baym contour. The resulting
equations of motion are first transformed to Wigner coordinates (average and
relative time), and then re-expressed in terms of differential operators.
Finally, we perform a Fourier transform with respect to the relative time, and
take the first-order limit in the electric field to produce the quantum
Boltzmann equation for dynamical mean-field theory. We next discuss the
structure of the equations and their solutions, describing how these equations
reduce to the Drude result in the limit of a constant relaxation time. We also
explicitly demonstrate the equivalence between the Kubo and nonequilibrium
approaches to linear response. There are a number of interesting modifications
of the conventional quantum Boltzmann equation that arise due to the underlying
bandstructure of the lattice.Comment: (14 pages, proceedings of the Workshop on Progress in Nonequilibrium
Green's Functions III, Kiel Germany
Emission and absorption noise in the fractional quantum Hall effect
We compute the high-frequency emission and absorption noise in a fractional
quantum Hall effect (FQHE) sample at arbitrary temperature. We model the edges
of the FQHE as chiral Luttinger liquids (LL) and we use the non-equilibrium
perturbative Keldysh formalism. We find that the non-symmetrized high frequency
noise contains important signatures of the electron-electron interactions that
can be used to test the Luttinger liquid physics, not only in FQHE edge states,
but possibly also in other one-dimensional systems such as carbon nanotubes. In
particular we find that the emission and absorption components of the excess
noise (defined as the difference between the noise at finite voltage and at
zero voltage) are different in an interacting system, as opposed to the
non-interacting case when they are identical. We study the resonance features
which appear in the noise at the Josephson frequency (proportional to the
applied voltage), and we also analyze the effect of the distance between the
measurement point and the backscattering site. Most of our analysis is
performed in the weak backscattering limit, but we also compute and discuss
briefly the high-frequency noise in the tunneling regime.Comment: 26 pages, 11 figure
Condensation of Cavity Polaritons in a Disordered Environment
A model for direct two band excitons in a disordered quantum well coupled to
light in a cavity is investigated. In the limit in which the exciton density is
high, we assess the impact of weak `pair-breaking' disorder on the feasibility
of condensation of cavity polaritons. The mean-field phase diagram shows a
`lower density' region, where the condensate is dominated by electronic
excitations and where disorder tends to close the condensate and quench
coherence. Increasing the density of excitations in the system, partially due
to the screening of Coulomb interaction, the excitations contributing to the
condensate become mainly photon-like and coherence is reestablished for any
value of disorder. In contrast, in the photon dominated region of the phase
diagram, the energy gap of the quasi-particle spectrum still closes when the
disorder strength is increased. Above mean-field, thermal, quantum and
fluctuations induced by disorder are considered and the spectrum of the
collective excitations is evaluated. In particular, it is shown that the angle
resolved photon intensity exhibits an abrupt change in its behaviour, going
from the condensed to the non-condensed region.Comment: 17 pages, 9 eps figures; published versio
Measuring correlated electron dynamics with time-resolved photoemission spectroscopy
Time-resolved photoemission experiments can reveal fascinating quantum
dynamics of correlated electrons. However, the thermalization of the electronic
system is typically so fast that very short probe pulses are necessary to
resolve the time evolution of the quantum state, and this leads to poor energy
resolution due to the energy-time uncertainty relation. Although the
photoemission intensity can be calculated from the nonequilibrium electronic
Green functions, the converse procedure is therefore difficult. We analyze a
hypothetical time-resolved photoemission experiment on a correlated electronic
system, described by the Falicov-Kimball model in dynamical mean-field theory,
which relaxes between metallic and insulating phases. We find that the
real-time Green function which describes the transient behavior during the
buildup of the metallic state cannot be determined directly from the
photoemission signal. On the other hand, the characteristic
collapse-and-revival oscillations of an excited Mott insulator can be observed
as oscillating weight in the center of the Mott gap in the time-dependent
photoemission spectrum.Comment: 12 pages, 5 figure
Transport Theory beyond Binary Collisions
Using the Schwinger-Keldysh technique, we derive the transport equations for
a system of quantum scalar fields. We first discuss the general structure of
the equations and then their collision terms. Taking into account up to
three-loop diagrams in \phi^3 model and up to four-loop diagrams in \phi^4
model, we obtain the transport equations which include the contributions of
multi-particle collisions and particle production processes, in addition to
mean-field effects and binary interactions.Comment: 30 pages, 21 figures, minor changes, to appear in Phys. Rev.
Dynamic equation for quantum Hall bilayers with spontaneous interlayer coherence: The low-density limit
The bilayer systems exhibit the Bose-Einstein condensation of excitons that
emerge due to Coulomb pairing of electrons belonging to one layer with the
holes belonging to the other layer. Here we present the microscopic derivation
of the dynamic equation for the condensate wave function at a low density of
electron-hole () pairs in a strong magnetic field perpendicular to the
layers and an electric field directed along the layers. From this equation we
obtain the dispersion law for collective excitations of the condensate and
calculate the electric charge of the vortex in the exciton condensate. The
critical interlayer spacing, the excess of which leads to a collapse of the
superfluid state, is estimated. In bilayer systems with curved conducting
layers, the effective mass of the pair becomes the function of the
pair coordinates, the regions arise, where the energy of the pair is
lowered (exciton traps), and lastly pairs can gain the polarization in
the basal plane. This polarization leads to the appearance of quantized
vortices even at zero temperature.Comment: 8 page
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