Related papers: Spectrum of the quantum Neumann model
We review the quantum spectral curve (QSC) formalism for anomalous dimensions of planar ${\cal\ N}=4$ SYM, including its $\gamma$-deformation. Leaving aside its derivation, we concentrate on formulation of the "final product" in its most…
The $q\bar q$ spectrum is studied in a generalized constituent quark model constrained in the study of the $NN$ phenomenology and the baryon spectrum. An overall good fit to the available experimental data is obtained. A detailed analysis…
We study the spectral properties of the transfer matrix for a gonihedric random surface model on a three-dimensional lattice. The transfer matrix is indexed by generalized loops in a natural fashion and is invariant under a group of motions…
This review is based on the lectures given by the author at the Les Houches Summer School 2016. It describes the recently developed Quantum Spectral Curve (QSC) for a non-perturbative planar spectrum of N=4 Super Yang-Mills theory in a…
The quantum molecule consisting of three quantum dots that forms a triangle with its centers is studied. The electron wave function in the nanosystem is written using the linear combination of orbital quantum wells. The dispersion equation…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
Exploring the noise spectrum impacting a qubit and extending its coherence duration are fundamental components of quantum technologies. In this study, we introduce parametric spectroscopy, a method that merges parametric modulation of a…
We explicitly construct the algebraic model of affine Jacobian of a generic algebraic curve of high genus and use it to compute the Euler characteristic of the Jacobian and investigate its structure.
This is a brief review of several algebraic constructions related to generalized fermionic spectra, of the type which appear in integrable quantum spin chains and integrable quantum field theories. We discuss the connection between…
We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded in the continuous spectrum. (3)Limiting…
We study the spectral properties of the anisotropic part of Hamiltonian entering the quantum dynamics of the Mixmaster universe. We derive the explicit asymptotic expressions for the energy spectrum in the limit of large and small volumes…
We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric…
In this paper, we study the multiplicative behaviour of quantum channels, mathematically described by trace preserving, completely positive maps on matrix algebras. It turns out that the multiplicative domain of a unital quantum channel has…
The correlation spectrum of fully developed one-dimensional mappings are studied near and at a weakly intermittent situation. Using a suitable infinite matrix representation, the eigenvalue equation of the Frobenius-Perron operator is…
In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum…
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $\sigma$--model…
For a noncommutative space X, we study Inj(X), the set of isomorphism classes of indecomposable injective X-modules. In particular, we look at how this set, suitably topologized, can be viewed as an underlying "spectrum" for X. As…
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…
Based on the measurement of quantum correlation functions, the quantum statistical properties of spectral measurements are studied for broadband radiation fields. The spectral filtering of light before its detection is compared with the…
Exact non-perturbative partition functions of coupling constants and external fields exhibit huge hidden symmetry, reflecting the possibility to change integration variables in the functional integral. In many cases this implies also some…