Related papers: A semiclassical tetrahedron
We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck's constant, both classical and quantal distributions…
We point out a correspondence between classical and quantum states, by showing that for every classical distribution over phase--space, one can construct a corresponding quantum state, such that in the classical limit of $\hbar\to 0$ the…
In this paper it is shown that the quantum state of a multiverse made up of classically disconnected regions of the space-time, whose dynamical evolution is dominated by a homogeneous and isotropic fluid, is given by a squeezed state. These…
Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental…
A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are…
We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of…
We consider quantum dots with a parabolic confining potential. The qualitative features of such mesoscopic systems as functions of the total number of electrons N and their total angular momentum J, e.g. magic numbers, overall symmetries…
Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a…
We define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators, of which we give a complete characterization. Lastly, we prove a generalization of the…
How complex is the structure of quantum geometry? In several approaches, the spacetime atoms are obtained by the SU(2) intertwiner called quantum tetrahedron. The complexity of this construction has a concrete consequence in recent efforts…
Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the…
We apply a quantum version of dimensional reduction to Gaussian coherent states in Bargmann space to obtain squeezed states on complex projective spaces. This leads to a definition of a family of squeezed spin states with excellent…
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…
We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from the basic localized modes in various collective models arising from the quantum hierarchy described by Wigner-like…
Inspired by the spin geometry theorem, two operators are defined which measure angles in the quantum theory of geometry. One operator assigns a discrete angle to every pair of surfaces passing through a single vertex of a spin network. This…
We show that when the thermal wavelength is comparable to the spatial size of a system, thermodynamic observables like Pressure and Volume have quantum fluctuations that cannot be ignored. They are now represented by operators; conventional…
We describe a scheme of constructing classical integrable models in 2+1-dimensional discrete space-time, based on the functional tetrahedron equation - equation that makes manifest the symmetries of a model in local form. We construct a…
The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A…
We consider semiclassical self-adjoint operators whose symbol, defined on a two-dimensional symplectic manifold, reaches a non-degenerate minimum $b_0$ on a closed curve. We derive a classical and quantum normal form which allows us, in…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…