Related papers: Aspects of integrability in a classical model for …
We consider the problem of quantum-classical correspondence in integrable field theories. We propose a method to construct a field theoretical coherent state, in which the expectation value of the quantum field operator exactly coincides…
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…
The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the…
We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the…
We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof…
Understanding the non-equilibrium dynamics of extended quantum systems after the trigger of a sudden, global perturbation (quench) represents a daunting challenge, especially in the presence of interactions. The main difficulties stem from…
Realizing bosonic field v(x) as current of massless (chiral) fermions we derive hierarchy of quantum polynomial interactions of the field v(x) that are completely integrable and lead to linear evolutions for the fermionic field. It is…
We consider a quantum system of non-interacting fermions at temperature T, in the framework of linear response theory. We show that semiclassical theory is an appropriate framework to describe some of their thermodynamic properties, in…
In a previous work [arXiv1905.01121] we have derived a quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical gravitational field. As standard matter is made of fermions, such…
A hybrid formalism is proposed for interacting classical and quantum sytems. This formalism is mathematically consistent and reduces to standard classical and quantum mechanics in the case of no interaction. However, in the presence of…
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a…
The role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures. We find that an otherwise simple…
We present a classical simulation method for fermionic quantum systems which, without loss of generality, can be represented by parity-preserving circuits made of two-qubit gates in a brick-wall structure. We map such circuits to a…
We study fermionic and bosonic systems coupled to a real or synthetic static gauge field that is quantized, so the field itself is a quantum degree of freedom and can exist in coherent superposition. A natural example is electrons on a…
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…
We study the classical properties of a supersymmetric system which is often used as a model for supersymmetric quantum mechanics. It is found that the classical dynamics of the bosonic as well as the fermionic degrees of freedom is fully…
We investigate the thermodynamics of integrable classical field theories under the effect of a random initial configuration, motivated by the nonequilibrium evolution of quantum field theories. The approach to thermal equilibrium is…
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…