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For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
Theoretical predictions for inclusive semileptonic B decay rates are rewritten in terms of the Upsilon(1S) meson mass instead of the b quark mass, using a modified perturbation expansion. This method gives theoretically consistent and…
A practical method for finding free energy barriers for transitions in high-dimensional classical and quantum systems is presented and used to calculate the dissociative sticking probability of H2 on a metal surface within transition state…
We introduce an adiabatic perturbation theory for quantum systems with degenerate energy spectra. This perturbative series enables one to rigorously establish conditions for the validity of the adiabatic theorem of quantum mechanics for…
Decay laws of moving unstable quantum systems with oscillating decay rates are analyzed over intermediate times. The transformations of the decay laws at rest and of the intermediate times at rest, which are induced by the change of…
An angular effective mass formalism previously introduced is used to study the density of states in warped and non-warped energy bands. Band warping may or may not increase the density-of-states effective mass. Band "corrugation," referring…
Using mass perturbation theory, we infer the bound-state spectrum of massive QED$_2$ and compute some decay widths of unstable bound states. Further, we discuss scattering processes, where all the resonances and particle production…
The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We introduce the…
We calculate the eigenvalues and their corresponding eigenfunctions of the Bohrs collective Hamiltonian with the help of the modified Poschl-Teller potential model within -unstable structure. Our numerical results for the ground state beta…
The framework of the Perturbed Static Path Approximation (PSPA) is used to calculate the partition function of a finite Fermi system from a Hamiltonian with a separable two body interaction. Therein, the collective degree of freedom is…
The decay of quantum complex systems through a potential barrier is often described with transition-state theory, also known as RRKM theory in chemistry. Here we derive the basic formula for transition-state theory based on a generic…
Besides perturbation theory (which clearly requires the knowledge of the exact unperturbed solution), variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum…
In solid-state physics, energies of crystals are usually computed with a plane-wave discretization of Kohn-Sham equations. However the presence of Coulomb singularities requires the use of large plane-wave cut-offs to produce accurate…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
Experimentally observable Quantum Accelerator Modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable…
The time evolution of the thermally activated decay rates is considered. This evolution is of particular importance for the recent nanoscale experiments discussed in the literature, where the potential barrier is relatively low (or the…
The resonant state expansion, a rigorous perturbation theory, recently developed in electrodynamics, is applied to non-relativistic quantum mechanical systems in one dimension. The method is used here for finding the resonant states in…
The finite size theory of metastability in a quartic potential is developed by the semiclassical path integral method. In the quantum regime, the relation between temperature and classical particle energy is found in terms of the first…
In this work, we develop a perturbation theory to analyze resonant states near a bound state in the continuum (BIC) in photonic crystal slabs. The theory allows us to rigorously determine the asymptotic behavior of $Q$-factor and the…
The dynamics of the nuclear-spin quantum computer with large number (L=1000) of qubits is considered using a perturbation approach, based on approximate diagonalization of exponentially large sparse matrices. Small parameters are introduced…