Related papers: Self-duality and scattering map for the hyperbolic…

For autonomous systems it is well known how to extract tunneling probabilities from wavepacket calculations. Here we present a corresponding approach for periodically time-dependent Hamiltonians, valid at all frequencies, field strengths,…

We consider a quantum system S interacting with another system S and susceptible of being absorbed by S. The effective, dissipative dynamics of S is supposed to be generated by an abstract pseudo-Hamiltonian of the form H = H0 + V -- iC *…

In this thesis, we take a journey through two different but not dissimilar stories with an underlying theme of combinatorics emerging from scattering amplitudes in quantum field theories. The first part tells the tale of the…

Let $X$ be a two-dimensional smooth manifold with boundary $S^{1}$ and $Y=[1,\infty)\times S^{1}$. We consider a family of complete surfaces arising by endowing $X\cup_{S^{1}}Y$ with a parameter dependent Riemannian metric, such that the…

Twisted van der Waals materials provide a tunable platform for investigating two-dimensional superconductivity and quantum phases. Using spectra-imaging scanning tunneling microscopy, we study the superconducting states in twisted bilayer…

We define a natural concept of duality for the h-Hopf algebroids introduced by Etingof and Varchenko. We prove that the special case of the trigonometric SL(2) dynamical quantum group is self-dual, and may therefore be viewed as a…

We develop the spectral and scattering theory for self-adjoint Hankel operators $H$ with piecewise continuous symbols. In this case every jump of the symbol gives rise to a band of the absolutely continuous spectrum of $H$. We construct…

For any $n\geq4$ even, we establish a complete scattering theory for the linear wave equation on the $(n+1)$-dimensional de Sitter space. We prove the existence and uniqueness of scattering states, and asymptotic completeness. Moreover, we…

The creation of artificial gauge fields in neutral ultracold atom systems has opened the possibility to study the effects of spin-orbit coupling terms in clean environments. This work considers the multi-channel scattering properties of two…

Recently Feher and the author have constructed the action-angle dual of the trigonometric BC(n) Sutherland system via Hamiltonian reduction. In this paper a reduction-based calculation is carried out to verify canonical Poisson bracket…

We investigate the scattering of scalar plane waves in two dimensions by a heterogeneous layer that is periodic in the direction parallel to its boundary. On describing the layer as a union of periodic laminae, we develop a solution of the…

We consider Dotsenko-Fateev matrix models associated with compactified Calabi-Yau threefolds. They can be constructed with the help of explicit expressions for refined topological vertex, i.e. are directly related to the corresponding…

These lecture notes are devoted to the integrability of discrete systems and their relation to the theory of Yang-Baxter (YB) maps. Lax pairs play a significant role in the integrability of discrete systems. We introduce the notion of Lax…

Let $H_0$, $H$ be a pair of self-adjoint operators for which the standard assumptions of the smooth version of scattering theory hold true. We give an explicit description of the absolutely continuous spectrum of the operator…

We present a fairly new and comprehensive approach to the study of stationary flows of the Korteweg-de Vries hierarchy. They are obtained by means of a double restriction process from a dynamical system in an infinite number of variables.…

A geometric interpretation of the duality between two real forms of the complex trigonometric Ruijsenaars-Schneider system is presented. The phase spaces of the systems in duality are viewed as two different models of the same reduced phase…

We study scattering and inverse scattering theories for asymptotically complex hyperbolic manifolds. We show the existence of the scattering operator as a meromorphic family of operators in the Heisenberg calculus on the boundary, which is…

This work is a continuation and extension of the note published in the Russian Math Surveys 1997 n 6. For any pair of solutions of the spectral problem for the second order selfadjoint real Schrodinger Operator on the graph their Symplectic…

In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants…

We study the spectral properties of the Laplace operator associated to a hyperbolic surface in the presence of a unitary representation of the fundamental group. Following the approach by Guillop\'e and Zworski, we establish a factorization…