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The running of quantum field theories can be studied in detail with the use of a local renormalization group equation. The usual beta-function effects are easy to include, but by introducing spacetime-dependence of the various parameters of…
We derive suitable uncertainty relations for characteristics functions of phase and number variables obtained from the Weyl form of commutation relations. This is applied to finite-dimensional spin- like systems, which is the case when…
We establish large deviation formulas for linear statistics on the $N$ transmission eigenvalues $\{T_i\}$ of a chaotic cavity, in the framework of Random Matrix Theory. Given any linear statistics of interest $A=\sum_{i=1}^N a(T_i)$, the…
Generic and significant regularities are shown to occur in the quasienergy spectra of the generalized quantum kicked particle for arbitrary quasimomentum, a quantity most relevant in atom-optics experimental realizations of this…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space…
A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
We proposed a third quantization scheme to derive the quantum dynamics of the functional phase space distribution in quantum field theory (QFT). The derivation is straightforward and algorithmic. This readily yields the ballistic quantum…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
Phase transitions between two competing vacua of a given theory are quite common in physics. We discuss how to construct the space-time solutions that allow the description of phase transitions between different branches (or asymptotics) of…
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
In the existing expositions of the Karolyhazy model, quantum mechanical uncertainties are mimicked by classical spreads. It is shown how to express those uncertainties through entities of the future unified theory of general relativity and…
A three-dimensional integrable generalization of the St\"ackel systems is proposed. The classification of such systems is obtained which results in two families. The first one is the direct sum of the two-dimensional case which is…
We propose a definition of phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. This generalizes all the definitions based on the curvature anomalies of thermodynamical…
We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan…
The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The…
Bochner's theorem gives the necessary and sufficient conditions on a function such that its Fourier transform corresponds to a true probability density function. In the Wigner phase space picture, quantum Bochner's theorem gives the…
A distribution of electromagnetic fields presents a statistical assembly of a particular type, which is at scale h a quantum statistical assembly itself and has also been instrumental to concretisation of the basic probability assumption of…
Motivated by the engineering applications of uncertainty quantification, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered…