1,050 research outputs found
Excitonic condensation in quasi-two-dimensional systems
We present a low energy model for the Bose-Einstein condensation in a
quasi-two-dimensional excitonic gas. Using the flow equations of the
Renormalization group and a model with the dynamical critical exponent
we calculate the temperature dependence of the critical density,
coherence length, magnetic susceptibility, and specific heat. The model can be
relevant for the macroscopic coherence observed in GaAs/AlGaAs coupled quantum
wells.Comment: 4 Revtex page
Uniform in time estimates for the weak error of the Euler method for SDEs and a Pathwise Approach to Derivative Estimates for Diffusion Semigroups
We present a criterion for uniform in time convergence of the weak error of
the Euler scheme for Stochastic Differential equations (SDEs). The criterion
requires i) exponential decay in time of the space-derivatives of the semigroup
associated with the SDE and ii) bounds on (some) moments of the Euler
approximation. We show by means of examples (and counterexamples) how both i)
and ii) are needed to obtain the desired result. If the weak error converges to
zero uniformly in time, then convergence of ergodic averages follows as well.
We also show that Lyapunov-type conditions are neither sufficient nor necessary
in order for the weak error of the Euler approximation to converge uniformly in
time and clarify relations between the validity of Lyapunov conditions, i) and
ii).
Conditions for ii) to hold are studied in the literature. Here we produce
sufficient conditions for i) to hold. The study of derivative estimates has
attracted a lot of attention, however not many results are known in order to
guarantee exponentially fast decay of the derivatives. Exponential decay of
derivatives typically follows from coercive-type conditions involving the
vector fields appearing in the equation and their commutators; here we focus on
the case in which such coercive-type conditions are non-uniform in space. To
the best of our knowledge, this situation is unexplored in the literature, at
least on a systematic level. To obtain results under such space-inhomogeneous
conditions we initiate a pathwise approach to the study of derivative estimates
for diffusion semigroups and combine this pathwise method with the use of Large
Deviation Principles.Comment: 47 pages and 9 figure
Magnetic instability of a two-dimensional Anderson non-Fermi liquid
We show that in the Anderson model for a two-dimensional non-Fermi liquid a
magnetic instability can lead to the itinerant electron ferromagnetism. The
critical temperature and the susceptibility of the paramagnetic phase have been
analytically calculated. The usual Fermi behaviour is re-obtained taking the
anomalous exponent to be zero.Comment: 3 pages, Revte
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