Related papers: Studies in Integrable Quantum Lattice Models and C…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
We numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
The aim of this book is to develop "from the ground up" many of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon theory. As such, we spend a significant amount of time on…
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…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
We define a new class of integrable vertex models associated to quantum groups at roots of unit
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…
In this chapter we review results on the lattice Schwinger model. In par-ticular, we show how the effect of the anomaly is reproduced on the lattice. We connect these results to recent developments in the field of quantum simulation of…
In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…
We propose in this work a concept of integrability for quantum systems, which corresponds to the concept of noncommutative integrability for systems in classical mechanics. We determine a condition for quantum operators which can be a…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…
The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
In these lecture notes we aim for a pedagogical introduction to both classical and quantum integrability. Starting from Liouville integrability and passing through Lax pair and r-matrix we discuss the construction of the conserved charges…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
The structure of Collapse Models is investigated in the framework of Quantum Measure Theory, a histories-based approach to quantum mechanics. The underlying structure of coupled classical and quantum systems is elucidated in this approach…
Relations between differential calculi, quantum groups, integrable systems, and q-analysis are studied. Some new Hirota type formulas are established for qKP along with variations on classical Hirota formulas.