Related papers: Multichannel generalization of eigen-phase preserv…
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…
We present the general ideas on SuperSymmetric Quantum Mechanics (SUSY-QM) using different representations for the operators in question, which are defined by the corresponding bosonic Hamiltonian as part of SUSY Hamiltonian and its…
We extend the standard intertwining relations used in Supersymmetrical (SUSY) Quantum Mechanics which involve real superpotentials to complex superpotentials. This allows to deal with a large class of non-hermitean Hamiltonians and to study…
The exactly solvable eigenproblems in Schr\"odinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I…
Gauge theories in 2+1 dimensions can admit monopole operators in the potential. Starting with the theory without monopole potential, if the monopole potential is relevant there is an RG flow to the monopole-deformed theory. Here, focusing…
We construct supersymmetric (SUSY) generalized MIC-Kepler system and show that the systems with half integral Dirac quantization condition \mu= \pm{1/2}, \pm{3/2}, \pm{5/2},..... belong to a SUSY family (hierarchy of Hamiltonian) with same…
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first…
Transformation optics aims to identify artificial materials and structures with desired electromagnetic properties by means of pertinent coordinate transformations. In general, such schemes are meant to appropriately tailor the constitutive…
R-matrix method is used to construct supersymmetric extensions of theta - Euclidean group preserving N = 1/2 supersymmetry and its three- parameter generalization. These quantum symmetry supergroups can be considered as global counterparts…
We consider a class of generally non-self-adjoint eigenvalue problems which are nonlinear in the solution as well as in the eigenvalue parameter ("doubly" nonlinear). We prove a bifurcation result from simple isolated eigenvalues of the…
The propagation of waves through transmission eigenchannels in complex media is emerging as a new frontier of condensed matter and wave physics. A crucial step towards constructing a complete theory of eigenchannels is to demonstrate their…
Recently the semileptonic decays $B\to X_s e^+ e^-$, $B\to X_s \mu^+ \mu^-$ in generic supersymmetric extensions of the Standard Model have been studied in ref.~\cite{noi}. In this talk I review the main points of this analysis. SUSY…
We calculated the eigenvalues for a general N-channel coupled system with parity-time symmetry due to equal loss/gain. We found that the eigenspectrum displays a mixing of parity-time symmetric and broken phases, with N-2 of the eigenvalues…
We construct Euclidean 5d supersymmetric gauge theories on the five-sphere with vector and hypermultiplets. The SUSY transformation and the action are explicitly determined from the standard Noether procedure as well as from off-shell…
We describe three different approaches to the extended (N=2) supersymmetrization of the multicomponent KP hierarchy. In the first one we utilize only superfermions while in the second only superbosons and in the third superbosons as well as…
An N=2 SUSY extension of the Schr\"odinger symmetry is shown to exist in the solution space of the free planar L\'evy-Leblond equation, an N=1 part of which survives for the gauged version of the equation and also when it is coupled to…
Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic…
Two-parameter generalizations of depolarizing channels are introduced and studied. These so-called Cartan-covariant channels have a covariance Lie group that forms a Cartan decomposition of SU$(D)$. The regions of completely positive and…
We consider special supersymmetry (SUSY) transformations with $m$ generators $\overleftarrow{s}_{\alpha }$ for a certain class of models and study some physical consequences of Grassmann-odd transformations which form an Abelian supergroup…
We present a complete characterization of diagonal unitary covariant (DU-covariant) superchannels, i.e. higher-order transformations transforming quantum channels into themselves. Necessary and sufficient conditions for complete positivity…