Related papers: On relations between vertex operators, quasiclassi…
We compute the two-point correlation function of the area operator for semiclassical states of loop quantum gravity in the limit of large spins. The cases of intrinsic and extrinsic coherent states are considered, along with a new class of…
In semiclassical studies of systems with mixed phase space, the neighbourhood of bifurcations of co-dimension two is felt strongly even though such bifurcations are ungeneric in classical mechanics. We discuss a scenario which reveals this…
We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization", which allows one to associate a unique quantum operator to every function…
Two operators for quantum gravity, angle and quasilocal energy, are briefly reviewed. The requirements to model semi-classical angles are discussed. To model semi-classical angles it is shown that the internal spins of the vertex must be…
A Hermitian quantum phase operator is formulated that mirrors the classical phase variable with proper time dependence and satisfies trigonometric identities. The eigenstates of the phase operator are solved in terms of Gegenbauer…
We develop a so-called theory of ensembles in phase space and use it to investigate the construction of a quantum-classical hybrid theory. We use Galilei covariance and the Lie algebra of the Galilei group as a guide to constructing the…
We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the…
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
For time-periodical quantum systems generalized Floquet operator is found to be integral of motion.Spectrum of this invariant is shown to be quasienergy spectrum.Analogs of invariant Floquet operators are found for nonperiodical systems…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
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.
Notions of robust and "classical" states for an open quantum system are introduced and discussed in the framework of the isometric-sweeping decomposition of trace class operators. Using the predictability sieve proposed by Zurek,…
A nonequilibrium statistical operator method is developed for ensembles of particles obeying non-Hamiltonian equations of motion in classical phase space. The main consequences of non-zero compressibility of phase space are examined in…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…
This chapter provides a non-technical overview and motivation for the recent interactions between algebraic quantum field theory (AQFT) and rather abstract mathematical disciplines such as operads, model categories and higher categories.
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
Any account of the emergence of classicality from quantum theory must address the fact that the quantum operators representing positions and momenta do not commute, whereas their classical counterparts suffer no such restrictions. To…