One generalization of the Dicke-type models

We discuss one family of possible generalizations of the Jaynes-Cummings and the Tavis-Cummings models using the technique of algebraic Bethe ansatz related to the Gaudin-type models. In particular, we present a family of (generically) non-Hermitian Hamiltonians that generalize paradigmatic quantum-optical models. Further directions of our research include studying physical properties of the obtained generalized models.Comment: 4 pages, 0 figure

Integrable Floquet systems related to logarithmic conformal field theory

We study an integrable Floquet quantum system related to lattice statistical systems in the universality class of dense polymers. These systems are described by a particular non-unitary representation of the Temperley-Lieb algebra. We find a simple Lie algebra structure for the elements of Temperley-Lieb algebra which are invariant under shift by two lattice sites, and show how the local Floquet conserved charges and the Floquet Hamiltonian are expressed in terms of this algebra. The system has a phase transition between local and non-local phases of the Floquet Hamiltonian. We provide a strong indication that in the scaling limit this non-equilibrium system is described by the logarithmic conformal field theory.Comment: 22 pages, 2 figure

Cayley-Type Conditions for Billiards within kk Quadrics in RdR^d

The notions of reflection from outside, reflection from inside and signature of a billiard trajectory within a quadric are introduced. Cayley-type conditions for periodical trajectories for the billiard in the region bounded by $k$ quadrics in $R^d$ and for the billiard ordered game within $k$ ellipsoids in $R^d$ are derived. In a limit, the condition describing periodic trajectories of billiard systems on a quadric in $R^d$ is obtained.Comment: 10 pages, some corractions are made in Section

Fluorescence energy transfer in quantum dot/azo dye complexes in polymer track membranes

Fluorescence resonance energy transfer in complexes of semiconductor CdSe/ZnS quantum dots with molecules of heterocyclic azo dyes, 1-(2-pyridylazo)-2-naphthol and 4-(2-pyridylazo) resorcinol, formed at high quantum dot concentration in the polymer pore track membranes were studied by steady-state and transient PL spectroscopy. The effect of interaction between the complexes and free quantum dots on the efficiency of the fluorescence energy transfer and quantum dot luminescence quenching was found and discussed

Conformal symmetry in quasi-free Markovian open quantum systems

Conformal symmetry governs the behavior of closed systems near second-order phase transitions, and is expected to emerge in open systems going through dissipative phase transitions. We propose a framework allowing for a manifest description of conformal symmetry in open Markovian systems. The key difference from the closed case is that both conformal algebra and the algebra of local fields are realized on the space of superoperators. We illustrate the framework by a series of examples featuring systems with quadratic Hamiltonians and linear jump operators, where the Liouvillian dynamics can be efficiently analyzed using the formalism of third quantization. We expect that our framework can be extended to interacting systems using an appropriate generalization of the conformal bootstrap.Comment: 15 pages, supplementary Wolfram Mathematica notebook available at https://github.com/idnm/third_quantization v2: minor revision (references added, typos corrected) v2: Minor revisions done and typos correcte