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In a series of three projects a new technique which allows for higher-loop renormalisation on a manifold with boundary has been developed and used in order to assess the effects of the boundary on the dynamical behaviour of the theory.…
The states of hydrogen atom with principal quantum number n <= 3 and zero magnetic quantum number in constant homogeneous magnetic field H are considered. The perturbation theory series is summed with the help of Borel transformation and…
Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical…
We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…
Many important applications in biochemistry, materials science, and catalysis sit squarely at the interface between quantum and statistical mechanics: coherent evolution is interrupted by discrete events, such as binding of a substrate or…
The `strong-coupling' perturbation theory over the inverse interaction constant $1/g$ near the nontrivial solution of Lagrange equation is formulated. The ordinary `week-coupling' perturbation theory over $g$ is described also to compare…
We study the propagation of coherent states in self-interacting bosonic quantum field theories in the semi-classical (mean-field) regime. Relying on Hepp's method and a detailed analysis of the associated classical and quantum field…
The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…
For a long time, the predictive limits of perturbative quantum field theory have been limited by our inability to carry out loop calculations to arbitrarily high order, which become increasingly complex as the order of perturbation theory…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
We consider periodic second-order equations having an ordered pair of lower and upper solutions and show the existence of asymptotic trajectories heading towards the maximal and minimal periodic solutions which lie between them.
Accurate solution of the many-electron problem including correlations remains intractable except for few-electron systems. Describing interacting electrons as a superposition of independent electron configurations results in an apparent…
An extended coherent state for describing a system of two interacting quanum objects is considered. A modified perturbation theory based on using the extended coherent states is formulated.
We present a full introduction to the recent devised perturbation theory for strong coupling in quantum mechanics. In order to put the theory in a proper historical perspective, the approach devised in quantum field theory is rapidly…
A perturbation method is presented which can be applied to the description of a wide range of physical problems that deal with dynamics of dipolar coupled spins in solids. The method is based on expansion of the operator exponent in a…
Isometric fluctuation relations are deduced for the fluctuations of the order parameter in equilibrium systems of condensed-matter physics with broken discrete or continuous symmetries. These relations are similar to their analogues…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…
The semiclassical backreaction equations are solved in closed Robertson-Walker spacetimes containing a positive cosmological constant and a conformally coupled massive scalar field. Renormalization of the stress-energy tensor results in…