相关论文: Quantum footprints of Liouville integrable systems
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
't Hooft's derivation of quantum from classical physics is analyzed by means of the classical path integral of Gozzi et al.. It is shown how the key element of this procedure - the loss of information constraint - can be implemented by…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
We present a generic treatment of wave-packet revivals for quantum-mechanical systems. This treatment permits a classification of certain ideal revival types. For example, wave packets for a particle in a one-dimensional box are shown to…
We reexamine a set of existing procedures aimed at recovering the effective description of the dynamics of LQG in the context of cosmological solutions. In particular, the studies of those methods, to which the choice of cuboidal graphs and…
We establish a previously unexplored conservation law for the Quantum Fisher Information Matrix (QFIM) expressed as follows; when the QFIM is constructed from a set of observables closed under commutation, i.e., a Lie algebra, the spectrum…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant…
Our goal is to combine the techniques of Xiaokui Yang, Valentino Tosatti, and others to establish a Liouville-type result for almost complex manifolds. The transition to the non-integrable setting is delicate, so we will devote a section to…
Lattice models or structures are geometrical objects with mathematical forms, that are used to represent physical systems. They have been used widely in diverse fields, namely, in condensed matter physics, to study degrees of freedom of…
We show explicitly that high harmonics of the classical Liouville density distribution in the chaotic regime can be obtained efficiently on a quantum computer [1,2]. As was stated in [1], this provides information unaccessible for classical…
An overview of the quantum integrable systems (QIS) is presented. Basic concepts of the theory are highlighted stressing on the unifying algebraic properties, which not only helps to generate systematically the representative Lax operators…
We study scaling and renormalization in two dimensional quantum gravity in a covariant framework. After reviewing the definition of a proper path integral measure, we use scaling arguments to rederive the KPZ relations, the fractal…
We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.
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…
The relation between quantum systems associated to root systems and radial parts of Laplace operators on symmetric spaces is established. From this it follows the complete integrability of some quantum systems.
We provide a detailed analysis of the disk path integral of timelike Liouville theory, conceived as a tractable and precise toy-model quantum cosmology in two dimensions. Disk path integrals with the insertion of matter field operators,…
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…
In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a…
In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax…