1,497 research outputs found
Non-equilibrium quantum condensation in an incoherently pumped dissipative system
We study spontaneous quantum coherence in an out of equilibrium system,
coupled to multiple baths describing pumping and decay. For a range of
parameters describing coupling to, and occupation of the baths, a stable
steady-state condensed solution exists. The presence of pumping and decay
significantly modifies the spectra of phase fluctuations, leading to
correlation functions that differ both from an isolated condensate and from a
laser.Comment: 5 pages, 2 eps figure
Variational discrete variable representation for excitons on a lattice
We construct numerical basis function sets on a lattice, whose spatial
extension is scalable from single lattice sites to the continuum limit. They
allow us to compute small and large bound states with comparable, moderate
effort. Adopting concepts of discrete variable representations, a diagonal form
of the potential term is achieved through a unitary transformation to Gaussian
quadrature points. Thereby the computational effort in three dimensions scales
as the fourth instead of the sixth power of the number of basis functions along
each axis, such that it is reduced by two orders of magnitude in realistic
examples. As an improvement over standard discrete variable representations,
our construction preserves the variational principle. It allows for the
calculation of binding energies, wave functions, and excitation spectra. We use
this technique to study central-cell corrections for excitons beyond the
continuum approximation. A discussion of the mass and spectrum of the yellow
exciton series in the cuprous oxide, which does not follow the hydrogenic
Rydberg series of Mott-Wannier excitons, is given on the basis of a simple
lattice model.Comment: 12 pages, 7 figures. Final version as publishe
Numerical time propagation of quantum systems in radiation fields
Atoms, molecules or excitonic quasiparticles, for which excitations are
induced by external radiation fields and energy is dissipated through radiative
decay, are examples of driven open quantum systems. We explain the use of
commutator-free exponential time-propagators for the numerical solution of the
associated Schr\"odinger or master equations with a time-dependent Hamilton
operator. These time-propagators are based on the Magnus series but avoid the
computation of commutators, which makes them suitable for the efficient
propagation of systems with a large number of degrees of freedom. We present an
optimized fourth order propagator and demonstrate its efficiency in comparison
to the direct Runge-Kutta computation. As an illustrative example we consider
the parametrically driven dissipative Dicke model, for which we calculate the
periodic steady state and the optical emission spectrum.Comment: 23 pages, 11 figure
Quantum Monte Carlo results for bipolaron stability in quantum dots
Bipolaron formation in a two-dimensional lattice with harmonic confinement,
representing a simplified model for a quantum dot, is investigated by means of
quantum Monte Carlo simulations. This method treats all interactions exactly
and takes into account quantum lattice fluctuations. Calculations of the
bipolaron binding energy reveal that confinement opposes bipolaron formation
for weak electron-phonon coupling, but abets a bound state at intermediate to
strong coupling. Tuning the system from weak to strong confinement gives rise
to a small reduction of the minimum Frohlich coupling parameter for the
existence of a bound state.Comment: 5 pages, 2 figures, final version to appear in Phys. Rev.
Thermodynamics and Excitations of Condensed Polaritons in Disordered Microcavities
We study the thermodynamic condensation of microcavity polaritons using a
realistic model of disorder in semiconductor quantum wells. This approach
correctly describes the polariton inhomogeneous broadening in the low density
limit, and treats scattering by disorder to all orders in the condensed regime.
While the weak disorder changes the thermodynamic properties of the transition
little, the effects of disorder in the condensed state are prominent in the
excitations and can be seen in resonant Rayleigh scattering.Comment: 5 pages, 3 eps figures (published version
Thermal Rounding of the Charge Density Wave Depinning Transition
The rounding of the charge density wave depinning transition by thermal noise
is examined. Hops by localized modes over small barriers trigger
``avalanches'', resulting in a creep velocity much larger than that expected
from comparing thermal energies with typical barriers. For a field equal to the
depinning field, the creep velocity is predicted to have a {\em
power-law} dependence on the temperature ; numerical computations confirm
this result. The predicted order of magnitude of the thermal rounding of the
depinning transition is consistent with rounding seen in experiment.Comment: 12 pages + 3 Postscript figure
The new physics of non-equilibrium condensates: insights from classical dynamics
We discuss the dynamics of classical Dicke-type models, aiming to clarify the
mechanisms by which coherent states could develop in potentially
non-equilibrium systems such as semiconductor microcavities. We present
simulations of an undamped model which show spontaneous coherent states with
persistent oscillations in the magnitude of the order parameter. These states
are generalisations of superradiant ringing to the case of inhomogeneous
broadening. They correspond to the persistent gap oscillations proposed in
fermionic atomic condensates, and arise from a variety of initial conditions.
We show that introducing randomness into the couplings can suppress the
oscillations, leading to a limiting dynamics with a time-independent order
parameter. This demonstrates that non-equilibrium generalisations of polariton
condensates can be created even without dissipation. We explain the dynamical
origins of the coherence in terms of instabilities of the normal state, and
consider how it can additionally develop through scattering and dissipation.Comment: 10 pages, 4 figures, submitted for a special issue of J. Phys.:
Condensed Matter on "Optical coherence and collective phenomena in
nanostructures". v2: added discussion of links to exact solution
Existence and Uniqueness of Tri-tronqu\'ee Solutions of the second Painlev\'e hierarchy
The first five classical Painlev\'e equations are known to have solutions
described by divergent asymptotic power series near infinity. Here we prove
that such solutions also exist for the infinite hierarchy of equations
associated with the second Painlev\'e equation. Moreover we prove that these
are unique in certain sectors near infinity.Comment: 13 pages, Late
Computing Hilbert Class Polynomials
We present and analyze two algorithms for computing the Hilbert class
polynomial . The first is a p-adic lifting algorithm for inert primes p
in the order of discriminant D < 0. The second is an improved Chinese remainder
algorithm which uses the class group action on CM-curves over finite fields.
Our run time analysis gives tighter bounds for the complexity of all known
algorithms for computing , and we show that all methods have comparable
run times
Sliding motion of a two-dimensional Wigner crystal in a strong magnetic field
We study the sliding state of a two-dimensional Wigner crystal in a strong
magnetic field and a random impurity potential. Using a high-velocity
perturbation theory, we compute the nonlinear conductivity, various correlation
functions, and the interference effects arising in combined AC + DC electric
effects, including the Shapiro anomaly and the linear response to an AC field.
Disorder is found to induce mainly transverse distortions in the sliding state
of the lattice. The Hall resistivity retains its classical value. We find that,
within the large velocity perturbation theory, free carriers which affect the
longitudinal phonon modes of the Wigner crystal do not change the form of the
nonlinear conductivity. We compare the present sliding Wigner crystal in a
strong magnetic field to the conventional sliding charge-density wave systems.
Our result for the nonlinear conductivity agrees well with the
characteristics measured in some experiments at low temperatures or large
depinning fields, for the insulating phases near filling factor = 1/5. We
summarize the available experimental data, and point out the differences among
them.Comment: appeared in RPB vol. 50, 4600 (1994); LaTex file; 3 figures available
from [email protected]
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