Related papers: On the spectrum of Dehn twists in quantum Teichmul…
It is shown that the N-th power of the light-cone evolution operator of 2N-periodic quantum discrete Liouville model can be identified with the Dehn twist operator in quantum Teichmuller theory.
The coherent states for twist-deformed oscillator model provided in article [1] are constructed. Besides, it is demonstrated that the energy spectrum of considered model is labeled by two quantum numbers - by so-called main and azimutal…
In the quantum Teichmuller theory, based on Penner coordinates, the mapping class groups of punctured surfaces are represented projectively. The case of a genus three surface with one puncture is worked out explicitly. The projective factor…
The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of quantum mechanics. In some cases, its spectrum can be determined by combining the WKB…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
Multidimensional Heisenberg algebras, whose creation and annihilation operators are the N-dimensional vectors, can be injected into simple Lie algebras g. It is demonstrated that the spectrum of their deformations can be investigated using…
The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D…
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…
We summarize our recently proposed approach to quantum field theory on noncommutative curved spacetimes. We make use of the Drinfel'd twist deformed differential geometry of Julius Wess and his group in order to define an action functional…
This article is concerned with obtaining the standard tau function descriptions of integrable equations (in particular, here the KdV and Ernst equations are considered) from the geometry of their twistor correspondences. In particular, we…
We give a concise presentation of the construction of the Liouville quantum gravity (LQG) eigenvalues and eigenfunctions, i.e., the spectrum associated to the infinitesimal generator of Liouville Brownian motion, the canonical diffusion in…
In this paper, the problem of assessing the twistability of a given bona fide cross-spectral density is tackled for the class of Schell-model sources, whose shift-invariant degree of coherence is represented by a real and symmetric…
We study the quantization of Hitchin systems in terms of beta-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the…
In this note it is proved that the complete spectral data of selfadjoint Schr\"odinger operators on unbounded domains can be described with an associated Dirichlet-to-Neumann map. In particular, a characterization of the isolated and…
Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering…
We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic…
Quantum integrable spin chains are known to possess a large family of long-range deformations generated by the local, boost and bilocal operators. Although these deformations are well-understood on the level of the pairwise commuting…
A simple quantum generalisation of the Liouville-Arnold criterion of classical integrability is proposed: A system is quantum-integrable if it has an abelian Lie group of Wigner symmetries of dimension equal to the number of degrees of…
A class of non-selfadjoint, $\PT$-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is explicitly constructed through the method of the quantum normal…
We consider Laplacians with non unitary twists acting on sections of flat vector bundles over compact hyperbolic surfaces. These non self-adjoint Laplacians have discrete spectrum inside a parabola in the complex plane. For representations…