Related papers: Classically and Quantum Integrable Systems with Bo…
The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced…
Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…
We study the ground state energy of integrable $1+1$ quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing a new, ``R-channel TBA'', where the boundary is represented by a…
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
The existence of a classical limit describing interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to a previously established classical limit with a…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single…
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components…
A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of…
We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
Integrable open-boundary condition for the q-deformed Essler-Korepin-Schoutens extended Hubbard model of strongly correlated electrons, are studied in the framework of the boundary quantum inverse scattering method. Diagonal boundary…
We introduce a universal framework for boundary transfer matrices, inspired by Sklyanin's two-row transfer matrix approach for quantum integrable systems with boundary conditions. The main examples arise from quantum symmetric pairs of…
We present the classification of quadratically integrable systems of the cylindrical type with magnetic fields in quantum mechanics. Following the direct method used in classical mechanics by [F Fournier et al 2020 J. Phys. A: Math. Theor.…
We have performed an analytical study of quantum-classical equivalence for quantum $XY$-spin chains with arbitrary interactions to explore the classical counterpart of the factorizing magnetic fields that drive the system into a separable…
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space…
Near-term quantum processors are limited in terms of the number of qubits and gates they can afford. They nevertheless give unprecedented access to programmable quantum systems that can efficiently, although imperfectly, simulate quantum…
We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…