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Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for…
Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g. random Schr\"odinger operators and control theory. We review recent results and announce new ones regarding…
Excitation energy transfer in light-harvesting aggregates is highly efficient, yet whether quantum coherence plays an operational role in transport remains debated. A central challenge is that coherence is usually inferred from…
It is shown that under certain conditions the resonant transport in mesoscopic systems can be described by modified (quantum) rate equations, which resemble the optical Bloch equations with some additional terms. Detailed microscopic…
Semyanistyi's fractional integrals have come to analysis from integral geometry. They take functions on $R^n$ to functions on hyperplanes, commute with rotations, and have a nice behavior with respect to dilations. We obtain sharp…
We propose a new implementation of target mass corrections to nucleon structure functions which, unlike existing treatments, has the correct kinematic threshold behavior at finite Q^2 in the x -> 1 limit. We illustrate the differences…
We study localization effects of disorder on the spectral and dynamical properties of Schroedinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection…
We study a variational problem for the first Schrodinger eigenvalue on closed Riemannian surfaces. More precisely, we explore concentration-compactness properties of sequences formed by its extremal potentials.
A Gaussian resolution method for the computation of equilibrium density matrices rho(T) for a general multidimensional quantum problem is presented. The variational principle applied to the ``imaginary time'' Schroedinger equation provides…
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…
The intensity relations for electromagnetic transition rates in the rotational coupling scheme have been a basic tool to understand the properties of nuclear collective rotations. In particular the correction terms to the leading-order…
It is shown that any Hermitian operator can be expanded in terms of a set of operators formed from biorthogonal basis, and the expansion coefficients are given as products of weight functions and weak values, shedding a new light on the…
The properties of the square bias transformation are studied, in particular, the precise moment-type estimate for the $L_1$-metric between the transformed and the original distributions is proved, a relation between their characteristic…
Multi-group covariance estimation for matrix-variate data with small within group sample sizes is a key part of many data analysis tasks in modern applications. To obtain accurate group-specific covariance estimates, shrinkage estimation…
In this paper, we consider a quaternionic short-time Fourier transform (QSTFT) with normalized Hermite functions as windows. It turns out that such a transform is based on the recent theory of slice polyanalytic functions on quaternions.…
In two recent papers, an isometric conformal transformation has been introduced that eliminates potential interaction terms from the Schr\"odinger equation for central potential problems. The method has been demonstrated for both the…
We use Chiral Perturbation Theory to compute the nucleon mass-shift due to finite volume and temperature effects. Our results are valid up to next-to-leading order in the "\eps-regime" (mL ~ m\beta << 1) as well as in the "p-regime" (mL ~…
In this paper, we are basically discussing on a class of Baranchik type shrinkage estimators of the vector parameter in a location model, with errors belonging to a sub-class of elliptically contoured distributions. We derive conditions…
For $N$ compatible substitution rules on $M$ prototiles $t_1,\dots,t_M$, consider tilings and tiling spaces constructed by applying the different substitution rules at random. These give (globally) random substitution tilings. In this paper…
Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an…