Related papers: Is the K-matrix approach adequate for describing o…
Multiple scale techniques are well-known in classical mechanics to give perturbation series free from resonant terms. When applied to the quantum anharmonic oscillator, these techniques lead to interesting features concerning the solution…
A formalism for study of spectral correlations in non-Gaussian, unitary invariant ensembles of large random matrices with strong level confinement is reviewed. It is based on the Shohat method in the theory of orthogonal polynomials. The…
The multiple scattering method T-matrix (MSTMM) can be used to solve the electromagnetic response of systems consisting of many compact scatterers, retaining a good level of accuracy while using relatively few degrees of freedom, largely…
Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations that can involve loss and gain require a different approach. In this theory work, we present a universal…
In quantum field theory, characteristics of resonances are related to self-energy diagrams, which are ultra-violet divergent and require renormalization. We demonstrate the proper way to define the resonance coupling $g_M$ such that the…
We review self-consistent spectral methods for nuclear matter calculations. The in-medium T-matrix approach is conserving and thermodynamically consistent. It gives both the global and the single-particle properties the system. The T-matrix…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
We evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations. We decompose the covariance matrix into the disconnected (Gaussian) part,…
We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all n-point…
We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry,…
The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be…
We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an…
The aim of this communication is to present in a concentrated form the main ideas of a method, developed by the author, for treating strongly nonequilibrium collective phenomena typical of the interaction of radiation with matter, as well…
K-fusion frames are generalizations of fusion frames in frame theory. This article characterizes various kinds of property of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed.
Here we discuss a particle-based approach to deal with systems of many identical quantum objects (particles) which never employs labels to mark them. We show that it avoids both methodological problems and drawbacks in the study of quantum…
The estimation of multiple parameters is a ubiquitous requirement in many quantum metrology applications. However, achieving the ultimate precision limit, i.e. the quantum Cram\'er-Rao bound, becomes challenging in these scenarios compared…
A quantum algorithm for combinatorial search is presented that provides a simple framework for utilizing search heuristics. The algorithm is evaluated in a new case that is an unstructured version of the graph coloring problem. It performs…
An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in…
This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric…
Manifold regularization methods for matrix factorization rely on the cluster assumption, whereby the neighborhood structure of data in the input space is preserved in the factorization space. We argue that using the k-neighborhoods of all…