相关论文: Unified theory of bound and scattering molecular R…

This article concerns the long-time dynamics of quantum particles in the semi-classical regime. First, we show that for the nonlinear Hartree equation with short-range interaction potential, small-data solutions obey dispersion bounds and…

The dynamics of quantum systems are generally described by a family of quantum channels (linear, completely positive and trace preserving maps). In this note, we mainly study the range of all possible values of…

Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or…

We develop an approach to scattering theory for generalized $N$-body systems. In particular we consider a general class of three quasi-particle systems, for which we prove Asymptotic Completeness.

Our primary goal is to provide a rigorous treatment of scattering nonlocality in semiconductor nanostructures. On the one hand, starting from the conventional density-matrix formulation and employing as ideal instrument for the study of the…

In this paper, we develop a theory of learning nonlinear input-output maps with fading memory by dissipative quantum systems, as a quantum counterpart of the theory of approximating such maps using classical dynamical systems. The theory…

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…

We define generalized bialgebras and Hopf algebras and on this basis we introduce quantum categories and quantum groupoids. The quantization of the category of linear (super)spaces is constructed. We establish a criterion for the classical…

The topological recursion of Eynard and Orantin governs a variety of problems in enumerative geometry and mathematical physics. The recursion uses the data of a spectral curve to define an infinite family of multidifferentials. It has been…

We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…

We propose a divide-and-conquer algorithm to find recursively the Scattering matrix of general tight-binding structures. The Scattering matrix allows a direct calculation of transport properties in mesoscopic systems by using the Landauer…

We show the transition from a fully quantized interaction to a semiclassical one in entangled small number quantum systems using the quantum trajectories approach. In particular, we simulate the microwave Ramsey zones used in Rydberg atom…

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…

It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization…

An informal introduction to our recent work on the principal chiral model with boundary. We found that both classically integrable boundary conditions and quantum boundary S-matrices were classified by the symmetric spaces G/H. The…

The last few years have seen rapid development of applications of quantum computation to quantum field theory. The first algorithms for quantum simulation of scattering have been proposed in the context of scalar and fermionic theories,…

For spacetimes containing quiescent singularity hypersurfaces we propose a general notion of junction conditions based on a prescribed singularity scattering map, as we call it, and we introduce the notion of a cyclic spacetime (also called…

The semiclassical Boltzmann equation is widely used to study transport effects. However, being semiclassical and borrowing heavily from classical mechanics, the formalism calls for verification from the perspective of quantum mechanics.…

We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…

The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…