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A detailed review is given of the semiclassical approximation to quantum gravity in the canonical framework. This includes in particular the derivation of the functional Schr\"odinger equation and a discussion of semiclassical time as well…
Understanding the emergence of classical behavior from a quantum theory is vital to establishing the quantum origin for the temperature fluctuations observed in the Cosmic Microwave Background (CMB). We show that a real-space approach can…
Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…
Appearance of adiabatic geometric phase shift in the context of noncommutative quantum mechanics is studied using an exactly solvable model of 2D simple harmonic oscilator in Moyal plane, where momentum non-commutativity are also considered…
Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required.…
In this work, surface diffusion is studied with a different perspective by showing how the corresponding open dynamics is transformed when passing, in a continuous and smooth way, from a pure quantum regime to a full classical regime; the…
Non-adiabatic quantum effects, often experimentally observed in semiconductors nano-devices such as single-electron pumps operating at high frequencies, can result in undesirable and uncontrollable behaviour. However, when combined with the…
The nonequilibrium dynamics of two dimensional Su-Schrieffer-Heeger model, in the presence of staggered chemical potential, is investigated using the notion of dynamical quantum phase transition. We contribute to expanding the systematic…
Semiclassical methods have been applied very successfully to describe the nontrivial transition from the quantum to the classical regime in $\textit{single}$-particle or at least $\textit{few}$-particle systems. Challenges on the way to an…
The quantum phase-space dynamics driven by hyperbolic P\"oschl-Teller (PT) potentials is investigated in the context of the Weyl-Wigner quantum mechanics. The obtained Wigner functions for quantum superpositions of ground and first-excited…
In this dissertation the Weyl-Wigner approach is presented as a map between functions on a real cartesian symplectic vector space and a set of operators on a Hilbert space, to analyse some aspects of the relations between quantum and…
A first principles quantum formalism to describe the non-adiabatic dynamics of electrons and nuclei based on a second quantization representation (SQR) of the electronic motion combined with the usual representation of the nuclear…
An $\hbar$-expansion is presented for the ensemble-averaged spectral function of noninteracting matter waves in random potentials. We obtain the leading quantum corrections to the deep classical limit at high energies by the Wigner-Weyl…
This article proposes a Variational Quantum Algorithm to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in…
In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time asymptotics for the quantum Fokker-Planck…
We investigate the well-known Shin-Metiu model for an electronic crossing, using both a standard Born-Huang (BH) framework and a novel phase space (PS) electronic Hamiltonian framework. We show that as long as we are not in the strongly…
It is demonstrated how the equilibrium semiclassical approach of Coffey et al. can be improved to describe more correctly the evolution. As a result a new semiclassical Klein-Kramers equation for the Wigner function is derived, which…
An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical…