Related papers: The quantum angular Calogero-Moser model
The plasmon excitations in Coulomb-coupled spherical two-dimensional electron gases (S2DEGs) reveal an interesting dependence on the displacement vector between the centers of the spheres with respect to the axis of quantization for the…
We discuss integrable many-body systems in one dimension of Calogero-Moser-Sutherland type, both classical and quantum as well as nonrelativistic and relativistic. In particular, we consider fundamental properties such as integrability, the…
Central spin models, where a single spinful particle interacts with a spin environment, find wide application in quantum information technology and can be used to describe, e.g., the decoherence of a qubit over time. We propose a method of…
A brief and incomplete review of known integrable and (quasi)-exactly-solvable quantum models with rational (meromorphic in Cartesian coordinates) potentials is given. All of them are characterized by (i) a discrete symmetry of the…
We study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which not only gives a canonical description of bosonic quantum computing using…
The quantisation of the reduced first-order dynamics of the nonrelativistic model for Chern-Simons vortices introduced by Manton is studied on a sphere of given radius. We perform geometric quantisation on the moduli space of static…
We develop a self-consistent approach to study the spectral properties of a class of quantum mechanical operators by using the knowledge about monodromies of $2\times 2$ linear systems (Riemann-Hilbert correspondence). Our technique applies…
We study a model of quantum computation based on the continuously-parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close…
The quantum three-rotor problem concerns the dynamics of 3 equally massive particles moving on a circle subject to pairwise attractive cosine potentials and can model coupled Josephson junctions. Classically, it displays order-chaos-order…
We find and solve a large class of integrable dynamical systems which includes Calogero-Sutherland models and various novel generalizations thereof. In general they describe $N$ interacting particles moving on a circle and coupled to an…
A nonrelativistic particle on a circle and subject to a cos^{-2}(k phi) potential is related to the two-dimensional (dihedral) Coxeter system I_2(k), for k in N. For such `dihedral systems' we construct the action-angle variables and…
We prove that the energy-critical half-wave maps equation \[ \partial_t \mathbf{S} =\mathbf{S} \times |\nabla| \mathbf{S}, \quad (t,x) \in \mathbb{R} \times \mathbb{T} \] arises as an effective equation in the continuum limit of completely…
The wave functions of a quantum isotropic harmonic oscillator in N-space modified by barriers at the coordinate hyperplanes can be expressed in terms of certain generalized spherical harmonics. These are associated with a product-type…
System consisting of a number of trapped atoms evolving under the influence of external inhomogenous magnetic field undergoes spin dephasing: classically, since each atom feels different field along its trajectory, the spin rotation rates…
The $B_N$-type Calogero-Sutherland-Moser system in one-dimension is shown to be equivalent to a set of decoupled oscillators by a similarity transformation. This result is used to show the connection of the $A_N$ and $B_N$ type models and…
Various infinite-dimensional versions of Calogero-Moser operator are discussed in relation with the theory of symmetric functions and representation theory of basic classical Lie superlagebras. This is a version of invited talk given by the…
We study the dynamics of entanglement in spin gases. A spin gas consists of a (large) number of interacting particles whose random motion is described classically while their internal degrees of freedom are described quantum-mechanically.…
We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which…
The Seiberg-Witten curve and differential for ${\cal N}=2$ supersymmetric SU(N) gauge theory, with a massive hypermultiplet in the adjoint representation of the gauge group, are analyzed in terms of the elliptic Calogero-Moser integrable…
We present the deformed (for the presence of Calogero potential terms) one-dimensional quantum oscillator with the exceptional Lie superalgebra $F(4)$ as spectrum-generating superconformal algebra. The Hilbert space is given by a $16$-ple…