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New exact formulas are derived for systems involving Landau-Zener transition rates and for absorption spectra in quantum dots. These rectify previous inaccurate approximations utilized in experimental studies. The exact formulas give an…
This work deals with the numerical solution of systems of oscillatory second-order differential equations which often arise from the semi-discretization in space of partial differential equations. Since these differential equations exhibit…
Exactly solvable multistate Landau-Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also be operators that satisfy the integrability conditions with…
We study two interacting electrons in a two-dimensional system under a strong magnetic field and show that their numerically exact solutions organize into a set of {\em sub-Landau levels} characterized by relative angular momentum quantum…
We propose an analytical framework to model the effect of single and multiple mechanical surface oscillators on the dynamics of vertically polarized elastic waves propagating in a semi-infinite medium. The formulation extends the canonical…
This series of papers has two broader aims: 1) Construct a theory for multi-partite open quantum systems comprising several layers of structure with self-consistent back-actions. Develop the graded influence action formalism…
The surface integral method for estimating ionic-covalent interactions in diatomic systems been successful in producing cross sections for mutual neutralisation (MN) in reasonable agreement with experimental results for branching fractions…
We propose a closed-form spectral framework for relative log-density estimation in linearly parameterized probabilistic models, including unnormalized and conditional models. This is achieved by representing the Kullback-Leibler (KL)…
We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from…
We derive an explicit mapping between the spectra of conserved local operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is presented explicitly for the Heisenberg XXZ…
We derive effective Hamiltonians for the fractional quantum Hall effect in n=0 and n=1 Landau levels that account perturbatively for Landau level mixing by electron-electron interactions. To second order in the ratio of electron-electron…
In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $\nu$, of diffusive type. In particular, we assume $\nu$ is symmetric and…
HgTe/HgCdTe quantum wells with the inverted band structure have been probed using far infrared magneto-spectroscopy. Realistic calculations of Landau level diagrams have been performed to identify the observed transitions. Investigations…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
We propose in this paper a gradient-type dynamical system to solve the problem of maximizing quantum observables for finite dimensional closed quantum ensembles governed by the controlled Liouville-von Neumann equation. The asymptotic…
We examine the problem of finite Fermi systems having a degenerate single-particle spectrum and show that the Landau approach, applied to such a system, admits the possibility of merging single-particle levels. It is demonstrated that the…
We formulate and analyze a double-slit proposal for quantum annealing, which involves observing the probability of finding a two-level system (TLS) undergoing evolution from a transverse to a longitudinal field in the ground state at the…
We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment…
In this note we study the generation of attractive oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, i.e., a partial linearizing state feedback, and an immersion and invariance…
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…