Related papers: Construction of dynamical semigroups by a function…
A general and systematic regularization is developed for the exact solitonic form factors of exponential operators in the (1+1)-dimensional sine-Gordon model by analytical continuation of their integral representations. The procedure is…
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon…
In this article we apply a recently established transference principle in order to obtain the boundedness of certain functional calculi for semigroup generators. In particular, it is proved that if $-A$ generates a $C_0$-semigroup on a…
In this article we fully describe the domain of the infinitesimal generator of the optimal state semigroup which arises in the theory of the linear-quadratic problem for a specific class of boundary control systems. This represents an…
This paper provides sharp lower estimates near the origin for the functional calculus $F(-uA)$ of a generator $A$ of an operator semigroup defined on the (strictly) positive real line; here $F$ is given as the Laplace transform of a measure…
Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasi-periodic solutions the issue of convergence of the series is plagued of the…
In this paper we study the regular semigroups weakly generated by a single element x, that is, with no proper regular subsemigroup containing x. We show there exists a regular semigroup $F_1$ weakly generated by x such that all other…
In a recent paper we presented a general perturbation result for generators of $C_0$-semigroups. The aim of the present paper is to replace, in case the unperturbed semigroup is analytic, the various conditions appearing in this result by…
While the properties of the Kondo model in equilibrium are very well understood, much less is known for Kondo systems out of equilibrium. We study the properties of a quantum dot in the Kondo regime, when a large bias voltage V and/or a…
We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we…
We propose a novel numerical algorithm utilizing model reduction for computing solutions to stationary partial differential equations involving the spectral fractional Laplacian. Our approach utilizes a known characterization of the…
We consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant its generators $\hat L_n$ with $n\ge 1$ satisfy the…
Using a real-time renormalization group method we determine the complete dynamics of the spin-boson model with ohmic dissipation for coupling strengths $\alpha\lesssim 0.1-0.2$. We calculate the relaxation and dephasing time, the static…
We apply the recently developed method of differential renormalization to the Wess-Zumino model. From the explicit calculation of a finite, renormalized effective action, the $\beta$-function is computed to three loops and is found to agree…
Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant…
The one-loop effective action for a scalar field defined in the ultrastatic space-time where non standard logarithmic terms in the asymptotic heat-kernel expansion are present, is investigated by a generalisation of zeta-function…
It is shown that the rate limiting time constant for the formation of the Kondo state in a quantum dot can be extracted analytically from known perturbation theoretic results. The prediction obtained is verified via numerical simulations in…
Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using…
An effective Hamiltonian for the localized spins in the one-dimensional Kondo lattice model is derived via a unitary transformation involving a bosonization of delocalized conduction electrons. The effective Hamiltonian is shown to…
It is shown that a simple modification of the dimensional regularization allows to compute in a consistent and gauge invariant way any diagram with less than four loops in the SO(10) unified model. The method applies also to the Standard…