اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDynamical Lower Bounds for 1D Dirac Operators
243
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Quantum dynamical lower bounds for continuous and discrete one-dimensional Dirac operators are established in terms of transfer matrices. Then such results are applied to various models, including the Bernoulli-Dirac one and, in contrast to the discrete case, critical energies are also found for the continuous Dirac case with positive mass.
قيم البحث
اقرأ أيضاً
An analytic definition of a $mathbb{Z}_2$-valued spectral flow for paths of real skew-adjoint Fredholm operators is given. It counts the parity of the number of changes in the orientation of the eigenfunctions at eigenvalue crossings through $0$ alon
g the path. The $mathbb{Z}_2$-valued spectral flow is shown to satisfy a concatenation property and homotopy invariance, and it provides an isomorphism on the fundamental group of the real skew-adjoint Fredholm operators. Moreover, it is connected to a $mathbb{Z}_2$-index pairing for suitable paths. Applications concern the zero energy bound states at defects in a Majorana chain and a spectral flow interpretation for the $mathbb{Z}_2$-polarization in these models.
In 1964 J. M. Luttinger introduced a model for the quantum thermal transport. In this paper we study the spectral theory of the Hamiltonian operator associated to the Luttingers model, with a special focus at the one-dimensional case. It is shown tha
t the (so called) thermal Hamiltonian has a one-parameter family of self-adjoint extensions and the spectrum, the time-propagator group and the Green function are explicitly computed. Moreover, the scattering by convolution-type potentials is analyzed. Finally, also the associated classical problem is completely solved, thus providing a comparison between classical and quantum behavior. This article aims to be a first contribution in the construction of a complete theory for the thermal Hamiltonian.
Given two intervals $I, J subset mathbb{R}$, we ask whether it is possible to reconstruct a real-valued function $f in L^2(I)$ from knowing its Hilbert transform $Hf$ on $J$. When neither interval is fully contained in the other, this problem has a u
nique answer (the nullspace is trivial) but is severely ill-posed. We isolate the difficulty and show that by restricting $f$ to functions with controlled total variation, reconstruction becomes stable. In particular, for functions $f in H^1(I)$, we show that $$ |Hf|_{L^2(J)} geq c_1 exp{left(-c_2 frac{|f_x|_{L^2(I)}}{|f|_{L^2(I)}}right)} | f |_{L^2(I)} ,$$ for some constants $c_1, c_2 > 0$ depending only on $I, J$. This inequality is sharp, but we conjecture that $|f_x|_{L^2(I)}$ can be replaced by $|f_x|_{L^1(I)}$.
We establish quantitative bounds on the rate of approach to equilibrium for a system with infinitely many degrees of freedom evolving according to a one-dimensional focusing nonlinear Schrodinger equation with diffusive forcing. Equilibrium is descri
bed by a generalized grand canonical ensemble. Our analysis also applies to the easier case of defocusing nonlinearities
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the associated fr
actional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
